Internal energy of an ideal gas depends on

One atmosphere is equal to

If $P_1$ is the partial pressure of a gas and $x_1$ is its mole fraction in a mixture,then the correct relation between $P_1$ and $x_1$ is:

At $27^{\circ} C$, a closed vessel contains a mixture of equal weights of helium (mol. wt. = $4$), methane (mol. wt. = $16$) and sulphur dioxide (mol. wt. = $64$). The pressure exerted by the mixture is $210 \ mm$. If the partial pressures of helium, methane and sulphur dioxide are $p_1, p_2$ and $p_3$ respectively, which one of the following is correct?

At a certain temperature, the time required for the complete diffusion of $200 \ mL$ of $H_2$ gas is $30 \ min$. The time required for the complete diffusion of $50 \ mL$ of $O_2$ gas at the same temperature will be: (in $min$)

In a mixture of $CO_2$ and $CH_4$ in a closed vessel at a constant temperature,the total pressure is $8.3 \times 10^4 \, Pa$. If the partial pressure of $CO_2$ is $2.8 \times 10^4 \, Pa$,what will be the partial pressure of $CH_4$?