• the sum of protons and neutrons which are both approximately 1 amu(electrons are almost negligible)
• reported as amu (atomic mass units) and varies between elements and isotopes
• nearly synonymous with mass number

• a constant number that describes the weighted average of all naturally occurring isotopes of a particular element

Planck Relation

(Equation)

• based on the theory that energy emitted as electromagnetic radiation from matter comes in discrete bundles called quanta
• E=hf where E is energy, h is planck's constant, and f is frequency
• describes the energy of each quanta released

• Ground State is the state of lowest energy in which all electrons are in the lowest possible orbitals
• Excited state is the state in which at least one electron has moved to a subshell of higher than normal energy

Bohr Model

(L and E)

• describes the angular momentum and energy of an electron in orbit
• as electron moves out from nucleus, its energy becomes less negative
• Bohr's model only works on hydrogen, because it does not account for repulsion between electrons (it only looks at the interactions between one electron and its nucleus)
• angular momentum: L=nh/2π
• energy: E = -(R_H/n²)

• when electrons are excited to higher energy levels, they must return due to the instability of the excited state yielding the release of energy in the form of a photon
• the photons are unique based on the energy of the transition resulting in unique emission spectums
• elements can be identified by recording the energy of the photons released and analyzing the resulting line spectrum

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Wavelengths/Energy of Electron Orbital Transitions

(Equation)

• The energy of the emitted photon corresponds to the difference in energy between the higher-energy initial state and the lower-energy final state
• E = hc/λ = -R_H(1/n_i² - 1/n_f²)

• Describe the hydrogen emission lines corresponding to transitions from different energy levels
• Lyman series describes emission lines from n≥2 to n=1
• Balmer series describes emission lines from n≥3 to n=2
• Paschen series describes emission lines from n≥4 to n=3
• Progression shows how magnitude of energy changes lessen when moving out from the nucleus

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• for an electron to undergo a transition to a higher energy level, it must absorb an exact amount of energy at a specific wavelength
• wavelengths that don't match the exact energy will pass through w/out affecting the energy of the electron
• elements can be uniquely identified by their absorption of photons for this reason
• absorption spectrum is inverse of emission spectrum and must be used for gases 

• it is impossible to simultaneously determine the position and momentum of an electron
  • to assess position electron has to stop moving
• forces us to define electrons using series of quantum numbers

• No two electrons in an atom can have the same set of quantum numbers
• allows us to determine specific electrons based on the four quantum numbers even though we cannot determine position and momentum at the same time

• Describes the energy level and radius of an electron shell in which the electron in question can be found
• denoted as n
• can be any positive integer
• maximum number of electrons in a shell = 2n²

Azimuthal Quantum Number

Angular Momentum Quantum Number

• describes the shape and number of subshells in a given shell (n)
• denoted by l
• it can be any number from 0 to n−1
• If n=2, l can equal -2, -1, 0, 1, or 2
• maximum number of electrons in a subshell = 4l + 2
• referred to as s, p, d, f, g, h...(continues alphabetically)
• l=0 is s, 1 is p, 2 is d

• specifies the particular orbital within a subshell
• denoted as m_l
• can be any value between -l and +l
• orbital shapes are defined on probability density (likelihood that something will take up particular space)

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• describes the one of two possible spin orientations of the 1 of 2 electrons in an orbital
• denoted as m_s
• can be equal to +1/2 or -1/2

• electrons must fill from lower-to-higher energy level subshells and each subshell will fill completely before electrons begin to enter the next one
• n+l rule - the lower sum of the values of the first and second quantum number, the lower the energy of the subshell
  • 5d or 6s? which will fill first?
    • 5d: n=5, l=2; n+l=7
    • 6s: n=6, l=0; n+l=6
  • 6s is lower energy and will fill first

• anions - additional electrons fill according to the same rules as neutral atoms
• cations - start with neutral atom and remove electrons from subshells with the highest value for n first, then highest l value
  • Fe³⁺ electron configuration
    • Fe: [Ar]4s²3d⁶
    • electrons are removed from the highest n value first, so 4s loses electrons first instead of 3d
    • Fe³⁺: [Ar]3d⁵

• In subshells with more than one orbital, orbitals are filled so that there is a maximum number of half-filled orbitals with parallel spins 
• half-filled and fully-filled orbitals have lower energies than other states

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• Chromimum (Group 4 in d block)
  
  • Expected: [Ar]4s²3d⁴
  • Actual: [Ar]4s¹3d⁵
• Copper (Group 9 in d block)
  • Expected: [Ar]4s²3d⁹
  • Actual: [Ar]4s¹3d¹⁰
• shifts like these exist for f subshell as well but less important (never p subshell)

• atoms w/ unpaired electrons will have a net spin and will therefore orient their spins in alignment with a magnetic field

[image][image]

• materials w/ atoms that have only paired electrons will be slightly repelled by a magnetic field instead of attracted

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• electrons that are in the outermost energy shell and therefore experience the weakest effective nuclear charge
• easiest electrons to remove from atom and are the "active" electrons of an element
• IA and IIA - valence electrons are in highest s subshell
• IIIA through VIIA - valence electrons are in highest s and p subshell
• Transition elements - valence electrons are in highest s and d subshells

• make up the left side and middle of the periodic table
  • separated from nonmetals by metalloid "staircase"
  • include the active metals (groups 1-2), transition metals (groups 3-12), and lanthanide and actinide series
• considered to be lustrous (shiny), malleable, ductile, have high melting points and densities
• experience low effective nuclear charge and therefore have low electronegativity, larger atomic radii, smaller ionic radii, low ionization energy, and low electron affinity
• many are good conductors of heat and electricity due to their ability to easily transfer electrons

• found in the upper right side of the periodic table separated from metals by metalloid "staircase"
  • include elements from groups 14-18
• considered to be brittle in solid state with little to no luster (shine)
• characterized by high ionization energies, high electron affinities, high electronegativities, small atomic radii, and large ionic radii
• poor conductors of heat and electricity due to their higher effective nuclear charges
• less unified in chemical and physical properties

• "staircase" group of elements that separate the metals and the nonmetals
• share chemical and physical properties intermediate to metals and nonmetals
• variable melting points, boiling points, and densities sharing characteristics of metals and nonmetals
• reactivities are many times dependent on the elements with which they react
  • boron reacts like a nonmetal with sodium but like a nonmetal with fluorine

• measure of the net positive charge experienced by valence electrons of an atom
• Z_eff increases with increasing numbers of protons leading to tighter binding of electron cloud (smaller atomic radius)
• Z_eff partially mitigated by nonvalence electrons which cancel some of the positive charge leading to looser binding of the electron cloud (larger atomic radius)

