Question

A mixture of methane and ethene in a molar ratio of $x:y$ has an average molecular mass of $20 u$ . The mean molar mass when they are mixed in the molar ratio of $y:x$ will be -

• A. $20 u$
• B. $25 \, u$
• C. $24 u$
• D. $15 u$

Answer 1

Answer: (C)

Mol. wt. of $CH_{4}=16$
Mol. wt. of $C_{2}H_{4}=28$
$\therefore 20=\frac{16 x + 28 y}{x + y}$
or $16x+28 \, y=20 \, x+20 \, y$
or $4x=8y$
or $x=2y$
In the gaseous mixture when the mole ratio of $CH_{4}$ and $C_{2}H_{4}$ is $y:x$
then $avg. \, mol. \, wt=\frac{16 y + 28 x}{x + y}=\frac{16 y + 56 y}{3 y}$
$=\frac{72 y}{3 y}=24 u$