The rate of diffusion of methane $(CH_4)$ at a given temperature is twice that of gas $X$. The molecular weight of gas $X$ is:

$A$ closed container contains a mixture of non-reacting gases $A$ and $B$. The partial pressures of $A$ and $B$ are $4.5 \ bar$ and $5.5 \ bar$ respectively. Find the mole fractions of $A$ and $B$ respectively.

The rate of diffusion of a gas $A$ is $\sqrt{5}$ times more than that of gas $B$. If the molar mass of $A$ is $x \ g \ mol^{-1}$, the molar mass of $B \ (\text{in } g \ mol^{-1})$ is (in $x$)

Show the relationship between different units of pressure.

The ratio of rates of diffusion of gases $X$ and $Y$ is $1:5$ and that of $Y$ and $Z$ is $1:6$. The ratio of rates of diffusion of $Z$ and $X$ is

The $O_2$ gas is collected over water at $400 \ K$ temperature in a $2 \ L$ vessel. If the total pressure of the mixture is $33.26 \ bar$ and the pressure of dry $O_2$ gas is $32.20 \ bar$,find the vapour pressure of water under the same conditions.