• equal to 1/2 the distance between centers of 2 atoms of an element
  • cannot be measure w/ single atom as electrons are constantly moving making finding outer boundary impossible
• atomic radius decreases when going from left to right across a period 
  • Z_eff increases due to increasing numbers of protons
  • additional electrons added only to outermost shell
    • inner-shell electrons which mitigate Z_eff remain unchanged across period
• atomic radius increases when moving down a group or family
  • additional electrons added to new more outer electron shell when moving down group
    • additional layers of inner-shell electrons mitigate effects of Z_eff
  • Z_eff remains essentially constant

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• dependent on how many electrons are lost or gained by an element in its most stable ionic state
  • tricky with transition metals due to multiple possible oxidation states
  • also tricky with metalloids due to being able to either lose or gain electrons depending on situation
• for nonmetals, ionic radii decrease when moving from left to right on the periodic table
  • nonmetals farther from noble gas group require more electrons to achieve stable octet
  • having more electrons in relation to number of protons helps mitigate Z_eff
  • O^2- is bigger than F^-
• for metals, ionic radii decrease when moving from left to right on periodic table
  • metals in group 1 lose fewer electrons in comparison to metals in other groups
  • experience a smaller increase in Z_eff due to loss of electrons

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Ionization Energy

(Ionization Potential)

• energy required to move an electron from a gaseous species 
• ionization energy increases from left to right across a period and bottom to top in a group
  • the greater the Z_eff experienced by an atom's valence electrons, the less likely they are to leave
  • elements in group 1 easily lose electrons and are referred to as active metals while those in group 18 are the least likely to give up electrons and are referred to as noble gases
• elements can have multiple ionization energies due to the fact that many elements lose more than one electron to achieve a stable octet
  
  • 2nd, 3rd, etc. ionization energies grow dramatically in elements that have a stable octet
    • Na⁺ has a very high second ionization energy
  • 2nd, 3rd, etc. ionization energies grow much less in elements that achieve a stable octet through electron loss
    • Mg⁺ has a relatively unchanged second ionization energy in comparison to its first

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• energy dissipated by a gaseous species when it gains an electron
• despite being an exothermic process and having ΔH_rxn that is negative, electron affinities are reported as positive numbers representing the energy dissipated
• increases across a period from left to right and in a group from bottom to top (except noble gases which have electron affinities of 0)
  • The higher Z_eff between the nucleus and the valence shell electrons, the greater the energy release will be when the atom gains the electron

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• measure of the attractive force that an atom will exert on an electron in a chemical bond
• commonly measured using the Pauling electronegativity scale
  • ranges from 0.7 for Cesium to 4.0 for Fluorine
  • noble gases have negligible electronegativities
• increases across a period from left to right and in a group from bottom to top

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• found in group 1
• have all classical physical properties of metals except that their densities are far lower
• have very low Z_eff values compared to other elements in same period
  • low ionization energies
  • low electron affinities
  • low electronegativities
• react readily with nonmetals, especially halogens, in violent reactions leading to formation of strong bases (alkali)

• found in group 2
• share many of the features of alkali earth metals but are more dense and have smaller atomic radii due to higher Z_eff
• react to form divalent cations (unlike univalent cations of alkali metals)

• found in group 16
• group of nonmetals and metals that are crucial to biological function (include oxygen and sulfur)
• small atomic radii and large ionic radii
• contain 6 valence electrons and commonly form divalent anions
• at high concentrations, many of these elements, no matter how biologically useful, can be toxic or damaging (example: ROS)

• found in group 17
• highly reactive nonmetals with seven valence electrons
• commonly found as ions (halides) or diatomic molecules (Cl₂, I₂, etc.)
• variable physical properties
• extremely reactive with the active metals

• found in group 18
• minimal chemical reactivity due to filled valence shells making them great as commercial light sources (i.e. neon lights)
• have low boiling points and found as gases at room temperature

• found in groups 3-12
• considered to be metals as they have low electron affinities, are malleable, very hard, have high melting and boiling points, and are good conductors
• able to have multiple oxidation states allowing them to form a variety of ionic compounds
  • different oxidation states are many times associated with different colors
• tend to associate in solution with either water (hydration complexes) or with nonmetals to form complexes
  • causes d-orbitals to split into two energy sublevels enabling many complexes to absorb certain frequencies of light (why many times these complexes can be found in biological processes like photosynthesis)

• general rule of thumb that states that atoms tend to bond with other atoms so that their valence shell has eight electrons like the configurations of the noble gases
• has numerous exceptions
• Incomplete octet - some elements are stable with fewer than eight electrons like hydrogen, helium, lithium, beryllium, or boron
• Expanded octet - any element in period 3 or higher can hold more than eight electrons by incorporating their d-orbitals
• Odd numbers of electrons - molecules w/ odd numbers of valence electrons cannot distribute those electrons to provide each participating atom with 8 electrons 

• one or more electrons from an atom with low electronegativity (usually metals) are transferred to an atom of higher electronegativity (usually nonmetals)
• resulting electrostatic attractions hold these molecules together
• Properties
  • extremely high melting and boiling points
  • dissolve in water and other polar solvents (hydrogen-bonding)
  • good conductors of electricity in molten or aqueous states
• a crystalline lattice structure results
  • Ex. NaCl
  • repeating positive and negative ions re arranged to maximize attractive forces between opposite charges and minimize repulsive forces between like charges

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• electron pair shared between two atoms (usually nonmetals) of similar electronegativities
  • energy required to form ions is more than that released by ionic bond formation
  • atoms share electrons through an attraction of each electron in the shared pair for two positive nuclei of bonded atoms
• electrons are not always shared equally depending on the degree of difference in electronegativities
  • minute difference in electronegativity makes nonpolar bond
  • notable difference in electronegativity makes polar bond
  • large/significant difference in electronegativity makes ionic bond
• if both shared electrons in bond are provided by only one of the atoms in the interaction, it is known as coordinate covalent bond
• formed as discrete molecular units w/ weak intermolecular interactions
  
  • lower melting and boiling points
  • poor conductors of electricity in liquid and aqueous states

• bond length
  • average distance between two nuclei of atoms in a bond
  • bond length decreases as number of electron pairs shared between atoms (bond order) increases
    • triple bond shorter than double shorter than single
• bond energy
  • energy required to break a bond by separating its components into their isolated, gaseous atomic states
  • greater bond order means higher bond energy
  • higher bond energy means stronger bond
• polarity
  • degree of distribution of electron density in covalent bond based on differences in electronegativity between atoms in a bond
  • atoms in nonpolar covalent bonds have equal or nearly equal electronegativity resulting in equal distribution
  • atoms with relatively different electronegativities unequally distribute electron densities with more electronegative atoms receiving greater electron density
    • dipole moment is created in which more electronegative atom is referred to as partial negative δ⁻

• both of the shared electrons in bond originated on same atom
• usually caused by lone pair of one atom attacking unhybridized p-orbital of another atom to form a bond
• common in Lewis acid-base chemistry
  • lewis acid - any compound that accepts electrons in acid-base reaction
  • lewis base - any compound that donates electrons in acid-base reaction

