Question

A mixture of methane and ethane in the molar ratio of $x:y$ has a mean molar mass of $20$. What would be the mean molar mass, if the gases are mixed in the molar ratio of $y:x$?

• A. 26
• B. 24
• C. 20.8
• D. 19

Answer 1

The correct option is A 26

Molar mass of Methane($C{H}_4$) - $12+4=16$

Molar mass of Ethane($C_2{H}_6$) - $24+6=30$

molar ration of methane and ethane is $x:y$

we know that number of moles = $\frac{weight}{mass}$

weight of methane = $16x$

weight of ethane = $30y$

mean molar mass given = $20$

$16x+30y=20(x+y)$ Equation1

When molar ration changed

now, let mean molar mass = $M$

$16y+30x=(x+y)M$ Equation2

From equation1, find the value of $x$.

$16x+30y=20x+20y$

$10y=4x$

$x=\frac{5}{2}y$ put in Equation2 and find the value of $M$.

$16y+30\frac{5}{2}y=(\frac{5}{2}y+y)M$

$M=91y\frac{2}{7y}=26$

Hence, option A is the correct answer.