Two non-reactive monoatomic ideal gases have their atomic masses in the ratio 4: 5. The ratio of their partial pressures when enclosed in a vessel kept at a constant temperature, is 1: 2. The ratio of their densities is.

Question

Two non-reactive monoatomic ideal gases have their atomic masses in the ratio 4: 5. The ratio of their partial pressures when enclosed in a vessel kept at a constant temperature, is 1: 2. The ratio of their densities is. (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

Using ideal gas equation: P=(ρ R T/M) ∴ (P1/P2)=(ρ1/M1) × (M2/ρ2) ∴ (1/2)=(ρ1/ρ2) × (5/4) ∴ (ρ1/ρ2)=(2/5)=0.4

Q. Two non-reactive monoatomic ideal gases have their atomic masses in the ratio $4 : 5$ . The ratio of their partial pressures when enclosed in a vessel kept at a constant temperature, is $1 : 2$ . The ratio of their densities is_________.

Using ideal gas equation: $P = \frac{ρRT}{M}$
$∴ \frac{P _{1}}{P _{2}} = \frac{ρ _{1}}{M _{1}} \times \frac{M _{2}}{ρ _{2}}$
$∴ \frac{1}{2} = \frac{ρ _{1}}{ρ _{2}} \times \frac{5}{4}$
$∴ \frac{ρ _{1}}{ρ _{2}} = \frac{2}{5} = 0.4$

Q. Two non-reactive monoatomic ideal gases have their atomic masses in the ratio 4:5. The ratio of their partial pressures when enclosed in a vessel kept at a constant temperature, is 1:2. The ratio of their densities is_________.

Using ideal gas equation: P=MρRT​ ∴P2​P1​​=M1​ρ1​​×ρ2​M2​​ ∴21​=ρ2​ρ1​​×45​ ∴ρ2​ρ1​​=52​=0.4

Q. Two non-reactive monoatomic ideal gases have their atomic masses in the ratio $4 : 5$ . The ratio of their partial pressures when enclosed in a vessel kept at a constant temperature, is $1 : 2$ . The ratio of their densities is_________.

Using ideal gas equation: $P = \frac{ρRT}{M}$
$∴ \frac{P _{1}}{P _{2}} = \frac{ρ _{1}}{M _{1}} \times \frac{M _{2}}{ρ _{2}}$
$∴ \frac{1}{2} = \frac{ρ _{1}}{ρ _{2}} \times \frac{5}{4}$
$∴ \frac{ρ _{1}}{ρ _{2}} = \frac{2}{5} = 0.4$