• system of notation developed to keep track of bonded and nonbonded electron pairs
• Rules for drawing lewis structures
  1. draw out the backbone of the compound with the least electronegative atom (aside from hydrogen) at the center
  2. count all valence electrons of the atoms
  3. draw single bonds between the central atom and atoms surrounding it
  4. complete octets of all atoms bonded to the central atom, using the remaining valence electrons
  5. place any extra electrons on the central atom. If the central atom has less than an octet, try to write double or triple bonds between the central and surrounding atoms using the lone pairs on the surrounding atom
• resonance structures - identical compounds can many times yield alternate structures based on electron pair arrangements; the correct structure is always a mixture of all possible resonance forms
  • there are usually one or more forms that contribute more or less to the resonance hybrid
    • major contributors
    • minor contributors
  • determining the most stable resonance form allows you to determine the most major contributor
    • lewis structure w/ small or no formal charges
    • w/ less separation between opposite charges (+1 and -1>+2 and -2)
    • in which negative formal charges are placed on more electronegative atoms

• **Note that formal charge differs from oxidation number as formal charge underestimates effects of electronegativity while oxidation number overestimates effects of electronegativity
• determine the number of valence electrons available to each atom in compound
• determine the number of nonbonding electrons surrounding each atom
• assuming that each electron pair is split evenly between two nuclei in a bond, determine the number of bonding electrons interacting with each atom (1/2 N_bonding)
• Subtract the number of nonbonding and bonding electrons from the number of total valence electrons as follows:
  • formal charge = V - N_nonbonding - (1/2)N_bonding

Valence Shell Electron Pair Repulsion Theory

VSEPR

• states that the 3D arrangement of atoms surrounding a central atom is determined by the repulsions between bonding and nonbonding electron pairs
  • these pairs arrange themselves as far apart as possible to minimize repulsive forces
• Process of determining electronic geometries
  • determine lewis dot structure of molecule
  • count total number of bonding and nonbonding electron pairs in the valence shell of the central atom
  • arrange electron pairs around the central atom so that they are as far apart as possible

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• electronic geometry describes the spatial arrangement of all pairs of electrons around the central atom including bonding and nonbonding pairs
  • ideal bond angle
    • electronic geometry allows for determination of ideal bond angles
    • considering nonbonding electron pairs allows us to determine derivations from expected bonding angles
      1. nonbonding electron pairs cause decreases in bonding angles
• molecular geometry describes the spatial arrangement of only bonding pairs of electrons
  • coordination number
    • number of atoms that surround and are bonded to a central
    • different coordination numbers result in different molecular geometries

• presence of polar bonds does not necessarily mean that a molecule is polar
• polarity relies on the presence of an overall separation of charge across a molecule
  • for a molecule to be polar, the molecular geometry of the molecule must be such that dipole moments don't cancel each other out

• When two atoms bond to form a compound, atomic orbitals interact to form a molecular orbital
  • describes the probability of finding the bonding electrons in a given space
  • obtained by combining the wave functions of the separate atomic orbitals
• overlap of two atomic orbitals describes the molecular orbital
  • if signs of two atomic orbitals are same, a bonding orbital forms
  • if signs of two atomic orbitals are opposite, a nonbonding orbital forms
• this overlap can occur in two separate patterns
  • sigma σ bond
    • two orbitals overlap head-to-head
    • allow for free rotation about their axes because electron density of bonding orbital is a single linear accumulation between atomic nuclei
  • pi π bond
    • two orbitals overlap in such a way that there are two parallel electron cloud densities
    • do not allow for free rotation due to electron densities of orbitals being parallel and unable to be twisted in such a way that allows continuous overlapping of clouds of electron densities

• bonding electrons in nonpolar covalent bonds appear to be shared equally between two atoms but are located randomly throughout the orbital at any given moment
  • gives opportunity for formation of transient dipoles
  • rapid polarizations and counterpolarizations of electron clouds result in the formation of short-lived dipole moments that orient themselves with other molecules
• attractive or repulsive interactions of these short-lived and rapidly shifting dipoles in nonpolar molecules
• a type of Van der Waals force
• the weakest of intermolecular forces

• polar molecules tend to orient themselves in such a way that oppositely charged ends of the respective molecular dipoles are closest to each other
  • arrangement is energetically favorable due to formation of attractive electrostatic force
• present in solid and liquid phases but become negligible in gaseous phases due to significantly increased distance between gas particles
• not different from london dispersion forces in kind but in duration

• ionic compounds are unable to form molecules due to the way that the positive cations and negative anions arrange themselves together in solid state to create infinitely large lattice structures
  
  • we instead use formula unit for ionic compounds (NaCl is formula unit of larger lattice structure)
  • formula weight used to describe these compounds
• covalently bonded compounds form molecules which are the smallest units of compounds
  • molecules use molecular weight

• empirical formula
  • simplest whole-number ratio of elements in a compound
  • in case of benzene, empirical formula is CH
• molecular formula
  • exact number of atoms of each element in compound 
  • multiple of empirical formula
  • in case of benzene, molecular formula is C₆H₆

• percent of a specific compound that is made up of a given element
• can be calculated from either empirical or molecular formula
  • molecular formula can actually be calculated from percent composition and molar mass of compound
• determined by following equation:

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• two or more reactants form one product
• common example
  • formation of water from hydrogen in air
  • 2 H_2(g) + O_2(g) → 2 H₂O_(g)

• single reactant breaks down to form two or more products
• usually requires heat, high-frequency radiation, or electrolysis to begin reaction (catalysts)
  • sometimes regular sunlight provides enough energy to initiate the reaction
    • silver chloride decomposes from UV portion of sunlight to silver and chlorine 
• common example
  • 2 HgO_(s) → 2 Hg_(l) + O_2(g) (in presence of heat)

• type of reaction that involves some fuel source (usually a hydrocarbon) and an oxidant (usually oxygen) typically leading to the production of water and carbon dioxide
• Common example
  • CH₄ + 2O₂ → CO₂ + 2H₂O

• reaction in which one atom/ion in a compound is replaced by another atom/ion in an element
• often further classified as oxidation-reduction reactions due to atoms undergoing changes in oxidation number
  • electron transfer
• common example
  • Cu_(s) + AgNO_3(aq) → Ag_(s) + CuNO_3(aq)

Double-displacement Reactions

or metathesis reactions

• elements from two different compounds swap places w/ each other to form 2 new compounds
• occurs when one of the products is removed from solution as precipitate or gas or when two of the original species combine to form weak electrolyte that remains undissociated insolution
• common example
  • CaCl_2(aq) + 2AgNO_3(aq) → Ca(NO₃)_2(aq) + 2AgCl_(s)
  • two soluble compounds react to make at least one precipitate

• special type of double displacement reaction in which an acid reacts with a base to produce a salt (and usually water)
• common example
  • HCl_(aq) + NaOH_(aq) → NaCl_(aq) + H₂O_(l)

