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qty obtained by dividing sum of measurement by the # of measurements [Exi/n] |
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Ressult around which other resutlrs are equally distributed. Usually immune to outliers, depends on # of datapoints. |
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Describes agreement between replicate measurements carries out in same fashion. |
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Sqrt[E(xi-xbar)^2/(n-1)] n-1= degrees of freedom. |
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RSD= s/xbar*10^p (p=2 -> percent; p=3 -> ppt) etc. |
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Difference in max/min values w=xmax-xmin |
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Denotes the closemess of a measure |
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Compare to true value E=xi-xt(true) |
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Determinant(Systematic)Errors: |
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Unidrectional, causing mean to differ from true value
Effect:inaccuracy Sources: instrumental imperfections/instability in power supplies) |
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nonideal chemical/physical behavior of analytical sys. (slowness, incompleteness of rxn) non specificity |
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endpoint vs. equivalence pt |
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Caused by carelessmess, inattention or physical limitations
-less sensitive to color change -bias in interpolating data |
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more serious as sample size decreases |
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scales with measurements dependent on sample size |
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How do you treat instrumental errors? |
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How do you prevent personal errors? |
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How do you treat method errors: |
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detect and adjust with standards |
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Independent Analysis(treat method errors) |
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send away to test or use different method to give same result |
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run sample with no analyte present |
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Effect-Inaccuracy Sources- personal, arising from carelessness or laziness or ineptitude. |
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arithmetic mistakes, incorrectly recording data, spilling solution, act of god. |
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Indeterminate Errors-(Random errors) |
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Effect-Imprecision occure when system of measurment is extended to maximum sensitivity
additive process of individually insignificant events occuring simultaneously |
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handfull of replicate experiments, scientists carry out
tiny fraction of infinite number of possible exp. |
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infinite number of possible exps |
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true mean of entire pop. i.e. N->infinity |
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Population Std. Deviation |
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(sigma) Sqrt[E(xi-u)^2/N] |
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68.3% of area under curve |
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Sqrt[EE(xi-xbar)^2/N-nj] where N is the number of experiments and nj is the number of data sets xbar is mean for each data set |
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interval surrounding mean value, expected to contain true value, u, with a given probability. |
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if s is a good approx for sigma-> mu= |
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When you don't know sigma and only have s |
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employ students t test
additional constraint of degrees of freedom |
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confidence interval for t test: |
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Qexp=|xq-xn|/w
xq is outlier, xn is closest neighbor, w is spread including outlier
compare to Qcrit: If Qexp>Qcrit, you may throw this point out |
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When considering rejection |
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Definition
was a gross error involved? Repeat analysis Report median as we (or instead) as mean |
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Standar deviation for addition, subtraction |
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Std. deviation for multiplication and division: |
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Sy/Y=Sqrt[(Sa/a)^2+(Sb/b)^2+....] |
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Expresses simplest whole number ratio |
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Specific # of atoms in a molecule |
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formula weight, or formula mass |
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mass in grams of one mole of substance
sum of atomic weights of all atoms
referred to as gfw,MW,gmw,g/mol |
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GF= a/b(mol ratio)*Mm of substance sought/mM of substance measured. |
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Larfe, coarse particles
low solubility
thermal stability @drying temp
known composition |
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size of colloidal suspension: |
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crystalline suspension size: |
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no rendency to settle, brownian motion trumps gravitational force.
not retained on traditional filtering media |
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easily settle and are filterable |
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relative supersaturation: |
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RS=(Q-S)/S Q: instantaneous/localized concentration of solute S: Solubility |
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Relationship of R.S to particle size |
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Definition
S is large-> colloids
S is small-> solubility |
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Definition
formation of initial particles of solid(4-5 ions, molecules, or atoms) many small particles |
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further growth on existing particles ("nuclei") few large particles |
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colloids :( this is bad
exponential RS growth |
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Crystals :) this is good
linear RS |
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Increase temp(S goes up)(RS goes down) Dilute solutions(Q goes down, RS goes down) *don't want Q to be high
Slow addition(same reason, don't want spikes in Q)
Stirring (Constat Q down)
control pH (S up and RS down) |
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Definition
"in Situ" formation (in medium) of ppting reagent by slow chemical process. |
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What makes a colloid stable? |
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due to ion adsorption(surface effect)of particle (i.e. surface bonding of ions) |
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Degree of Adsorption is proportional to: |
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Definition
concentration of more prevalent ion. |
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occurs when washing colloidal ppt with pure water disperses electrolyte layer, repulsice forces take over, forcing particles apart. |
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How can yo improve the particle size of Crystalline ppts? |
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minimize Q
i)use dilute solutions ii)adjusting pH of ppt medium |
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Why does digestion yeild purer, more easily filtered crystals? |
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Definition
it is due to solution and recrystallization increses @ higher Temps.
recrystallization seems to involve bridging between adjacent particles |
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Definition
otherwise soluble compounds are removed from solution during precipitation |
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When does surface adsoprtion become significant? |
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Definition
when ppts have large specific surface area (sa/unit mass) this is more of a problem with colloids |
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How can you minimize surface adsorption? |
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Definition
digestion
washing with colatile electrolyte reprecipitation |
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Definition
different element replaces one of ions in crystal lattice (two ions must have same charge and same size +-5%) |
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How can you minimize mixed crystal formation? |
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Definition
separation of interferent before final pptation
choosing different ppt reagint that doesn't contain co-ppt |
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Definition
occurs with rapid crystal growth, not sufficient time for displacement of counterions, so become trapped |
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how do you minimize occlusion and mechanical entrapment? |
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Definition
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mechanical entrapment "occlusion on steroids" |
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Definition
several crystals grow together, trapping pocket of solution |
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What kind of error results from a coppt that is not a compound of analyte ion |
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Definition
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What kind of error results if coppt does form compount of analyte ion? |
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sign of error depends on relative mass of impurity. |
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Why do you heat a sample? |
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Definition
to remove solvent and volatile species |
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Term
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Definition
conversion of ppt to a different chemical form (weighing form) |
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besed on measurement of quantity of reagent necessary to react completely with the analyte |
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Definition
mass of species that reacts with exactly 1ml of solution |
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massA/massSample *10^p
if p is 2 % p=3 ppt p=6 ppm etc |
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volume of conc. reagent diluting volume of solvent |
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process of titrametric analysis: |
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start with standard solution-reagent solution of known conc. upon which methd isbased. |
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properties of "standard titrant" |
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stable reacts rapidly reacts completely selective |
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properties of a primary standard |
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Definition
high purity stable toward air absence of waters of hydration readily available at moderate cost expectation of reasonale solubility in titration medium reasonably large formula mass so relative error of wighing is minimized |
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properties of a secondary standard |
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Definition
impure compound ofknown Assay |
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