1. Tardigrade
  2. Question
  3. Physics
  4. Two non-reactive monatomic ideal gases have their atomic masses in the ratio 2:3 . The ratio of their partial pressures, when enclosed in a vessel kept at a constant temperature is 4:3 . The ratio of their densities is

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. Two non-reactive monatomic ideal gases have their atomic masses in the ratio $ 2:3 $ . The ratio of their partial pressures, when enclosed in a vessel kept at a constant temperature is $ 4:3 $ . The ratio of their densities is

AMUAMU 2017

Solution:

According to an ideal gas equation, pressure
$p = \frac{\rho RT}{M}$,
where $\rho$ is the density of the gas and $M$ is the atomic mass of the gas.
$\therefore p_1 = \frac{\rho_1 RT}{M_1} \,\,\,...(i)$
and $p_2 = \frac{\rho_2 RT}{M_2}\,\,\,...(ii)$
Divide $(i)$ by $(ii)$, we get
$\frac{p_1}{p_2} = \frac{\rho_1}{\rho_2} \frac{M_2}{M_1}$
$\frac{\rho_1}{\rho_2} = \frac{p_1}{p_2} \frac{M_1}{M_2}$
Here, $\frac{\rho_1}{\rho_2} = \frac{4}{3} \times \frac{2}{3} = \frac{8}{9}$