Chemistry, Third edition

10 · GASES, LIQUIDS AND SOLIDS

1.Theaverage speedof gas particles at a particular temperature depends upon the

mass of the gas molecules, with smaller molecules (such as N 2 ) moving faster

than heavier ones (like Cl 2 ). Even relatively heavy molecules travel at average

speeds of several hundred metres per second at room temperature!

2.The average speed of molecules in a gas also increaseswith the temperature of the

gas, but the spread of speeds is greater at higher temperatures.

Ideal gas equation

The kinetic theory of gases reduces to a remarkably simple mathematical form,

known as the ideal gas equation.

PVnRT

wherePis the pressure of a gas (Pa), Vis the volume of gas (m^3 ),Tthe gas tempera-

ture (K), and nthe number of moles of gas. Ris the ‘universal gas constant’ with a

value of 8.3145 J mol^1 K^1.

Key points about the ideal gas equation

1.The ideal gas equation shows that P,V,nandTare not independent. These vari-

ables cannot take on any values we like – nature has dictated that if three of them

are known, then the fourth is fixed.

2.The equation contains no factor which is specificto any gas. The type of gas

(helium, chlorine, oxygen, water vapour, etc.) is irrelevant.

3.The rearranged forms of the ideal gas equation are often used in calculations:

nRT PV nRT PV

V—— ; T——; P—— ; n——

PnRV RT

4.The inter-relationships between P,V,nandT, summarized in the gas laws of

Charles, Boyle and Avogadro, are ‘inbuilt’ into the ideal gas equation, and the

equation makes the separate use of these laws in calculations redundant. For

example, the ideal gas equation shows that if the pressure and the number of

moles of gas does not change, then Vis proportional to T. In other words, it pre-

dicts Charles’ law.

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Molecular speed

Number of moleculeshaving speed shown

Cl 2 (300 K)

N 2 (300 K)

N 2 (3000 K)

Fig. 10.9The spread of molecular speeds in chlorine and nitrogen gases.