*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:, and

● Royal Society of Chemistry, 'Discover Maths for Chemists' website

*●*

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

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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});

**, in m**

*V*= volume^{3};

**, in numbers of moles, mol.**

*n*= quantity

**R****= gas constant**which has a value: 8.314 J mol K

^{-1};

**, in degrees Kelvin, K.**

*T*= absolute temperatureCalculations 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

Additional help:* * Self-assessment for 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