Chemistry, Third edition

IDEAL GAS EQUATION

Examples in the use of the ideal gas equation

Note that, to make calculations easier, always express Tin kelvin, Vin cubic metres,

Pin pascals, and nin moles.

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Example 10.1

Calculate the volume of 1.0000 mol of gas at exactly 20C at a

pressure of 101.325 kPa.

Answer

T 20 273.15293.15 K

Rearranging the ideal gas equation,

V

nRT



1.00008.3145293.15

0.024 055 m^3 (to five significant figures)

P 101 325

Remembering that 1 m^3 1000 dm^3 ,

volume0.024 055  1000 24.055 dm^3

Comment

This is the molar volume of a gas at ‘room temperature and pressure’.

Example 10.2

Calculate the number of molecules of methane in 0.50 m^3 of the

gas at a pressure of 2.0  102 kPa and a temperature of exactly

300 K.

Answer

2.0 102 kPa2.0 105 Pa

n

PV



2.0 105 0.50

40 (to two significant figures)

RT 8.3145 300

To convert moles to molecules, we multiply by Avogadro’s constant NA:

number of molecules 6.022 1023  40 2.4 1025

Experimental measurements of the deviations of real

gases from ideal behaviour

An ideal gas is one that exactly follows the ideal gas equation. Rearranging the ideal

gas equation for n, we obtain:,

n

PV

RT

If we use 1 mole of a gas (anygas) then the ratio PV/RTis predicted to have a

numerical value of 1 at all pressures. If a gas does not obey the ideal gas law, the ratio

will be either greater than 1 or less than 1.

Ideal gas law

Calculate the pressure of

1.0 mol of helium in a

2.0 dm^3 container at

20.0C.

Exercise 10I