## Overview This topic covers the ideal gas law and the equation of state. It develops the kinetic theory of gases and leads to the kinetic theory of pressure of a perfect gas. ## Mathematical Skills There are a number of opportunities for the development of mathematical skills in this unit. These include recognising and using expressions in decimal and standard form; using ratios, fractions and percentages; making order of magnitude calculations; changing the subject of an equation, including non-linear equations; sketching relationships which are modelled by k y x = . ## How Science Works There are opportunities within this topic for learners to use theories, models and ideas to develop scientific explanations. They can investigate how Newton’s laws of motion can be applied to the behaviour of an ideal gas to produce a model which links the pressure of an ideal gas to its density and the root mean square speed of its molecules. ### Learners should be able to demonstrate and apply their knowledge and understanding of: (a) the equation of state for an ideal gas expressed as pV nRT = where R is the molar gas constant and pV NkT = where k is the Boltzmann constant (b) the assumptions of the kinetic theory of gases which includes the random distribution of energy among the molecules (c) the idea that molecular movement causes the pressure exerted by a gas, and use 1 1 2 2 3 3 N p c mc V = =  where N is the number of molecules (d) the definition of Avogadro constant NA and hence the mole (e) the idea that the molar mass M is related to the relative molecular mass Mr by / kg= 1000 M M r , and that the number of moles n is given by total mass molar mass (f) how to combine 1 2 3 pV Nmc = with pV = nRT and show that the total translational kinetic energy of a mole of a monatomic gas is given by 3 2 RT and the mean kinetic energy of a molecule is 3 2 kT where A R k N = is the Boltzmann constant, and that T is proportional to the mean kinetic energy