Moles and gas volumes

At the end of this section you should be able to calculate the amount of

substance in moles, using gas volume.

Avogadro’s hypothesis

Equal volumes of gases at the same temperature and pressure contain

equal numbers of molecules

At room temperature and pressure (RTP):

• One mole of gas molecules occupies approximately 24.0dm3 (24000cm3)

• The volume per mole of gas molecules is 24.0 dm3 mol-1

To work out amount, in moles, in a solution, use the equations:

n = V(in dm3)

24.0

n = V(in dm3) 24000

Hence, V= n x 24000cm3

Worked examples

What amount, in mol, of gas molecules are in the following gas

volumes at RTP?

(i) 36 dm3 (ii) 250cm3

(i) n = 36 24.0

= 1.5mol

(ii) n = 250 24000 = 0.01mol

What is the volume of the following at RTP?

(i) 2 mol SO2 (ii) 0.15 mol H2

(i) V = 2 x 24000 cm3

= 48000 cm3

(ii) V = 0.15 x 24000 cm3

= 3600 cm3

What is the mass of the following at RTP?

(i) 0.6 dm3 N2

(ii) 1950 cm3 C2H4

NB: mass = mole x molecular mass

(i) Mole = 0.6 24.0

= 0.025 mol

from, mass = mole x M

M(N2) = 14 x 2 = 28

mass = 0.025 x 28 = 0.7g

(ii) Mole = 1950 24000

= 0.0813mol

mass = mole x M

M(C2H4) = (12 x 2) + 1x4 = 28

hence, mass = 0.0813 x 28 = 2.275g

What is the volume of the following at RTP?

(i) 1.282 g SO2

(ii) 2.5 g CO2

NB: For this question, you need to calculate the moles and then follow it up with volume

(i) Mole = mass/molecular massM(SO2) = 32 + 16x2 = 64

mole = 1.282 / 64 = 0.02 mol

from, V = n x 24000 cm3

= 0.02 x 24000 = 480.75cm3

Now try question 1 – 3Page 15

Question 8 (a) and (b)Page 35