Question 1

From the ideal gas equation $PV = nRT$, at constant volume and temperature, $P \propto n$. Given: $P_X = 2$ atm and $P_{total} = 6$ atm. So, partial pressure of gas Y, $P_Y = P_{total} - P_X = 6 - 2 = 4$ atm. Using the ratio of pressures: $\frac{P_X}{P_Y} = \frac{n_X}{n_Y}$ $\frac{2}{4} = \frac{W_X / M_X}{W_Y / M_Y}$ $\frac{1}{2} = \frac{10 / M_X}{80 / M_Y} = \frac{10}{80} \times \frac{M_Y}{M_X} = \frac{1}{8} \times \frac{M_Y}{M_X}$ $\frac{M_Y}{M_X} = \frac{8}{2} = 4$ The root mean square velocity is given by $v_{rms} = \sqrt{\frac{3RT}{M}}$. At the same temperature: $\frac{v_X}{v_Y} = \sqrt{\frac{M_Y}{M_X}} = \sqrt{4} = 2$ Therefore, the ratio is $2 : 1$.