• one reactant is typically used up faster than another in a given reaction
• reactant that is used up first limits the amount of product that can be formed
• when solving equations for limiting reagents:
  • be sure to look at moles to make comparisons, not grams
  • it is not the absolute mole quantities of the reactants present that determine the limiting reagent but the combination of absolute quantities with stoichiometric ratios

• theoretical yield 
  • maximum amount of product that can be generated as predicted from the balanced equation
  • makes assumption that all of limiting reagent is used up, no side reactions have occurred, and entire product has been collected
  • pretty much impossible to match
• actual yield
  • actual amount of product obtained during reaction
• percent yield
  • ratio of actual yield to theoretical yield

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• solid ionic compounds tend to be poor conductors of electricity due to rigid lattice structures that don't allow for easy movement of the ions
• in aqueous environments (in water), ions dissolve to make water (poor conductor on its own) into a good conductor of electricity
• electrolytes are solutes that enable solutions to carry currents (conduct electricity)
• strong electrolytes have solvate entirely in water making the solution a great conductor
• weak electrolytes solvate much less and nonelectrolytes do not solvate at all

• the rate of a reaction is proportional to the number of collisions per second between reacting molecules
• not all collisions are effective
  • molecules must collide in the same orientations
  • molecules must collide with sufficient energy to break existing bonds and form new ones
    • minimum energy of a collision is described by its activation energy, E_a
• Arrhenius equation

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*frequency factor is measure of how often molecules collide in a certain reaction

*understand relationships between variables and exponent rules that govern equation

• molecules collide w/ energy ≥ activation energy and form a transition state that is a theoretical hybrid of the products and reactants
  • old bonds weakened and new bonds beginning to form
• transition state complex can either proceed to end of reaction to create products or revert to previous reactants w/ no added energy
• progress of reaction from reactants to transition state to products is described by reaction coordinate and can be seen on free energy graph

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• reactant concentration (or partial pressure for gases)
  • higher concentrations of reactants push the reactions forward (or increase reaction rate) due to a higher frequency of molecular collisions
  • this affects frequency factor, A, of Arrhenius equation

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• temperature
  
  • temperature describes average kinetic energy of molecules in a space 
  • increasing temperature increases reaction rate as a larger proportion of reactants are able to gain enough energy to surpass activation energy
• medium in which reaction takes place
  • aqueous vs. nonaqueous solvents
    • interactions with molecules and chemical environment can severely affect reactivity of molecule
    • some reactions prefer aqueous while others prefer nonaqueous
  • physical state
    • solid, liquid, gas states can affect the interactions between molecules
  • general rule of thumb: polar solvents are almost always preferred due to their ability to polarize the bonds of reactants
• presence of catalyst
  • increase reaction rate by providing a path for a reaction that decreases the activation energy
  • may increase frequency or collisions, change relative orientation of reactants, donate electron density to reactants, or reduce intramolecular bonding w/in reactant molecules
  • always leave reactions identical to the way they enter them
• these factors cannot always be determined to increase or decrease reaction rate as they can all affect each other's abilities to increase reaction rate
  • heat and medium can affect catalyst efficiency or destroy catalyst altogether

• homogeneous - catalyst is in same phase (solid, liquid, gas) as reactants
• heterogeneous - catalyst is in a distinct phase from the reactants

• reaction rate can be determined by the disappearance of reactants overtime or the formation of products over time
• when determining rate by the rate of reactant disappearance, we use a negative(-) sign as reactants are being consumed
• when determining rate by the rate of product appearance, we use a positive(+) sign as reactants are being made
• it is expressed in units of concentration/second

rate = k [A]^x [B]^y 

• rate law is an expression that describes reaction rate in terms of k, reactant concentrations, and exponential rates of order
  • k - the reaction rate coefficient which is constant at any given temperature and specified activation energy
  • exponents x and y - orders of reaction; overall reaction order determined by addition of these values
  • rate law equations can be much more complex than this simple frame
• Important things to consider
  • orders of a reaction are not the same as the stoichiometric coefficients in the overall balanced equation and must be determined experimentally
  • equilibrium constant expression and rate law are not the same thing
  • k is only constant for a reaction at given activation energies and temperatures - not always the same value
  • principles of equilibrium (i.e. presence of reverse reaction) do not only apply to the end of the reaction - equilibrium is a driving force throughout entirety of reaction

• rate of formation of product is entirely independent of changes in concentration of the reactant(s)
  • rate = k
  • k has units of M/s
  • k = -slope of [A] vs. time graph
• because rate is independent of concentration, it can only be changed with changes in temperature or presence of catalyst

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• has rate that is directly proportional to only one reactant such that doubling the concentration of that reactant results in doubling of the rate of formation of product
  • rate = k[A]¹
  • k has units of s^-1
  • radioactive decay is a common example
  • concentration of reactant described by equation similar to Arrhenius
    • [A]_t = [A]₀e^-kt
  • k = -slope of ln[A] vs. time graph
• suggests that reaction begins when molecule undergoes chemical change all by itself, w/out a chemical interaction, and usually w/out a physical interaction with any other molecule

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• has rate that is either proportional to either concentrations of two reactants or to the square of the concentration of a single reactant
  • rate = k[A][B] or rate = k[A]²
  • k has units of M^-1s^-1
  • k = +slope when graphed as 1/[A] vs. time
• suggests a physical collision between two reactant molecules, especially if the rate law is first-order w/ respect to each reactant

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• point in reversible chemical reaction at which the rates of the forward and reverse reactions are equal, but neither has entirely stopped (this would be static equilibrium)
  • does not mean concentration have to be equal
• this is the point at which a system's entropy is at a maximum while the Gibbs free energy is at a minimum (ΔG=0)
• defined by constant K_eq which is temperature-dependent
  • equilibrium constant comes in many other forms (K_sp K_p K_w K_a etc.)
    • when talking about concentrations, we use K_c
  • equal to ratio of products over reactants
    • large magnitudes (large, positive exponents) of K_eq indicate much more product at equilibrium
    • small magnitudes (large, negative exponents) of K_eq indicate much more reactant at equilibrium
    • if K_eq = 1, then products and reactants are in equal amounts at equilibrium
  • also equal to ratio of rate of forward reaction over rate of reverse reaction (k_f / k_r)
  • when reaction occurs in more than one step, equilibrium constants for each step are multiplied to find overall reaction equilibrium constant
  • when determining equilibrium constant of reverse reaction, it is equal to the inverse of the forward reaction (1/K_c)

