CH3H1 Analytical Science for Global Challenges

what is precision and how is it described

gives you an idea of how reproducible a measurement is but it is limited by the random error

described using standard deviation

what is accuracy and how is it described

.gives an idea of how close to the true value a measurement is but is limited by the systematic error

described using the absolute or relative error

what is the mean and pros/cons

• sum of values divided by the number of values

• unbiased estimate of the mean value

• can be skewed by significant outliers

what is the median and pros/cons

• middle value of a data set

• less biased by outliers

what is the mode and pros/cons

• most common value

• applicable to discrete finite measurement values

• can be misleading

why is it good to take a large number of measurements in an experiment

larger the number, the closer the properties of the measurements will be to the true values

draw a positively skewed distribution

how much is within ± 2σ of the mean

~ 95%

what can cause errors in correlation

selection effects - if the experiment or observation is less sensitive to some combinations of parameters than others

• e.g. if an instrument cannot detect anything beyond a certain point

a few outliers

a third variable

• e.g. worldwide non-commercial space launches correlates to sociology doctorates awarded but they are actually linked by the economy

what are residuals

the differences between the y values and those predicted by the model

what does the coefficient of determination measure

how much of the variance in the measurements is explained by the fit to the data

why should you not use too many orders in a curve to fit data

you always get a better fit but overfitting the data means you also fit to random fluctuations in the measurements

what is the limit of detection

lowest value you can detect over noise

what is limit of quantification

lowest value you can quantify with certainty

what is limit of linearity

the value where the graph stops being linear

what happens when molecules in a sample interact with the stationary phase

the molecules rate of movement slows down

why do you get different distribution coefficients/different net rates of migration

each molecule interacts differently with mobile phase and stationary phase

what are the 4 types of chromatography

adsorption chromatography

ion-exchange chromatography

partition chromatography

size-exclusion chromatography

what type of molecule uses adsorption chromatography

polar groups

things dissolved in organic solvents

what type of molecule uses partition chromatography

things in polar solvents

what type of molecule uses size-exclusion chromatography

molecules with large size differences

fill in table

what does it mean if stationary phase support is planar in chromatography

when the stationary phase is supported on a flat plate or in pores of paper. mobile phase moves through Stationary phase by capillary action, gravity or electrostatic forces

what does it mean if stationary phase support is a column in chromatography

stationary phase held in a tube and mobile phase pushed through using gravity or pressure

what is normal phase in chromatography

• classic form of liquid chromatography using polar stationary phases and non-polar mobile phases

• the analyte is retained by the interaction of its polar functional groups with the polar groups on the surface of the stationary phase

what is reversed phase in chromatography

• the stationary phase is non-polar and the mobile phase is polar

• the analyses are attracted to the surface by their non-polar functional groups

what order do analytes elute from normal phase chromatography

starts with the least polar compound followed by other compounds in order of their increasing polarity

in what order do these compounds elute from a normal phase chromotogram:

• alcohol

• carboxylic acid

• ketone

• ketone

• alcohol

• carboxylic acid

what order do analytes elute from reversed phase chromatography

most polar analyte elutes first followed by other analytes in order of decreasing polarity

why is reversed phase chromatography common

its compatible with aqueous solutions

describe HPLC machine

sample is introduced into the mobile phase under high pressure

stationary phase is packed in a stainless steel column

injection port prevents system from depressurising

column is kept in an oven to keep temperature constant

detector can be UV / IR / refractive index

what are the 2 types of mobile phase possible for HPLC

isocratic elution: single or mixture of solvents remains constant

gradient: 2 or more solvents, ratios vary during analysis

what is isocratic elution

single or mixture of solvents remains constant

what does it mean when a mobile phase is gradient

2 or more solvents, ratios vary during analysis

what are HPLC modes of separation

most common is reverse phase (partition)

• can also be adsorption, ion exchange, affinity

why would you use gradient elution as a mobile phase

allows mixtures with a wide range of hydrophobicity/polarity to be separated in one analysis

can reduce run time and resolution

how is a gaseous analyte transported in gas chromatography

through a capillary column by a gaseous mobile phase, called the carrier gas

when do you use gas chromatography

to separate volatiles

• gases

• small organic molecules (bp usually < 300°C)

