A CHEM EXAM 3

central limit theorem

many indet errors tend toward Gaussian dist,

±1σ

68.26%

±2σ

95.44%

±3σ

99.72%

μ

mean

z in context of confidence intervals

num of stdev from mean for population

confidence interval formula w pop, μ, σ

diff between pop and sample

pop: entire set of possible measurements

sample: subset of measurements

we switch from z to t in sample data bc:

we dont know σ of population, so s (stdev) and t distribution are used

conf int for samp mean

• Xˉ = sample mean

• t = t value from t-table at given confidence and DOF = n − 1

• s = sample standard deviation

• n = number of measurements

effect of inc conf level on CI width

CI gets wider bc higher conf level req a larger t value, making ±t·s/√n larger

inc sample size n effect on CI width

narrower CI bc s/√n dec as n inc

null hypothesis (H₀)

default assumption that diff btw values can be explained by indet error

alt hyp (H_a)

diff btw values too large to be due to indet error

type I error

incorrectly rejecting null hyp (false pos)

type II error

failing to reject null (false neg)

α relation to conf int

conf level = 1 - α

@ 95% conf, α = 0.05

null and alt hyp used in paired t test

• H₀: dbar = 0, no significant difference between methods

• Hₐ: dbar ≠ 0, significant difference between methods

f test

whether two variance (s²) are sig diff

H₀ and H_a in F test

H₀: s₁² = s₂² (var equal)

H₀: s₁² ≠ s₂² (var diff)

how to calc F_exp

larger var / smaller var

decision rule in F test

if F_exp > F (α, v_num, v_den) → reject H₀, var sig diff

else → fail to rej H₀

when to use unpaired t test

when comparing means of two indep samples, not paired measurements

H₀ and H_a for unpaired t test

H₀: μ_a = μ_b → means equal

H_a: μ_a ≠ μ_b → means diff beyond random error

conf interval expressions for each sample in unpaired t test

why is DOF more complicated in unpaired t tests

each sample has own n and s, unc in diff depends on both sets

allows pooling

when F-test shows no significant difference

partition cofficient K_D in liq-liq or chrom partitioning

K_D= [S]_{phase 2} / [S]_{phase 1}

large K_D

solute spends more time in stationary phase → stronger ret/movement into that phase

types of solute-stat phase int

adsorption on solid surf

part into liq phase

ion-exchange int

size-exclusion 

electrophoretic sep (charge/size)

C18 sorbent retains 

hphobic (np) spec from aq matrice

analytes that silica SPE retains

low to mod pol spec from org matrices

aminopropyl SPE sorbent

retains more pol cmpds

cyanopropyl/diol sorbent

retains aq and org matrices

sep in GC

based on part between mob gas phase and stat liq phase in column

GC detector types

thermal conductivity det

flame ionization det

electron capture det

chromatogram

plot of det response vs time showing peaks

reversed phase hplc

stat phase nonpol and mob phase pol, nonpol retained, pol elutes first

truly neutral species

elute at same time

P’

Φ = vol frac of each solvent

P’ = pol index of  each solvent

***overall mob phase polarity

det commonly paired w hplc

UV vis

diff btw isocratic and grad elution

isocratic: mobile phase stays constant throughout run

grad: mob phase varied to improve sep and speed

cal curves in GC/hplc

peak of area vs known conc

ms can be used w gc/hplc

mass based det shows structural formation and quant data

two main velocity comp in cap electro

• electrophor velocity (due to analyte charge)

• electroosmotic flow velocity (bulk motion of soln through capillary)

MEKC

micelles in buffer allow sep of neutral and charged species based on part into micelles plus electro behavior

chromatographic res

t = ret time

w = baseline peak widths

larger R = better sep

bigger selec fac

better, bc enhance specificity

alt form that uses FWHM

improve res

inc ret factor so analytes spend more time int w stat phase

inc selec so one solute retains more than another

inc column eff to narrow peaks

ret factor

t = ret time

t_m = column void time

larger k

analyte spends more time retained on column relative to mob phase → strongerint w stat phase and longer ret

selectivity factor

k₂ > k₁ measures how well two an are diff sep

larger selec fac

better bc big diff in ret times → improved sep

N and H in chromatography

N = number of theoretical plates

H = height eq (small H, more eff)

relationship btw N, L, H

relates n and peak shape

n_c

peak capacity - max number of solt peaks that can be baseline res during sep

mass spec

measures ions in gas phase based on m/z

3 steps of mass spec

1. ionization (sample → gas phase ions

2. mass analysis - sep ions by m/z

3. det - measure ion abundance to prod spectrum

high vacuum used in MS bc

• prevents ion gas collisions

• prevent unwanted rxns

• allow stable trajectories

• red contamination

• maintain det sens

hard ionization (EI)

gives fragment ions, not intact mol

pros of EI

high sens, cheap, easily ID

cons of EI

fragmentation, req gaseous samples, low ionization eff

chemical ionization (CI)

soft - prod intact charged analytes

pros of CI

intact ions, good for identifying MM

cons of CI

multiple ions form, req gaseous sample

electrospray ioniz. (ESI)

for large, nonvolatile, bio mol

why does ESI prod complex spectra

multiple charge states and noncov adducts/complexes

pros of ESI

soft ioniz, works @ atm. press, great for biomol, couples well w/ LC-MS

cons of ESI

spray instability, complex spectra

matrix assisted laser desorption/ionization (MALDI) reqs what

analyte must be mixed w/ light abs matrix that assists desorption/ioniz

pros of MALDI

soft ioniz, large biomol, solids + liqs, imaging MS

cons of MALDI

low reproducibility, low ioniz eff, sample destroyed during process

MALDI pairs w/

TOF

Time of flight (TOF)

based on time req to travel fixed distance - lighter ions reach det faster

pros of lin TOF

unlimited range, high sens, fast analysis

cons of lin TOF

lower res, mass acc dec at high m/z,

reflectron TOF improves

res and mass accuracy by correcting KE diff, res up to 20,000

quadrupole

selects ions using varying electric fields, allow specific m/z to pass

pros of quadrupoles

cheap, small, good for targeted exp, fragmentation

cons of quadrupoles

low res, lim mass range, needs cleaning over time

adv of ion traps

detect all m/z in single scan, can perform seq frag

lim of ion traps

space charge effects (too many ions = distortion)

fourier transform ion cyclotron resonance (FTICR)

extremely high res, mass acc, high sens

downsides of FTICR

expensive, req cryogenic sys, slow analysis

orbitrap

ions orbit central electrode; freq of oscillation → m/z via fourier transform

strengths of orbitrap

very high res, mass acc, high sens

weaknesses of orbitrap

slower than TOF

why high vacuum for MS

prevent ion collisions, prevent chemical rxns, maintain stab traj, avoid contamination

diff pump

cheap, req exp oil

turbomol pump

no oil, long lifetime, very exp

rough/rot vane pump

cheap, but uses oil, scroll pumps to avoid oil but cost more