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• reaction is not always in equilibrium and can many times take long periods of time to reach equilibrium
• reaction quotient, Q, indicates how far the reaction has proceeded toward equilibrium
• equation is identical to equilibrium constant expression, but it describes the reaction in conditions outside of equilibrium
  • allows us to determine direction of reaction according to Le Chatelier's principle
    • Q < K_eq, concentrations of reactants higher than equilibrium concentrations and reaction proceeds forward
    • Q > K_eq, concentrations of products higher than equilibrium concentrations and reaction proceeds in reverse
  • allows us to determine Gibbs free energy for specified direction of reaction
    • Q < K_eq, ΔG of forward reaction is negative and therefore spontaneous
    • Q > K_eq, ΔG of forward reaction is positive and therefore nonspontaneous
  • if Q = K_eq, then the system is considered to be at dynamic equilibrium

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• states that if stress is applied to a system, system will shift to relieve applied stress
  • stress leads to reaction temporarily leaving dynamic equilibrium
  • reaction responds accordingly to return to minimum energy state of dynamic equilibrium
• stress can refer to changes in concentration
  • addition or removal of products or reactions shifts system out of equilibrium
  • system corrects by shifting reaction in the direction away from added species and toward removed species
    
    • add reactants/ remove product, reaction goes forward (rightward shift)
    • remove reactants/ add product, reaction goes in reverse (leftward shift)
• stress can refer to changes in pressure or volume
  • only important to chemical reactions involving gaseous species as liquid and solid are relatively incompressible
  • increasing or decreasing pressure results in changes in the partial pressures of all gases in a system resulting in it no longer being in dynamic equilibrium
  • system will react in accordance with Le Chatelier's principle and correct for this by trying to restore pressure
    • when decreasing volume/increasing pressure, reaction moves in direction that creates fewer moles of gas
    • when increasing volume/decreasing pressure, reaction moves in direction that creates more moles of gas
• stress can also come from changes in temperature
  • changing temperature results in a change in equilibrium constant as it is temperature-dependant
    • temperature does not immediately cause changes in concentrations or partial pressures, so Q remains constant for short time
    • temperature change, however, immediately affects equilibrium
  • in accordance with Le Chatelier's principle, system will attempt to return Q to equilibrium at new temperature by shifting reaction direction according to enthalpy (ΔH)
  • one may think of heat as a reactant when considering temperature changes and how a system corrects for them
    • endothermic reactions (ΔH>0): heat functions as a reactant
    • exothermic reactions (ΔH<0): heat functions as a product
  • increase in temperature
    • endothermic: reaction shifts right
    • exothermic: reaction shifts left
  • decrease in temperature
    • endothermic: reaction shifts left
    • exothermic: reaction shifts right

• kinetic product
  • formed at lower temperatures
  • less free energy is required to pass transition state (smaller E_a) than thermodynamic pathway leading to faster production
  • product typically less stable w/ a higher(less negative) ΔG than thermodynamic product 
• thermodynamic product
  • formed at higher temperatures
  • require more free energy to overcome activation barrier created transition state than kinetic pathways leading to slower production
  • product more stable w/ a more negative ΔG than the kinetic product

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• systems are sometimes difficult to differentiate from surroundings as they are not fixed and are based on the observations one is trying to make 
• 3 main classifications of systems
  • isolated - system cannot exchange energy or matter
  • closed - system can exchange energy but not matter
  • open - system can exchange energy and matter

• process is any change in one or more properties experienced by a system
• isothermal processes create special conditions that allow simplification of first law of thermodynamics:   ΔU = Q−W
• occur when system's temperature is constant allowing us to set internal energy (U) of system as a constant (ΔU=0)
  • this is because temperature and internal energy are directly proportional so an unchanging temperature means that internal energy is unchanging
  • along with isobaric, isothermal is common process as temperature is usually easy to control
• simplified first law: Q = W
• appears as hyperbolic curve on pressure-volume graph and work is represented by the area underneath the curve

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• process is any change in one or more properties experienced by a system
• adiabatic processes create special conditions that allow simplification of first law of thermodynamics:   ΔU = Q−W
• occur when no heat (Q = 0) is exchanged between system and surroundings making thermal energy of system constant
• simplified first law:  ΔU = -W
• appears hyperbolic on a P-V graph and work (and internal energy) is represented by area under curve

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• process is any change in one or more properties experienced by a system
• isobaric processes create special conditions that allow simplification of first law of thermodynamics:   ΔU = Q−W
• occur when the pressure of the system is constant 
  • this leads to no changes in the first law but holding condition constant removes a confounding variable
  • along with isothermal, isobaric processes are very common as pressure is easy to control
• simplified first law:  ΔU = Q−W (unchanged)
• appears as a flat line on a P-V graph (pressure is constant) with work being represented by the are underneath the line

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Isovolumetric Processes

isochoric

• process is any change in one or more properties experienced by a system
• isovolumetric processes create special conditions that allow simplification of first law of thermodynamics:   ΔU = Q−W
• occur when the volume of the system is constant 
  • because the gas cannot expand or compress, no work (W=0) can be performed
• simplified first law:  ΔU = Q (unchanged)
• appears as a vertical line on a P-V graph (volume is constant) with work being represented by the are underneath the curve which is always 0 as it is vertical

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• state function - macroscopic properties that are used to describe the state of a system in an equilibrium state
  • do not describe process of how system got to state - independent of path taken
  • useful for comparing one equilibrium state to another 
  • include pressure(P), density(ρ), temperature(T), volume(V), enthalpy(H), internal energy(U), Gibbs Free Energy(G), and entropy(S)
    • changing equilibrium state will change one of these properties
    • these properties are also dependent on one another (changing one can cause change in another)
• process function - quantitatively describe the pathway taken from one equilibrium state to another
  
  • most important are work(W) and heat(Q)
  • state functions are considered independent of these functions

• standard conditions 
  • presence of different equilibrium states at different pressures, temperatures, and other state function factors results in an infinite number of different equilibrium states
  • extremely important for kinetics, equilibrium, and thermodynamics
    • temperature, pressure, and concentrations held constant in standard conditions to simply task
  • 25°C (298K), 1 atm, 1M concentrations
• STP
  • used for ideal gas laws
  • hold temperature and pressure constant
  • 0°C (273K), 1 atm
• standard state
  
  • most stable form of substance under standard conditions
  • examples:
    • H_2(g), H₂O_(l), NaCl_(s), O_2(g), C_{(s, graphite)}

• molecules in liquid phase possess any range of instantaneous kinetic energies and move about freely
• evaporation/vaporization - some molecules moving with sufficient kinetic energies able to randomly escape liquid phase as gas
  • loss of high energy particle leads to decrease in temperature of remaining liquid (T is average of kinetic energy of all molecules)
  • endothermic process
  • boiling - type of vaporization in which rapid bubbling of entire liquid causes rapid release of liquid as gas
    • can only occur above boiling point of liquid as vaporization must occur simultaneously through entire volume of liquid (why there are bubbles)
• condensation - some molecules of gas are forced back into liquid phase by vapor pressure 
  • escaping molecules from liquid get trapped above (in container or atmospheric container) and exert a countering pressure that leads to condensation of some these molecules
• evaporation and condensation proceed at respective rates until equilibrium is struck (rates become equal)
  
