Analytical Chemistry

Problem definition (formulate the question)

determine an appropriate question that can be addressed by chemical analysis and setting appropriate specifications (agreed on features of an acceptable answer, including tolerances).

Selection of analytical method

selection of a suitable wet chemical or instrumental \n technique that could be applied to an obtainable sample to meet the specifications, given the analytical requirements (what the analysis must do).

Sampling and sample handling

\n involving the execution of a sampling plan to obtain an \n uncontaminated representative sample of appropriate size for analysis followed by good sample handling practices and the preparation of the sample for analysis (ample preparation)

Method Validation

making sure the method returns results that meet the specifications and otherwise can be trusted.

Data collection and interpretation

carrying out the validated method to obtain data (signal) \n which you convert into results (composition) which you interpret in a way that addresses the problem.

Reporting

report your results, being sure to draw warranted conclusions), which includes communicating what you learned accurately and fairly, without going beyond the mandate of your data, and in a way that is clear to your target audience.

Destructive analyses/techniques

are chemical analyses which consume the sample so that it \n cannot be recovered unchanged. Examples from general chemistry are acid-base titrations and combustion analyses, both of which chemically transform the sample.

Nondestructive techniques

are chemical analyses that do not consume the sample. A simple example of a nondestructive analysis is NMR spectroscopy. An NMR sample can typically be recovered by evaporation of the NMR solvent (for solid or nonvolatile liquid samples) or distillation of the sample (for liquid samples)

Trace analyte

an analyte present in very small amounts in a sample

Sensitivity

how responsive a method is to the analyte – and consequently able to be used to detect and quantify small levels of analyte

Detection threshold (limit of detection)

the lowest analyte level that can be detected by an analytical method

Quantitation threshold (limit of quantitation)

the lowest analyte level that is large enough to be \n quantified, not just detected – i.e. where there is enough analyte present to measure it accurately enough to tell how much is there.

Dynamic range

the range of concentrations over which an analytical method can be used. Outside the dynamic range the method either can’t be used to quantify analyte, either because there is no enough analyte present of because there is so much that the method no longer responds to analyte

Interferent

a substance present in a sample that interferes with analysis of the analyte (for example, since proteins bind small molecules they often interfere with their analysis.

Selectivity

the ability of an analysis to distinguish an analyte in the presence of other substances.

Robustness

the ability of an analysis to work well with a wide range of samples, as opposed to analyses that only work well for particular sample conditions (pH, temperature, etc., although it can also refer to the susceptibility of an analysis to interferents).

Sampling plan

a plan for collecting a (typically representative) sample and which will enable you to meet the analytical requirements.

Random sampling

divide the sample up into equal parts using a 2D or \n 3D grid and take samples from different regions randomly. This method is best used with samples that are expected to be spatially homogenous.

Systematic sampling

sampling according to a fixed system or plan.

Judgmental sampling (which may also be systematic or random)

Sampling according to a plan that is informed by the nature of the sample.

Stratified sampling

a form of judgmental sampling in which samples are divided into populations, each of which is sampled separately.

Grab sampling

taking a sample from the lot for analysis; this is by far the most common type, so much so that when you hear the word sampling without qualification you may assume it is grab sampling

In-situ sampling (in-situ monitoring)

using a sensor to monitor a sample without actually taking any.

formula of sampling

σanalysis2 = σsample2 + σmethod2 \n

σsampling

the standard deviation associated with sampling, a measure of the size of the \n random error associated with sampling

n (sampling)

the number of particles sampled

f analyte

the fraction of analyte particles in the sample

f other

the faction of other types of particles = 1 - f analyte

Relative sampling error (RSE)

\

K (sub) s

sampling constant = (sample mass)(%RSE)^2

Sample handling

how a sample is treated, including during its collection and analysis.

Sample contamination

the contamination of samples with impurities \n o During collection (by the containers and reagents used) \n o Improper storage (by containers, moisture, the atmosphere) \n o Due to degradation

Sample degradation

the degradation of samples, over time and/or due to exposure to \n excessive heat, moisture, air or other factors. Degradation can reduce the amount of \n analyte present or producing interferents.

Sample storage

the storage of samples under conditions of time, temperature, moisture, \n etc. to ensure they do not degrade or become contaminated

Lot

this term is sometimes used to describe the \n material to be sampled.

