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
Sources: instrumental imperfections/instability in power supplies)

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
-bias in interpolating data

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,
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
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
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

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
reprecipitation

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=3 ppt
p=6 ppm etc

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
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