  • vapor pressure increases w/ increasing temperature as more molecules have sufficient energy to leave liquid phase
• boiling point - temperature at which vapor pressure of liquid is equal to ambient pressure (such as atmospheric)

• atoms are confined to specific locations, but each atom/molecule still undergoes vibrational motions
  • vibrational motions increase with application of heat
• fusion/melting 
  • availability of energy microstates increases with increasing temperature allowing atoms/molecules to eventually break constraints of 3D structure and escape as liquid
• solidification/crystallization/freezing
  • availability of energy microstates decreases with decreasing temperature causing molecules to coalesce into 3D structure
• melting/freezing points - temperatures at which these respective processes occur
  
  • pure solids have distinct, precise melting point while amorphous solids melt over large ranges of temperatures due to less-order structure

• sublimation - substance goes directly from a solid to a gas (dry ice)
  • a good technique for purification (cold finger)
• deposition - substance goes directly from gas to solid

• graphs that show temperature and pressures at which substances will be thermodynamically stable in particular phase and at which phases are in equilibrium
• lines of equilibrium on these diagrams represent phase boundaries as well as where phase change equilibrium occurs
• triple point - point at which all three phases are in equilibrium and the three phase boundaries meet
• critical point - point at which liquid-gas phase boundary terminates
  • anything past this point on graph is in a phase that is an equal mix of liquid and gas (phases indistinguishable) known as supercritical fluid

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• temperature is average kinetic energy of particles in substance as determined by thermal energy - state function
• heat is the transfer of thermal energy - process function
• heat is equivalent to enthalpy(ΔH) at constant pressure (remember that enthalpy is state function)
  • endothermic process has ΔH>0 (+); heat is absorbed
  • exothermic process has ΔH<0 (-); heat is emitted
  • thermal equilibrium between objects only reached when temperatures are equal ΔH=0

• process of measuring heat transferred 
  • constant-volume calorimetry 
    • bomb calorimeter/decomposition vessel
    • adiabatic (no heat exchanged between calorimeter and universe)
    • Q_calorimeter = 0, so
      • ΔU_calorimeter=Q_calorimeter−W_calorimeter=0
      • q_system=−q_surroundings
  • constant-pressure calorimetry
    • coffee-cup calorimeter
• based on equation q=mcΔT
  • m=mass
  • c=specific heat (amount of energy required to raise temperature of one gram of substance by one degree Celsius/Kelvin)
  • ΔT=change in temperature
• heat capacity = mc
  • allows us to compare objects of same type with different masses
  • heat capacity of swimming pool may be 10,000kJ while that of cup of water may be 1kJ

• when heat is applied, temperature of substance increases steadily until melting/boiling point is reached when temperature remains constant
  • all heat energy used to overcome intermolecular forces holding structure during phase change
• q=mcΔT doesn't work
• q=mL must be used
  • m=mass
  • L=latent heat (enthalpy of an isothermal process)
    • can be enthalpy of fusion (ΔH_fus)
    • or enthalpy of vaporization (ΔH_vap)
• energy to change temperature of substance determined by:
  • q = mcΔT_(s)+mL_(fus)+mcΔT_(l)+mL_(vap)+mcΔT_(g)

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• state function that expresses heat changes at a constant pressure
  • enthalpy cannot be measured alone, so other methods like heat of formation must be used
• standard enthalpy of formation (ΔH°_f)
  • enthalpy required to produce one mole of a compound from its elements in their standard states (most stable physical state at 298K and 1atm)
  • ΔH°_f for any given element, by definition must be 0
• can be used in conjunction to determine standard enthalpy of reaction (ΔH°_rxn)

• enthalpy - state function that expresses heat changes at a constant pressure
  • enthalpy cannot be measured alone, so other methods like heat of reaction must be used
• standard enthalpy (ΔH°_rxn)
  • enthalpy change accompanying reaction being carried out under standard conditions
  • calculated by taking difference between sum of standard heats of formation for products and sum of standard heats of formation for reactants
  • ΔH°_rxn = ΣΔH°_f,products − ΣΔH°_f,reactants

• as state function and property of equilibrium state, enthalpy is not dependent on the path or process to change equilibrium states
• hess's law tells us that enthalpy changes of reactions are additive no matter the path of the reaction taken
  • one way of vaporizing bromine may be to just heat it while another may go through a series of steps, but ΔH is still equal as long as standard conditions are a constant
• this means that the enthalpy changes between several reactions in a system can be added together to achieve an overall ΔH

• average energy required to break a particular type of bond between atoms in gas phase
  • bond breaking is endothermic
  • bond making is exothermic (imparts stability such as through filling octet)
• ΔH°_rxn = ΣΔH_{bonds broken} − ΣΔH_{bonds formed} = total energy absorbed - total energy released

• enthalpy change associated with the combustion of a fuel
• involve using heat released from combustion reaction (reaction commonly using hydrocarbon as fuel and oxygen as oxidant)
  • measurements of enthalpy change require reactions to be spontaneous and fast making combustion reactions ideal

• states that energy spontaneously disperses from being localized to becoming spread out if it is not hindered from doing so
• entropy - measure of spontaneous dispersal of energy at a specific temperature
  • ΔS = Q_rev / T
    • ΔS = change in entropy
    • Q_rev = heat that is gained or lost in a reversible process
    • T = temperature in kelvin
• entropy is always increasing across universe, so it can never be negative (ΔS > 0)
• entropy is state function, so it is independent of process and can be calculated using standard entropies of products and reactants
  • ΔS°_rxn = ΣΔS°_{f, products} − ΣΔS°_{f, reactants}

• measure of change in enthalpy and change in entropy as a system undergoes a process
  • ΔG = ΔH−TΔS
• maximum amount of energy released (or absorbed) by a process assuming constant pressure and temperature
• because temperature is always positive, gibbs free energy is dependent on the signs of ΔH and ΔS
  • phase changes are great examples of temperature-dependent processes (why water doesn't boil until boiling point)

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• Free energy is related to the equilibrium constant(K_eq) of a reaction as it defines the spontaneity of a reaction 
  • remember that ΔG^o_rxn is only applicable w/ 1M conc.
  • ΔG^o_rxn = -RTlnK_eq
  • large K_eq value means a more negative ΔG^o_rxn and greater spontaneity
  • smaller K_eq value means a less negative/ more positive ΔG^o_rxn and less spontaneity or nonspontaneity
• This relationship allows us to also monitor the progress of a reaction, but through a different equation as the conc. have now changedΔG
  • ΔG_rxn is now used instead of ΔG^o_rxn to determine free energy change for reaction in progress
  • ΔG_rxn = ΔG^o_rxn + RTlnQ = RTln(Q/K_eq)
  • movement toward equilibrium associated w/ decrease in ΔG (more negative)
  • movement away from equilibrium associated w/ increase in ΔG (more positive)
  • at equilibrium, ΔG is equal to 0 as the reaction is at its point of greatest stability

