Quant Test One
Mean |
qty obtained by dividing sum of measurement by the # of measurements [Exi/n] |
Median |
Ressult around which other resutlrs are equally distributed. Usually immune to outliers, depends on # of datapoints. |
Precision |
Describes agreement between replicate measurements carries out in same fashion. |
Standard deviation |
Sqrt[E(xi-xbar)^2/(n-1)] n-1= degrees of freedom. |
Variance |
s^2, they are additive |
Relative std. deviation |
RSD= s/xbar*10^p (p=2 -> percent; p=3 -> ppt) etc. |
Spread/Range |
Difference in max/min values w=xmax-xmin |
Avg. Deviation from Mean |
E|xi-xbar|/n |
Accuracy: |
Denotes the closemess of a measure |
Absolute Error: |
Compare to true value E=xi-xt(true) |
Relative Error: |
xi-xt/xt*100% |
Determinant(Systematic)Errors: |
Unidrectional, causing mean to differ from true value Effect:inaccuracy |
Method Errors- |
nonideal chemical/physical behavior of analytical sys. (slowness, incompleteness of rxn) non specificity |
indicator error |
endpoint vs. equivalence pt |
Personal Errors: |
Caused by carelessmess, inattention or physical limitations -less sensitive to color change |
Constant error |
more serious as sample size decreases |
proportional error |
scales with measurements dependent on sample size |
How do you treat instrumental errors? |
calibration |
How do you prevent personal errors? |
care/self discipline |
How do you treat method errors: |
detect and adjust with standards |
Independent Analysis(treat method errors) |
send away to test or use different method to give same result |
Blank determination |
run sample with no analyte present |
variation in sample size |
constant error combatant |
Gross Errors |
Effect-Inaccuracy Sources- personal, arising from carelessness or laziness or ineptitude. |
Examples of gross errors |
arithmetic mistakes, incorrectly recording data, spilling solution, act of god. |
Indeterminate Errors-(Random errors) |
Effect-Imprecision occure when system of measurment is extended to maximum sensitivity additive process of individually insignificant events occuring simultaneously |
sample: |
handfull of replicate experiments, scientists carry out tiny fraction of infinite number of possible exp. |
population |
infinite number of possible exps |
population mean |
true mean of entire pop. i.e. N->infinity |
Population Std. Deviation |
(sigma) Sqrt[E(xi-u)^2/N] |
z |
(x-u)/sigma |
+-sigma |
68.3% of area under curve |
+-2Sigma |
95.4% under curve |
+-3Sigma |
99.7% under curve |
Spooled: |
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 |
Confidence Limits |
interval surrounding mean value, expected to contain true value, u, with a given probability. |
if s is a good approx for sigma-> mu= |
x+-zsigma |
for data set mu= |
xbar +-zsigma/Sqrt[N] |
When you don’t know sigma and only have s |
employ students t test additional constraint of degrees of freedom |
t= |
(x-mu)/s |
confidence interval for t test: |
mu=xbar+=ts/Sqrt[N] |
Q test |
Qexp=|xq-xn|/w xq is outlier, compare to Qcrit: If Qexp>Qcrit, you may throw this point out |
When considering rejection |
was a gross error involved? Repeat analysis Report median as we (or instead) as mean |
Standar deviation for addition, subtraction |
S=Sqrt[Sa^2+Sb^2+…..] |
Std. deviation for multiplication and division: |
Sy/Y=Sqrt[(Sa/a)^2+(Sb/b)^2+….] |
Stoichiometry: |
Weight relationship |
Empirical Formula |
Expresses simplest whole number ratio |
Chemical Formula |
Specific # of atoms in a molecule |
formula weight, or formula mass |
mass in grams of one mole of substance sum of atomic weights of all atoms referred to as gfw,MW,gmw,g/mol |
millimole |
10^-3 mol |
Gravimetric factor |
GF= a/b(mol ratio)*Mm of substance sought/mM of substance measured. |
Ideal Precipitate |
Larfe, coarse particles low solubility thermal stability @drying temp known composition |
size of colloidal suspension: |
1-1000 nm in diameter |
crystalline suspension size: |
1/10 mm or more |
colloid properties: |
no rendency to settle, brownian motion trumps gravitational force. not retained on traditional filtering media |
Crystal properties |
easily settle and are filterable |
relative supersaturation: |
RS=(Q-S)/S Q: instantaneous/localized concentration of solute S: Solubility |
Relationship of R.S to particle size |
S is large-> colloids S is small-> solubility |
nucleation |
formation of initial particles of solid(4-5 ions, molecules, or atoms) many small particles |
Particle Growth: |
further growth on existing particles (“nuclei”) few large particles |
Nucleation yeilds: |
colloids 🙁 this is bad exponential RS growth |
Particle growth yeilds: |
Crystals 🙂 this is good linear RS |
How can you minimize RD: |
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) |
Homogeneous ppt |
“in Situ” formation (in medium) of ppting reagent by slow chemical process. |
Colloidal precipitates: |
1-100nm |
What makes a colloid stable? |
due to ion adsorption(surface effect)of particle (i.e. surface bonding of ions) |
Degree of Adsorption is proportional to: |
concentration of more prevalent ion. |
peptization |
occurs when washing colloidal ppt with pure water disperses electrolyte layer, repulsice forces take over, forcing particles apart. |
How can yo improve the particle size of Crystalline ppts? |
minimize Q i)use dilute solutions |
Why does digestion yeild purer, more easily filtered crystals? |
it is due to solution and recrystallization increses @ higher Temps. recrystallization seems to involve bridging between adjacent particles |
Coprecipitation |
otherwise soluble compounds are removed from solution during precipitation |
When does surface adsoprtion become significant? |
when ppts have large specific surface area (sa/unit mass) this is more of a problem with colloids |
How can you minimize surface adsorption? |
digestion washing with colatile electrolyte |
Mixed Crystal formation: |
different element replaces one of ions in crystal lattice (two ions must have same charge and same size +-5%) |
How can you minimize mixed crystal formation? |
separation of interferent before final pptation choosing different ppt reagint that doesn’t contain co-ppt |
occlusion |
occurs with rapid crystal growth, not sufficient time for displacement of counterions, so become trapped |
how do you minimize occlusion and mechanical entrapment? |
slow the crystal growth |
mechanical entrapment “occlusion on steroids” |
several crystals grow together, trapping pocket of solution |
What kind of error results from a coppt that is not a compound of analyte ion |
positive error |
What kind of error results if coppt does form compount of analyte ion? |
sign of error depends on relative mass of impurity. |
Why do you heat a sample? |
to remove solvent and volatile species |
Ignition |
conversion of ppt to a different chemical form (weighing form) |
basis |
besed on measurement of quantity of reagent necessary to react completely with the analyte |
titer |
mass of species that reacts with exactly 1ml of solution |
weight by weight ratio |
massA/massSample *10^p if p is 2 % |
p function |
-log[] |
solution-diiluent ratio |
volume of conc. reagent diluting volume of solvent |
process of titrametric analysis: |
start with standard solution-reagent solution of known conc. upon which methd isbased. |
properties of “standard titrant” |
stable reacts rapidly reacts completely selective |
properties of a primary standard |
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 |
properties of a secondary standard |
impure compound ofknown Assay |