Question

In a gaseous mixture, if an alkane $\left(C_x{H}_{2x+2}\right)$ and an alkene $\left(C_y{H}_{2y}\right)$ are taken in $2:1$ mole ratio, the average molecular weight of the mixture is observed to be $20$. If the same alkane and alkene are taken in $1:2$ mole ratio, the average molecular weight of the mixture is observed to be $24$. Then, the value of $x$ and $y$ are respectively :

• A. $2,1$
• B. $1,2$
• C. $2,3$
• D. $3,2$

Answer 1

Answer: (B)

$1,2$

If the alkane, $C_x{H}_{2x+2}$ and alkene, $C_y{H}_{2y}$ is in the ratio of $2:1$, then

$M_{mix}=\frac{2.(14x+2)+1.\left(14y\right)}{3}=20$

$28x+14y=56$ ...( 1 )

If the alkane, $C_x{H}_{2x+2}$ and alkene, $C_y{H}_{2y}$ is in the ratio of $1:2$, then

$M_{mix}=\frac{1.(14x+2)+2.\left(14y\right)}{3}=24$

$14x+28y=70$ ...( 2 )

Solving equation (1) and (2), we get

$x=1,y=2$