Lesson 6, Topic 6
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# Vapour Density of Gases

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The vapour density of a gas is the number of times a given volume of the gas is as heavy as the same volume of hydrogen at a particular temperature and pressure. Since vapour density is a ratio of gas volume, it has no unit. It is related to the relative molecular mass by the formula.

Relative molecular mass = 2 x vapour density mass

Or

Vapour density = $$\frac{1}{2} \scriptsize \: \times \: Relative \: molecular \: mass$$

Example 1

Calculate the vapour density of sulphur (iv) oxide (SO2) (S =32, O = 16)

Solution:

Molar mass of SO2 = 32 + 16 x 2 = 64

Vapour density = $$\frac{1}{2} \scriptsize \: \times \: Relative \: molecular \: mass$$

VD = $$\frac{64}{2}$$

VD = 32

Example 2

If 400cm3 of a certain gas weigh 0.5g at s.t.p. Calculate

(a) Molar mass

(b) Vapour density

Solution:

(a) Molar volume of gas at stp = 22.4dm3

If 400cm3 of the gas weighs 0.5g at stp

22400cm3 of the gas will weigh

:- $$\frac{22400}{400} \: \times \: \frac{0.5g}{1}\\ = \scriptsize 28.0g/mol$$

(b) To calculate the vapour density.

Vapour density = $$\frac{1}{2} \scriptsize \: \times \: molar \: mass$$

= $$\frac{1}{2}\scriptsize \: \times \: 28 = 14.0$$

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