• trace analysis

• analysis of very complex mixtures

draw a typical gas chromatography instrument

what is the stationary phase in gas-liquid partition chromatography

a non-volatile liquid coated on the inside of the column or on a fine solid support

what is the theoretical plate model

it supposes that the chromatographic column contains a large number of separate layers, called theoretical plates

separate equilibrations of the sample between the stationary and mobile phase occur in these “plates”

the analyte moves down the column by transfer of equilibrated mobile phase from one plate to the next

what are the assumptions in the theoretical plate model

• chromatographic column is treated as a static system in equilibrium

• each species is in equilibrium between stationary and mobile phase

• column is of fixed length

• flow is held constant

what does the plate model describe

the mechanism of retention and gives an equation allowing calculation of the retention times of a solute and the column efficiency

what does the plate theory ignore

diffusion

how do you get better separation on the column with the plate model

more plates to give more equilibrium steps

what are the 2 ways the theoretical plate model serve as a way of measuring column efficiency

• stating the number of theoretical plates in a column (N)

  • the more plates the better

• stating the plate height H

  • the height equivalent to a theoretical plate

  • the smaller the better

what are the 2 things in the theoretical plate model that would make columns more efficient

more plates

smaller height of plates

what is the equation HETP = L/N for?

HETP = height equivalent to a theoretical plate

L = length of column

N = number of theoretical plates in a column

what is this equation for: N = (5.54t_R²) / w_1/2² = 16t_R² / w_b²

w_1/2 = peak width at half height

N = number of theoretical plates in a column

t_R = retention time of the analyte

w_b = peak width at base

how do different solutes in a mixture behave in column in theoretical plate model

as if they have different numbers of plates

which of these columns has high N and which has high H

top one has high N (number of theoretical plates) and low H (plate height)

bottom one has low N and high H

definition of plate height (theoretical plate model)

length of column required for each MP/SP equilibrium to be established

what is retention volume, V_R (in theoretical plate model)

volume of mobile phase required to elute a solute

what is retention time, t_R (in theoretical plate model)

time required to elute a solute

what is t₀ (in theoretical plate model)

time for solvent or non-retained solute to elute

what is k (in theoretical plate model)

capacity factor (partition ratio or retention factor)

draw a basic chromatography spectrum and label t_R, t₀ and t’_R

what is this equation used for: u = L / t₀

u = mobile phase velocity (cm s^-1)

L = column length (cm)

t₀ = time for solvent or non-retained solute to elute (s)

what is this equation used for: k_A = (t_R(A) - t₀) / t₀

calculating the capacity factor

what is the ideal value of k, capacity factor (theoretical plate model)

ideal is between 1 and 5

large number means there’s a long run time

what is k (capacity factor in theoretical plate model) independent of

column dimension and mobile-phase velocity

what is the distribution constant, K_C (theoretical plate model)

the ratio of solute concentrations in stationary and mobile phase

what does this equation do

allow you to calculate the distribution constant

what does the separation factor, ⍺, describe (theoretical plate model)

the selectivity of the chromatographic system for a particular pair of bands

the ability of a certain set of experimental conditions to discriminate between 2 components

how do you calculate the separation factor (theoretical plate model)

⍺ = k_B / k_A

what is the best way to compare how well a compound is retained on 2 different columns and why

capacity factor as it is independent of column size

what is resolution (chromatography)

the degree of separation of 2 adjacent bands

what does this equation tell you

allows you to calculate resolution based on retention times (tR) and either base width or half height width

what is a good R_s value (chromatography)

R of 1.5 gives > 99% separation

what do high values of R_s compensate for (chromatography)

• increased band broadening

• column ageing

• small variations in conditions

how do you have to change the column length if you want to double the resolution

quadruple the column length

what is this equation for

calculating resolution

• N = average column plate number for the 2 bands of interest

• k = average capacity factor

• ⍺ = separation factor of 2 peaks

what are k, ⍺ and N controlled by

k, ⍺ = changing the column packing and by varying the composition of the mobile phase solvent