Bulk sample

the combination of all the samples \n that (ideally) adequately represent the material

Homogenized

rendered more uniform at a \n smaller size scale level, often by grinding or \n dissolution.

Lab sample

the homogenized sample from \n which all the samples tested are taken

Aliquot

a portion of the bulk or lab sample \n taken for analysis. The analyses of these samples \n are called replicates.

Sample pretreatment

things done to a sample to render it susceptible to analysis by an \n analytical method.

Preconcentration

increasing the concentration of \n an analyte to make it easier to \n detect or quantify

Extraction

Separating the analyte from \n potential interferents by \n partitioning it into a separate \n phase, commonly using liquid- \n liquid or solid phase extraction.

Derivatization

chemically reacting the analyte \n to make a new compound that is \n easier to analyze.

Standard operating procedures

a set of written and validated procedures that analysts can \n follow to carry out that method reliably.

Signal

the output of an analytical method, although the term signal is typically only used for \n instrument signals. Nevertheless, the signal is whatever the analytical method returns as an output \n – electrical current, voltage, mass, volume, etc.

Standards (sometimes called reference materials or, less commonly, controls)

a set of materials containing the analyte that can be used to determine how a method responds to analyte \n and/or demonstrate that it works.

Calibration

the process of testing a method to determine how the signal-generated depends on \n the property you want to measure (such the analyte’s concentration or mass)

Calibration curve (signal-response curve, calibration relationship

the relationship between \n analytical signal and analyte levels that is determined using standards. When the relationship is \n linear it is defined by a trendline. \n

Validated

validation is the process of showing that a method meets the analytical requirements – \n i.e. works. This is done by testing the method to demonstrate that it can be used reliably for its \n intended purpose.

Blanks

samples prepared like normal samples and standards but lacking the analyte. The signal \n they produce is called a blank signal and should be subtracted from the observed signals to \n give a corrected signal. The corrected signal is used in the analysis.

Replicates

measurements carried out on the same or different aliquots in order to determine the reliability (precision) of an analysis.

Quality assurance

procedures used to help assure that a method is reliably meeting the analytical requirements. It can involve things like

Direct \n calibration

Determine the calibration (signal-response) curve \n and then using it to determine the amount of analyte \n present in the sample.

Internal \n Standards

An internal standard that behaves chemically similar \n or identical to the analyte is added and the analytical \n method. The amount of analyte is determined from \n the relative size of its signal relative to that of the \n known-concentration standard.

Standard \n Addition

Standards are added to the sample and the signal is \n measured as the amount of standard increases. The \n resulting relationship (usually linear) is extrapolated \n backwards to see how much analyte must be \n “removed” from the original sample to give zero \n signal.

Matrix effects

occur when \n the sample matrix in which the \n analyte is \n embedded \n affects the \n signal- \n response \n curve

detection sample

3s(sample)/m

quantitation limit

10s(sample)/m

accuracy

how close a measurement is to the true or accepted value

precision

how close measurements of the same item are to each other

TC

to contain

TD

to deliver

Volumetric or transfer pipette

can only deliver one fixed \n volume. It has one fixed mark and will deliver the specified \n volume when filled to the mark and emptied.

Graduated or Mohr pipette

can deliver variable volumes by \n filling the pipette to one mark and emptying it to another.

Significant figures

digits that are known and thus can be specified with confidence.

Real rule

quantities should be written out to the same number of decimal places as the \n magnitude of the uncertainty

For addition and subtraction (sig fig rule)

the result has the same number of decimal places as the \n quantity with the fewest.

For Multiplication & division (sig fig rule)

the result has the same # as the factor with the fewest

For logarithms and powers of ten (sig fig rule)

For logarithms, the significant \n figures are in the mantissa while the characteristic just specifies the \n power of 10.

Corollary (sig fig rule)

The number of significant figures in an antilogarithm is \n the same number as the number of digits in the logarithm’s \n mantissa.

Propagation of error

the process of calculating the error in a calculated quantity from the \n error in the numbers used

Absolute error/absolute uncertainty, e

the absolute value of the uncertainty.

