Mathematical Skills and Analytical Methods for Chemists

Learning Outcomes

Learning Outcomes

Having successfully completed this module you will be able to:

• Demonstrate numeracy and ability to apply mathematical concepts to solve contextual problems.
• Describe chemical problems in terms of mathematical concepts.
• Demonstrate ability to frame a problem or concept in chemistry in the form of a mathematical equation or appropriate plot.
• Explain the principles of a range of analytical techniques including IR, NMR, and Raman spectroscopies and mass spectrometry.
• Select, use, and evaluate data sets using appropriate statistical methods.
• Interpret and evaluate data from a variety of analytical chemistry techniques
• Describe the principles and selection of sample preparation methods including preparation of standard solutions, liquid and solid phase extraction, and chromatographic separations.
• Select the appropriate analytical methods to evaluate a sample.

The course covers the following mathematical concepts and skills alongside an introduction of analytical chemistry techniques. Both are presented with practice in their application to problems in Chemistry: Mathematics content • numbers and orders of magnitude, units, quantity calculus, and estimations; • functions: exponentials and logarithms; • algebra: BODMAS, rearranging equations, solving algebraic and non-algebraic equations; • graph plotting, the equation of a straight line, and linear plots from non-linear expressions; • trigonometry: right angle triangles, diagonal dimensions of cubes and rectangles, definitions and applications of sin, cos, and tan, the cosine rule; • differentiation: by the rule (polynomials and various functions), the chain, product, and quotient rules, use of derivatives to find inflection points, maxima and minima; • integration: indefinite and definite integrals; • matricies and vectors: definitions, addition, subtraction, multiplication, determinants, and as systems of equations; • complex numbers. Analytical Chemistry Content. Introduction – setting analytical chemistry in context Introduction to analytical methods and statistics, precision and accuracy, standard deviation, error treatment, least squares, limits of detection and quantification. Sample preparation and chemical separations – partitioning between phases, liquid extraction, solid phase extraction, chromatographic separations (TLC, HPLC, and GC), plate theory, and detectors. Mass spectrometry and coupling these to chromatographic techniques – introduction to mass spectrometry, ionisation, high- and low- resolution modes, precise molecular weights, resolution and isotopes, instrumentation. Spectroscopic techniques for chemical identification – IR, Raman, and NMR. Instrumentation, data collection, and interpretation in an analytical chemistry context. Case studies – examples from research and industrial laboratories.

Lectures and problem-solving workshops.

Summative

This is how we’ll formally assess what you have learned in this module.