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

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

Tardigrade Admin · Accepted Answer

According to an ideal gas equation, pressure

p = \frac{ρRT}{M}

,
where

ρ

is the density of the gas and

M

is the atomic mass of the gas.

∴ p_{1} = \frac{ρ _{1} RT}{M _{1}} ... (i)

and

p_{2} = \frac{ρ _{2} RT}{M _{2}} ... (ii)

Divide

(i)

by

(ii)

, we get

\frac{p _{1}}{p _{2}} = \frac{ρ _{1}}{ρ _{2}} \frac{M _{2}}{M _{1}}

\frac{ρ _{1}}{ρ _{2}} = \frac{p _{1}}{p _{2}} \frac{M _{1}}{M _{2}}

Here,

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

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

$1 : 4$

$1 : 2$

$6 : 9$

$8 : 9$

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

1:4

1:2

6:9

8:9

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

$1 : 4$

$1 : 2$

$6 : 9$

$8 : 9$