N = changing the mobile phase flow rate, packing particle size and column dimensions

what are the 5 limits of the plate model

1. assumption that equilibrium is instantaneous

2. flow rate is not accounted for

3. plates don’t reflect the efficiency accurately

4. no other physical processes accounted for other than adsorption

5. plates are imaginary

what are the different peak dispersion processes proposed (as a development of plate theory)

• eddy diffusion

• longitudinal diffusion

• resistance to mass transfer in the mobile phase

• resistance to mass transfer in the stationary phase

what does this equation do

the van Deemter equation - predicts a minimum plate height at an optimum velocity and maximum efficiency

A = random movement through stationary phase (eddy diffusion)

B = diffusion in mobile phase (longitudinal diffusion)

C = interaction with stationary phase

H = plate height

u = average linear velocity

draw a typical Van Deemter plot

what does a Van Deemter plot do

its a plot of plate height vs average linear velocity of mobile phase

such plots are of considerable use in determining the optimum mobile phase flow rate

describe Eddy diffusion

mobile phase moves through the column which is packed with stationary phase. solute molecules will take different paths through the stationary phase at random. this causes broadening of the solute band because different paths are of different lengths

how do you control eddy diffusion

control size/shape of particles in column to control uniformity of stationary phase

does eddy diffusion change with flow rate

no

what impact does eddy diffusion have on peaks

broadens them as different paths are of different lengths

what is longitudinal diffusion

the natural movement of molecules from high concentration to low concentration areas along a column

how does longitudinal diffusion impact band broadening

band broadening decreases when flow rate increases due to less time on the column

when does longitudinal diffusion dominate the Van Deemter model

at low u

is longitudinal diffusion more important in GC or LC

GC as D_M(gas) > 10⁴ D_M(liquid)

what does the diffusion coefficient measure

the ratio at which a substance moves randomly from a region of high concentration to a region of lower concentration

what does this equation do

allows you to calculate term B in Van Deemter model (longitudinal diffusion)

how do you avoid mass transfer in the Van Deemter model

decease flow rate

what does this equation do: C_s = [(d_f)²] / D_s

calculates stationary phase mass transfer (C_s)

• d_f = stationary phase film thickness

• D_s = diffusion coefficient of analyte in SP

what does this equation do: C_M = [(d_p)²] / D_M

calculates mobile phase mass transfer (C_M)

• d_p = particle diameter

• D_M = diffusion in MP

what is mass transfer (Van Deemter model). draw a diagram

the analyte takes a certain amount of time to equilibrate between the stationary and mobile phase

if the velocity of the mobile phase is high, and the analyte has a strong affinity for the stationary phase then the analyte in the mobile phase will move ahead of the analyte in the stationary phase. this broadens the band of analyte

what makes band broadening as a result of mass transfer worse

higher velocity of the mobile phase

how do you optimise separation of a critical pair without increasing the run time of chromatography

• decrease particle size in column

• introduce solvent gradient

what is the rate theory of chromatography

the more realistic description of the processes at work inside a column

takes into account of the time taken for the solute to equilibrate between the stationary and mobile phase

what affects the band shape of a chromatographic peak in the rate theory of chromatography

rate of elution - it takes time for the solute to equilibrate between MP and SP

the different paths available to solute molecules as they travel between particles of the stationary phase

what are the steps to chromatographic method development

1. technique selection (HPLC, GC, IEX etc)

2. chromatographic system (SP, MP, pH, additives)

3. mobile phase composition/gradient

4. pH, temperature

5. draft method

6. validation

7. final method

what are the typical criteria of chromatographic method validation

• accuracy

• precision (repeatability, reproducibility)

• linearity (LoL)

• dynamic range

• sensitivity (LoD, LoQ)

• specificity

• robustness

what phase does the sample need to be in for mass spectrometry

gas-phase ions

what does mass spectrometry measure

mass to charge ratio (m/z)