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Measuring Pressure

(Units and Tools)

• pressure measured in atmospheres(atm), millimeters of mercury(mmHg) or torr, and pascal(Pa) which is the SI unit
  • 1 atm = 760 mmhg = 760 torr = 101.325 kPa
• measured using barometer
  • designed with outer chamber which experiences force of external pressure and inner column that exerts an opposing force based on its density
  • when atmospheric pressure is lower, column lowers due to reduced external force being applied and weight of mercury takes over
  • when atmospheric pressure is higher, column raises due to increased external force opposing weight of mercury
  • sphygmomanometers are used to measure blood pressure and have the same conceptual design

• ideal gases are hypothetical gases with molecules that have no intermolecular forces and occupy no volume
  • typically correct model when looking at gases at lower pressures and higher temperatures
  • real gases deviate heavily at high pressures and low temperatures due to reduced movement and closer association of gaseous molecules
• ideal gas law shows how pressure, volume, moles of gas, and temperature are related through a constant, R
  • PV=nRT
  • R = 8.21×10^-2 L•atm/mol•K 
    • R can also equal 8.314 J/K•mol when using pascal for pressure and cubic meters for volume

• states that all gases at constant temperature and pressure occupy volumes that are directly proportional to the number of moles of gas present
  • equal amounts of all gases at same temp and pressure occupy equal volumes
  • as number of moles of gas increases, volume increases in direct proportion
• n₁/V₁ = n₂/V₂

• states that for a given gas held at constant temperature, the volume of the gas is inversely proportional to its pressure
• P₁V₁ = P₂V₂

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• states that, at constant pressure, the volume of a gas is proportional to its absolute temperature expressed in Kelvin (negative numbers don't count)
• V₁/T₁ = V₂/T₂

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• states that the pressure and temperature of a gas are directly proportional when volume is held constant
• P₁/T₁ = P₂/T₂

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• combination of many of the preceding laws that relates pressure and volume (Boyle's) in the numerator, and relates variations in temperature to both volume (Charles's Law) and pressure (Gay-Lussac's Law)
• P₁V₁/T₁ = P₂V₂/T₂ 

• when two or more gases that do not chemically interact are in one vessel, each individual gas exerts its own partial pressure
• Dalton's Law states that the total pressure of a gaseous mixture is equal to the sum of the partial pressures of the individual components
  • P_T = P_A + P_B + P_C ...
• this allows partial pressure of gas to be found through its mole fraction
  • P_A = X_AP_T 
  • X_A = (moles of gas A)/(total moles of gas)

• at various applied pressures, the concentration of a gas solvated in liquid increases or decreases
  • characteristic of gas's vapor pressure
• Henry's Law states that solubility (concentration) and pressure are directly related
  • [A]₁/P₁ = [A]₂/P₂
  • or [A] = k_H × P_A
    
    • k_H is henry's constant
    • P_A is partial pressure of gas A

• demonstrates that all gases show similar physical characteristics and behavior irrespective of their particular chemical identity
• behavior of real gases deviates slightly for same reason that ideal gas law does not work
• Makes 5 major assumptions
  • gases are made up of particles w/ volumes that are negligible compared to the container
  • gas atoms or molecules exhibit no intermolecular attractions or repulsions
  • gas particles are in continuous, random motion, undergoing collisions with other particles and the container walls
  • collisions between any two gas particles or gas particles and container wall are elastic (kinetic energy and momentum are conserved)
  • the average kinetic energy of gas particles is proportional to absolute temperature of gas (in K) and it is the same for all gases at given temperature, irrespective of chemical identity or atomic mass
• can be applied to determine average molecular speeds and speed of diffusion/effusion 

• based on theory of kinetic molecular theory that average kinetic energy of a gas particle is proportional to absolute temperature of gas
  • KE = 1/2mv² = 3/2k_BT
  • k_B is Boltzmann constant = 1.38×10^-23J/K
• root-mean-square speed (μ_rms) - one way to define average speed is to determine the average kinetic energy per particle and then calculate the speed to which it corresponds
  • μ_rms = √(3RT/M)
  • R is ideal gas constant
  • M is molar mass

• Because all gas particles have same kinetic energy at same temperature, kinetic molecular theory predicts that particles with greater mass travel at slower average speeds
• Graham found that the rates at which two gases diffuse are inversely proportional to the square roots of their molar masses
  • r₁/r₂ = √(M₂/M₁)
  • r's are diffusion rates
  • M's are molar masses
• Effusion - flow of gas particles under pressure from one compartment to another through a small opening
  • Graham found that his law of diffusion also applied to effusion through same mathematical relationship

• real gases deviate from the ideas that create the ideal gas law and kinetic molecular theory based on two temperature and pressure
• pressure
  • as pressure of gas increases, particles are pushed closer and closer together and intermolecular attraction forces gradually become more and more significant until gas condenses at condensation/boiling point
  • at higher pressure, size of particles becomes relatively larger compared to distance between them causing gas to take up larger volume of container than predicted by ideal gas law (gas particles take up no space)
• temperature
  • as temperature of gas is decreased, average speed of gas molecules decreases and attractive intermolecular forces become increasingly significant until gas condenses at condensation/boiling point due to same forces
  • as temperature of gas decreases towards condensation point, intermolecular attractions cause gas to have smaller volume than would be predicted by ideal gas law making volume taken up by gas particles increasingly significant
• Van der Waals Equation solves this

• corrects for deviations in ideal gas law

[image]

• a and b are constants experimentally determined for each gas
  • a corrects for attractive forces between molecules and, as such, will be smaller for gases that are small and less polarizable and high for larger, more polar molecules
  • b corrects for the volume of molecules themselves and, as such, will be larger for larger molecules
  • numerical values for a are generally much larger than those for b

Soluble

1. containing ammonium (NH₄⁺) and alkali metal cations are water-soluble
2. containing nitrate (NO₃^-) and acetate (CH₃COO^-) anions are water-soluble
3. containing halides (Cl, Br, I) are water-soluble
   • except fluorides and salts containing Ag⁺, Pb²⁺, Hg₂²⁺
4. containing sulfate ion (SO₄^2-)
   • except Ca²⁺, Sr²⁺, Ba²⁺, and Pb²⁺

Insoluble

1. all metal oxides are insoluble
   
   • except those formed w/ alkali metals, ammonium, CaO, SrO, and BaO (hydrolyze to form corresponding metal hydroxides)
2. all hydroxides are insoluble
   • except those formed w/ alkali metals, ammonium, Ca²⁺, Sr²⁺, and Ba²⁺
3. all carbonates (CO₃^2-), phosphates (PO₄^3-), sulfides (S^2-), and sulfites (SO₃^2-) are insoluble
   • except those formed with alkali metals and ammonium 

