JEE Advanced · 2013 · 02 Jun 2013 · Paper 1 · Heat & Thermodynamics

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Two non-reactive monoatomic 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

(A)1 : 4
(B)1 : 2
(C)6 : 9
(D)8 : 9✓ Correct

Answer: (D)

Solution

Using the ideal gas equation

P V = n R T

, we can write:

P M = ρR T

where

M

is molar mass and

ρ

is density.

Therefore:

\frac{ρ _{1}}{ρ _{2}} = \frac{P _{1}}{P _{2}} \times \frac{M _{1}}{M _{2}}

Given

\frac{M _{1}}{M _{2}} = \frac{2}{3}

and

\frac{P _{1}}{P _{2}} = \frac{4}{3}

\frac{ρ _{1}}{ρ _{2}} = \frac{4}{3} \times \frac{2}{3} = \frac{8}{9}

Hence the answer is (D).

JEE Advanced · 2013 · 02 Jun 2013 · Paper 1 · Single correct option

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