Interactive Case Study:    Analysis of Linear Equations: Gas laws - pV = nRT

Produced by Graham Currell, University of the West of England, Bristol and David Read, University of Southampton, in association with:
Royal Society of Chemistry, 'Discover Maths for Chemists' website
, and

Essential Mathematics and Statistics for Science, 2nd Edition
Graham Currell and Antony Dowman, Wiley-Blackwell, 2009

This case study aims to develop the skills for performing the analysis of linear equations in science, and uses the ideal gas equation, pV = nRT, as the scientific context for developing these skills. This is achieved by a series of video tips and associated QVA tutorials - questions with video worked answers.

Introduction
Except at high pressures and low temperatures, the behaviour of most gases can be described by the ‘ideal gas’ equation:
pV = nRT
where
p = pressure, in Pascals, Pa (1 Pa = 1 N m-2); V = volume, in m3; n = quantity, in numbers of moles, mol.
R = gas constant which has a value: 8.314 J mol K-1; T = absolute temperature, in degrees Kelvin, K.

Calculations based on the analysis of the ideal gas equation, pV = nRT, using Excel are also developed in:
Study Guide: Analysis of Experimental Error/Uncertainty using Excel.

1. Rearrangement of equation:
QVA tutorial
Video Tip: SIX rules for rearranging equations.
Additional help: Study Guide: Rearranging equations.

2. Substitution of values:
QVA tutorial
Video Tip: Using the rules of BODMAS
Video Tip: Using 'powers of ten' for scientific (standard) notation in a calculator and Excel

3. Changing units:
QVA tutorial
Additional help: Study Guide: Units of Measurement in Science.

4. Analysis of a straight line:
QVA tutorial
Additional help: Study Guide: Analysis of Experimental Error/Uncertainty using Excel.
Additional help: Chapter 4, "Essential Mathematics and Statistics for Science"

5. Uncertainty in replicate measurements:
QVA tutorial
Additional help: Study Guide: Analysis of Experimental Error/Uncertainty using Excel.
Additional help: Sections 8.2, 8.3, "Essential Mathematics and Statistics for Science"

Any comments, corrections or suggestions welcome - graham.currell@uwe.ac.uk