Question

The flask $\left(A\right)$ and $\left(B\right)$ have equal volume. Flask $\left(A\right)$ contains $H_2$ gas at $300K$, while $\left(B\right)$ contains equal mass of $C{H}_4$ at $900K$. Calculate the ratio of average speed of molecules in flask $\left(A\right)$ and $\left(B\right)$.

Answer 1

The number of molecules of a gas is proportional to the number of moles.
Let the mass of each gas in the two flasks,

Molecular mass of $H_2$ =2

Molecular mass of ${CH}_4$= 16

$\therefore$ Number of moles of $H_2$=$\frac{m}{2}$

Number of moles of ${CH}_4$ =$\frac{m}{16}$

The ratio of the average speed of the number of moles of $H_2$

and ${CH}_4$=$\frac{m}{2}:\frac{m}{16}$ or 16:2 or 8:1.

Thus the number of molecules of $H_2$ in the flask A be eight times the number of molecules of ${CH}_4$ in flask B.