Analytical Chemistry:

Identification, characterization, and quantitative measurement of the chemical composition of a sample

Qualitative Analysis -

"what is in a sample?"

Quantitative Analysis -

"how much is in a sample?"

another name for target compound:

analyte

General Steps in a Quantitative Chemical Analysis:

1) Formulate a Question 2) Select an Analytical Procedure (to answer the question) 3) Sampling 4) Sample Preparation 5) Measurement Step (5a: classical or stoichiometric methods; 5b: physical-chemical methods) 6) Calibration and Standardization of Methods 7) Interpretation and Conclusions Based on Analysis

1) Formulate a Question:

Translate general questions about the material to be examined into a specific question that can be answered by chemical analysis (or measurements) What information is needed (amount, type, etc.)? What level of accuracy (precision) is required?

2) Select an Analytical Procedure (to answer the question):

obtain as much advance information about the sample as possible (size, composition, homogeneity, analyte, concentration, interferences).

3) Sampling:

Obtain a laboratory size sample which is representative of the bulk specimen

4) Sample Preparation:

Hit the literature! includes... drying dissolving sample pre-concentration isolation of analyte

Drying:

removal of excess water or solvent results often based on dry weight. Why? - reproducibility

Dissolving Sample:

H2O, acids, bases, organic solvents

Pre-concentration:

when the concentration of analyte is too small to detect.

Isolation of Analyte:

remove interfering substances by separation method: Distillation, precipitation, and chromatography.

When the isolation step is sufficiently selective, then a very ____________ method of measurement may be used.

non-selective

5A) Classical or Stoichiometric Methods

Based on chemical reactions with well defined stoichiometry

Gravimetric methods:

Analyte reacts quantitatively with excess reagent to produce an insoluble product that is weighed (slow, but high precision, 0.01%)

Volumetric Methods:

Analyte is reacted with a standard solution of reagent, changing color or other property of the solution (faster, precision ~0.1%)

What is more precise, gravimetric or volumetric? What is faster?

Gravimetric is more precise, volumetric is faster

5B) Physical-chemical methods:

Measurement of a physical property related to the concentration of analyte; include light absorption, refractive index, emission, density, conductivity, electrical potential... These methods are generally fast, selective, very sensitive but less precise than classical methods

6) Calibration and Standardization of Methods:

Accuracy of a result checked by analyzing a sample of known concentration (a "standard") Calibration of the instrument response with standards> Loss of sample during preparation checked by standard-addition method or pre-analyzed sample. Sampling erros are checked by replicate random samples

How is loss of sample during preparation checked?

by standard-addition method or pre-analyzed sample

How is sampling errors checked?

By replicate random samples

7) Interpretation and Conclusions Based on Analysis:

Statistical analysis of the results Report the quantitative findings with uncertainties! confidence intervals

Define absolute error (ei):

= measured value - true value

Define relative error (RE):

ei/true value

% Relative Error =

= RE * 100

The magnitude of the error in a measurement is an ___________________.

inverse indication of its accuracy

Deviation (di) =

xi - xbar

xbar =

xbar = 1/N*sum(xi) (see notes 2 page 1)

The magnitude of deviations in a series of measurements is an inverse indication of the measurement of ________.

precision

Determinate Errors:

correctable errors operating according to known laws (however often difficult to determine). Determinate errors affect accuracy, but when they are constant, do not impact precision.

List four types of determinate errors and their explanations

1. Instrument errors - tools, calibration, reagent purity 2. Operator errors - mistakes, blunders 3. Personal errors - color blindness, prejudice 4. Errors of method - side rxns, interferences

Random Errors:

errors brought about by the effects of uncontrollable variables, due to the limits of the instrument or observation. You can never see effect of random error unless the measurement approaches the limits of precision of a particular method.

Determinate errors effect _______ (accuracy or precision?), but do not effect _______ (accuracy or precision?)

accuracy, precision

Dealing with determinate errors:

Careful control of equipment, reagents, technique operator bias, and the method of analysis will minimize these errors.

How to check determinate errors?

standardization

Standardization technique:

analysis of a sample whose true value is known

Gaussian distribution results from ____ ______ __ _______ ______ with each contributing to the ____ ____

Gaussian distribution results from many sources of small errors with each contributing to the total error.

Confidence intervals:

determined by the area under the distribution curve within specified limits

Z-score:

(X-mu)/sigma

Z:

reduced variable indicating how many sigma's separate a result from the mean.

95% confidence

mu +/- 1.96

sigma(Xbar) =

sigma(Xbar) = sigma(x)/sqrt(N)

σ=

σ=lim(n→infi)[1/NΣ(x_{i}-μ)^{2}]^{1/2}

Sample standard deviation (s):

standard deviation based on a small number of samples of the parent population

s=

s = [(1/(N-1))Σ(x_{i}-xbar)^{2}]^{1/2}

How do we estimate confidence intervals based on s?

"Student's" t Distribution, for small N, the distribution is wider than a Gaussian distribution

Confidence interval equation, μ=

μ=x_{i}+/-ts

Confidence interval for averages: μ=

μ=xbar +/- 1.96σ/sqrt(N)

at 95% confidence, sigma is known

confidence interval (sigma unknown):

μ = xbar +/- ts/(sqrtN)

Ended notes 3 page 6