$A$ and $B$ are ideal gases. The molecular weights of $A$ and $B$ are in the ratio of $1: 4$. The pressure of a gas mixture containing equal weights of $A$ and $B$ is $P \text{ atm}$. What is the partial pressure (in $\text{atm}$) of $B$ in the mixture?

When $0.0168 \, mol$ of $O_2$ obtained from the decomposition of $KClO_3$ is collected over water at $25 \, ^\circ C$,the volume is $428 \, mL$ and the pressure is $754 \, mm$. What is the water vapor pressure at $25 \, ^\circ C$ in $mm$?

If $4 \ g$ of oxygen diffuses through a fine hole,how many grams of hydrogen will diffuse under the same conditions?

The graph shows the characteristics of one mole of an ideal gas at a pressure of $1 \ atm$ with respect to volume $(V)$ and temperature $(T)$. Identify the correct graph.

Under the same $P$ and $T$,which of the following pairs of gases will diffuse at the same rate through a small jet?

Two gases $X$ (molecular weight $M_{X}$) and $Y$ (molecular weight $M_{Y}$; $M_{Y} > M_{X}$) are at the same temperature $T$ in two different containers. Their root mean square velocities are $C_{X}$ and $C_{Y}$ respectively. If the average kinetic energies per molecule of two gases $X$ and $Y$ are $E_{X}$ and $E_{Y}$ respectively, then which of the following relation$(s)$ is(are) true?