The average molar mass of a mixture of methane (CH4) and ethane (C2H4)

1.	The average molar mass of a mixture of methane (CH4) and ethane (C2H4) present in the ratio of x : y is found to be 20.0 g mol-1. If the ratio was reversed, what would be the molar mass of the mixture?
Answer» Molar mass of CH₄ = 12 + 1(4) = 16 g mol^–1 Molar mass of C₂H₄ = 2(12) + 1(4) 28 g mol^–1 When these molecules are present in the x: y, their average molar mass = \(\frac{\mathrm{x}\times16\times y\times28}{\mathrm{x}+y} \) = 20 g mol^-1 i.e. 16x + 28y = 20(x + y) or 4x + 7y = 5(x + y) or x = 2y or \(\frac{\mathrm{x}}{y}\) = \(\frac{2}{1}\) = 2 : 1 If the ratio is reversed, now ratio x : y = 1 : 2 \(\therefore\) Average molar mass = \(\frac{1\times16+2\times20}{1+2}\) = 24 g mol^–1

The average molar mass of a mixture of methane (CH4) and ethane (C2H4) present in the ratio of x : y is found to be 20.0 g mol-1. If the ratio was reversed, what would be the molar mass of the mixture?

Answer»

Molar mass of CH₄ = 12 + 1(4) = 16 g mol^–1

Molar mass of C₂H₄ = 2(12) + 1(4) 28 g mol^–1

When these molecules are present in the x: y, their average molar mass

= \(\frac{\mathrm{x}\times16\times y\times28}{\mathrm{x}+y} \) = 20 g mol^-1

i.e. 16x + 28y = 20(x + y)

or 4x + 7y = 5(x + y)

or x = 2y

or \(\frac{\mathrm{x}}{y}\) = \(\frac{2}{1}\) = 2 : 1

If the ratio is reversed, now ratio x : y = 1 : 2

\(\therefore\) Average molar mass = \(\frac{1\times16+2\times20}{1+2}\) = 24 g mol^–1