Relative error/relative uncertainty

the calculated uncertainty divided by the \n value of the quantity

propagation of error in addition or subtraction

e=\[e(1)^2+e(2)^2+e(3)^2+...\]^(1/2)

propagation of error in multiplication or division

%e=\[%e(1)^2+%e(2)^2+%e(3)^2+...\]^(1/2)

Sample mean or estimated mean

𝑥̅ , the mean calculated from a finite number of data points

Mean, population mean, or true mean

μ, the mean that would be obtained from the entire \n population or lot under study – or an infinite number of data points were used.

Estimated standard deviation (esd) or sample standard deviation

sx, the standard \n deviation calculated from a finite number of data points.

Standard deviation or population standard deviation

σ, the standard deviation that would \n be obtained if an infinite number of data points were used.

Confidence interval

a range of values in which we expect the true mean will fall to a specified \n degree of confidence (percentage chance)

Student’s t

the number of standard deviations about the mean of \n that encompasses a given percentage of the Student’s t distribution.

Level of confidence (% level of confidence)

the confidence one wants to have that the \n mean actually falls within Student’s t estimated standard deviations of the sample mean.

Alpha-value, α-value

the chance one is willing to accept that the mean falls outside \n Student’s t standard deviations of the sample mean.

Confidence \n intervals

Hypothesis: Does your data agree with a known value?

How: Calculate the confidence interval for the desired degree of confidence and see if the known value falls within it. If so, you the data is consistent with the known mean.

requires: A data set and a known value.

t-test for comparison of means

Hypothesis: Do two data sets (methods, etc.) give the same \\n mean?

How: Calculate a t-value (called tcalc or tstat) using the t-test for comparison of means equations and compare it to the appropriate value of Student’s t (one-tailed or two-tailed). If tcalc > tcrit for the calculated DoF the difference is significant

requires: Any two data sets

paired t-test

hypothesis: Do different methods give the same results for the same set of samples?

How: Calculate a critical t-value (tcalc a.k.a. or tstat) using the paired t-test equations and compare it to the appropriate value of Student’s t (one-tailed or two-tailed). \n If tcalc > tcrit for n - 1 DoF the difference is significant

Requires: Paired data (data from the two methods on the exact same set of samples).

F tests

compare two methods’ precisions to see whether they are significantly different at the \n indicated confidence level

Q-test and G-test

may be used to discard one and only one outlier from a set of data

Instrumental analysis

the use of optical, mechanical, electrical, and other signal-generating tools \n to learn information about an analyte. Instrumental methods are distinguished from classical wet \n chemical methods like gravimetric analysis (weighing) and volumetric analysis (titrations)

instrumental analysis examples

UV-vis \n spectroscopy/spectrophotometry \n IR spectroscopy \n NMR spectroscopy \n Mass spectrometry \n Gas chromatography

Mass spectrometry

use electric (and sometimes magnetic) fields to measure the masses \n of ions. Examples are classified by \n o ion source (electron impact, chemical ionization, electrospray, etc.) \n o type of mass analyzer (i.e. ion separator, electrostatic sector, magnetic sector, \n quadrupole, time of flight, ion trap)

Analytical separations

separate mixtures and analyze the individual mixture components \n using spectroscopic, mass spectrometric, and other methods. Examples include gas and \n liquid chromatography, electrophoresis, and field flow fractionation.

Electrochemical methods (later in the course)

use an electric current and/or potential. \n Examples include potentiometry, coulometry, electrogravimetric analysis, \n amperometry, and voltammetry.

Scattering-based methods

use the scattering of light. Examples include turbidemetry \n (quantifying an analyte by measuring light attenuation by scattering), nephelometry \n (quantifying analyte by the intensity of the light it scatters), and particle size analysis methods \n based on X-ray and visible light scattering

Microscopy

spatially-image materials using light absorption, scattering, or emission \n (conventional light and fluorescence microscopy), tendency towards ionization (electron \n microscopy), surface conductivity (STM), or surface roughness (AFM)

Hyphenated methods

employ more than one type of method; the most common involve \n analytical separations (GC or LC) and mass spectrometry (MS), Gas chromatography- \n mass spectrometry (GC-MS) and liquid chromatography-mass spectrometry (LC-MS).

transmission

proton passes through

reflection

the photon appears to reflect or bounce off, for example, due to electron excitation at a metal surface (for mirrors) or the laws of optics (all surfaces)

Absorption

the photon is taken up or absorbed by atoms/molecules in the substances

absorption followed by emission (luminescence)

the photon is absorbed, causing another proton to be emitted at a lower energy