
qty obtained by dividing sum of measurement by the # of measurements [Exi/n] 


Ressult around which other resutlrs are equally distributed. Usually immune to outliers, depends on # of datapoints. 


Describes agreement between replicate measurements carries out in same fashion. 


Sqrt[E(xixbar)^2/(n1)] n1= degrees of freedom. 




RSD= s/xbar*10^p (p=2 > percent; p=3 > ppt) etc. 


Difference in max/min values w=xmaxxmin 




Denotes the closemess of a measure 


Compare to true value E=xixt(true) 



Determinant(Systematic)Errors: 

Unidrectional, causing mean to differ from true value
Effect:inaccuracy Sources: instrumental imperfections/instability in power supplies) 


nonideal chemical/physical behavior of analytical sys. (slowness, incompleteness of rxn) non specificity 


endpoint vs. equivalence pt 


Caused by carelessmess, inattention or physical limitations
less sensitive to color change bias in interpolating data 


more serious as sample size decreases 


scales with measurements dependent on sample size 

How do you treat instrumental errors? 


How do you prevent personal errors? 


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 


run sample with no analyte present 




EffectInaccuracy Sources personal, arising from carelessness or laziness or ineptitude. 


arithmetic mistakes, incorrectly recording data, spilling solution, act of god. 

Indeterminate Errors(Random errors) 

EffectImprecision occure when system of measurment is extended to maximum sensitivity
additive process of individually insignificant events occuring simultaneously 


handfull of replicate experiments, scientists carry out
tiny fraction of infinite number of possible exp. 


infinite number of possible exps 


true mean of entire pop. i.e. N>infinity 

Population Std. Deviation 

(sigma) Sqrt[E(xiu)^2/N] 




68.3% of area under curve 






Sqrt[EE(xixbar)^2/Nnj] where N is the number of experiments and nj is the number of data sets xbar is mean for each data set 


interval surrounding mean value, expected to contain true value, u, with a given probability. 

if s is a good approx for sigma> mu= 




When you don’t know sigma and only have s 

employ students t test
additional constraint of degrees of freedom 



confidence interval for t test: 



Qexp=xqxn/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 

When considering rejection 

was a gross error involved? Repeat analysis Report median as we (or instead) as mean 

Standar deviation for addition, subtraction 


Std. deviation for multiplication and division: 

Sy/Y=Sqrt[(Sa/a)^2+(Sb/b)^2+….] 




Expresses simplest whole number ratio 


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 




GF= a/b(mol ratio)*Mm of substance sought/mM of substance measured. 


Larfe, coarse particles
low solubility
thermal stability @drying temp
known composition 

size of colloidal suspension: 


crystalline suspension size: 



no rendency to settle, brownian motion trumps gravitational force.
not retained on traditional filtering media 


easily settle and are filterable 

relative supersaturation: 

RS=(QS)/S Q: instantaneous/localized concentration of solute S: Solubility 

Relationship of R.S to particle size 

S is large> colloids
S is small> solubility 


formation of initial particles of solid(45 ions, molecules, or atoms) many small particles 


further growth on existing particles (“nuclei”) few large particles 


colloids 🙁 this is bad
exponential RS growth 


Crystals 🙂 this is good
linear RS 


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)
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Stirring (Constat Q down)
control pH (S up and RS down) 


“in Situ” formation (in medium) of ppting reagent by slow chemical process. 



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. 


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 ii)adjusting pH of ppt medium 

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 


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 reprecipitation 


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 coppt 


occurs with rapid crystal growth, not sufficient time for displacement of counterions, so become trapped 

how do you minimize occlusion and mechanical entrapment? 


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 


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 


conversion of ppt to a different chemical form (weighing form) 


besed on measurement of quantity of reagent necessary to react completely with the analyte 


mass of species that reacts with exactly 1ml of solution 


massA/massSample *10^p
if p is 2 % p=3 ppt p=6 ppm etc 




volume of conc. reagent diluting volume of solvent 

process of titrametric analysis: 

start with standard solutionreagent 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 