• complex ion/ coordination compound is molecule in which cation is bonded to at least one electron pair donor known as ligand (complexation reaction)
• complex ions held together w/ coordinate covalent bonds
  • electron pair donor (lewis acid) and electron pair acceptor (lewis base) form very stable Lewis acid-base adducts
• chelation - central cation can be bonded to same ligand in multiple places
  • typically requires large organic ligands that can double back to form second (or even third) bond w/ central cations
  • hemoglobin and its interactions w/ iron cation are a great example of this

• abbreviated m
• equal to moles of solute / kilogram of solvent
• in water at 25°C, molality ≈ molarity as density of water at this temp is 1kg/liter
  • changes w/ increasing concentrations due to effects on density of solution
  • also changes at different temperatures (and pressures in the case of gases)
  • used for boiling point elevation and freezing point depression

• K_sp = [A]^a[B]^b
  • high K_sp means a lot of solute dissolves 
  • low K_sp means a little solute dissolves
  • varies by temperature
    • increased temperature typically means increased K_sp for solid solute
    • decreased temperature typically means decreased K_sp for gaseous solute
• ion product (IP) is the same shares the solubility equilibrium but describes where the solvation is in relevance to the equilibrium position (like Q)
  • IP<K_sp - solvation has not yet reached equilibrium and solute will continue to dissolve (unsaturated)
  • IP>K_sp - solvation has gone past equilibrium and will begin to precipitate (supersaturated)
  • IP = K_sp - solvation is in dynamic equilibrium (saturated)

• solubility of complex ion is determined by K_sp like other compounds
• formation of complex ion, however, increases the solubility of salt in a solution and is determined by the K_f (formation or stability constant)
  • complex ions contain multiple polar bonds between ligands and central metal ion allowing them to engage in very large amount of dipole-dipole interactions
  • we must distinguish between K_sp of solution and that of complex ion itself as forming complex ions often uses mixtures of solutions
    • K_sp - dissolution of original solution
    • K_f - subsequent formation of complex ion in solution

• solubility of salt is reduced when dissolved in solution already containing one of its constituent ions
  • presence of common ion has no effect on value of solubility product itself but does affect the molar solubility
  • follows Le Chatelier's principle

• accounts for vapor pressure depression caused by solutes in solution
  • more solute means lower vapor pressure of solvent proportionately 
  • think about partial pressures P_T = P_A + P_B
    • if pressure remains constant, as P_B increases, P_A must decrease
  • presence of solute molecules can block evaporation of solvent molecules but not condensation (boiling point elevation)
• described mathematically as P_A = X_AP°_A
  • P_A is vapor pressure of solvent w/ solute
  • P°_A is vapor pressure of pure solvent
  • X_A is mole fraction of solvent in solution
    • X_A = mol of solvent/mol of solution
• this holds true for only ideal solutions when attraction between molecules of different components of mixture = attraction between molecules of any one component in pure state

• when nonvolatile solute is dissolved in solvent to create solution, boiling point of solution will be greater than that of pure solvent
• described mathematically as: ΔT_b = iK_bm
  • i is van't Hoff factor (corresponds to number of particles into which compound dissociates in solution)
  • K_b is proportionality constant characteristic of particular solvent
  • m is molal concentration of solution

• presence of solute particles in solution interferes w/ formation of lattice arrangement of solvent molecules associated w/ solid state
  • greater amount of energy must be removed from solution for solution to solidify
  • solid particle dissolves in small amount of liquid phase in solid phase and decreases rate of freezing while not affecting rate of melting
    • melting > freezing causing more of solution to be found in liquid state
• described mathematically as: ΔT_f = iK_fm
  • i is van't Hoff factor which corresponds to number of particles into which compound dissociates in solution
  • K_f is proportionality constant characteristic of particular solvent
  • m is molal concentration of solution

• "sucking" generated by solutions in which water is drawn into solution due to higher concentration of solute in one area over another
  • water moves in direction of higher solute concentration
• described mathematically as: Π = iMRT
  • M is molar concentration
  • R is gas constant
  • T is temperature
  • i is van't Hoff factor which corresponds to the number of particles into which a compound dissociates

• autoionization constant for water:
  • K_w = [H₃O⁺][OH^-] = 1 × 10^-14
  • K_w = K_a×K_b
• K_a = acid dissociation constant
  • K_a = [H3O⁺][A-]/[HA]
  • small K_a(<1) = weak acid
  • large K_a = strong acid
• K_b = base dissociation constant
  • K_b = [OH^-][B⁺]/[BOH]
  • small K_b(<1) = weak base
  • large K_b = strong base

• according to Bronsted-Lowry definition, every acid must have a conjugate base and every base must have conjugate acid
• inert conjugates
  • conjugate base formed from strong acid always very weak or reaction wouldn't be driven forward
  • conjugate acid formed from strong base always very weak for same reason
• weak acids and bases form conjugates that are also weak, but are stronger than conjugates made from weak acids and bases

• electronegative elements positioned near acidic proton increases acid strength through inductive effect
  • pulls electron density out of bond holding acidic proton
  • weakens proton bonding and facilitates dissociation
  • the nearer the electronegative atom is to the acidic proton, the lower the pK_a(higher acidity)

[image]

• strong acid - strong base titrations will always have equivalence at pH 7 as complete dissociation occurs and no salts are formed
  • endpoint - point at which indicator changes color (should ideally be within 3-4 pH of equivalence point)

[image]

• weak acid-strong base titration vs. strong acid-weak base (pretty much opposites)
  • weak acid/strong base (left image) - production of weak conjugate base and even weaker conjugate acid leading to production of higher concentration of hydroxide ions
    • common ion effect on autoionization of water
    • basic equivalence point pH
  • strong acid/weak base(right image) - production of weak conjugate acid and even weaker conjugate base leads to production of higher concentration of hydrogen ions
    • acidic equivalence point pH

[image]     [image]

• half-equivalence point occurs in polyvalent acids and bases due to ability to gain/lose multiple H⁺ ions
  • center of buffer region is half-equivalence point where half of given species has been protonated/deprotonated

[image]

• consists of mixture of weak acid or weak base and its respective salt
  • create systems in which changes in pH due to small amounts of acid or base are resisted
• pH of buffer can be determined w/ Henderson-Hasselbalch Equation
  • pH = pK_a + log([A^-]/[HA])
  • changes in concentration of acid and respective salt cause change in pH
  • changes in concentration so as to maintain ratio of acid to salt do not cause pH change, but do increase buffering capacity (± 1 pH unit of pK_a)

• specific type of redox reaction in which an element undergoes both oxidation and reduction in producing its products
• many biological enzymes utilize disproportionation mechanism
  • catalase enzyme of peroxisomes catalyze peroxide reactions
    • 2H₂O₂ → 2H₂O + O₂
    • hydrogen peroxide is undergoing both oxidation and reduction
  • superoxide dismutase is another enzyme that uses this mechanism to turn ROS into peroxide and oxygen