Question

Two flasks of capacity 1 L and 2 L contain gases,
A and B respectively at same temperature. If
density of A is 2.5 g/L and that of B is 5 g/L and
the molar mass of A is twice of that of B, then the
ratio of pressure exerted by gases (A : B) is
(1) 1:2
(2) 1:4
13) 3:2
(4) 2:3​

Answer 1

Answer:

OPTION (2) 1 : 4

Explanation:

$\sf We\:know\:that , \\ \\ \sf P = \frac{dRT}{M} \\ \\ \sf Given\: that\: {d}_{A} = 2.5 g {L}^{-1} \: \: \: \: \: {d}_{B} = 5 g {L}^{-1} \\ \sf {M}_{A} = 2{M}_{B} \\ \\ \sf To\:Find\: \frac{{P}_{A}}{{P}_{B}} \\ \\ \sf In\:the\: equation\: R\:and\:T\:are \:constants \\ \\ \sf {P}_{A} \: \alpha \: \frac{{d}_{A}}{{M}_{A}} \\ \\ \sf Similarly \: {P}_{B} \: \alpha \: \frac{{d}_{B}}{{M}_{B}} \\ \\ \sf \longrightarrow \frac{{P}_{A}}{{P}_{B}} = \frac{{d}_{A}}{{M}_{A}} ÷ \frac{{d}_{B}}{{M}_{B}} \\ \\ \sf \longrightarrow \frac{{P}_{A}}{{P}_{B}} = \frac{{d}_{A}}{{M}_{A}} × \frac{{M}_{B}}{{d}_{B}} \\ \\ \sf \longrightarrow \frac{{P}_{A}}{{P}_{B}} = \frac{2.5}{2{M}_{B}} × \frac{{M}_{B}}{5} \\ \\ \sf \longrightarrow \frac{{P}_{A}}{{P}_{B}} = \frac{1}{4} \\ \\ \sf \longrightarrow {P}_{A} : {P}_{B} = 1 : 4 \\ \\ \sf So\:the\:correct\:choice\:is\:option\:(2)$

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Answer 2

Given: Volume of flask 1 (V₁) = 1 L

The volume of flask 2 (V₂) = 2 L

The density of gas A (ρ₁) = 2.5 g/ L

The density of gas B (ρ₂) = 5g/L

The molar mass of A is twice that of B

To Find: The ratio of pressure exerted by gases

Solution:

Let the pressure exerted by gas A be P₁

Let the pressure exerted by gas B be P₂

Let the Molar mass of A be M₁

Let the Molar mass of B be M₂

Since temperature is not given here we take the temperature of both the gases as the same

M₁ = 2M₂                                             ...1

According to Ideal Gas Law

PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant and T is the temperature

We know Mass = Volume x density

Volume = $\frac{Mass}{Density\\}$

Moles(n) = $\frac{Given Mass}{Molar mass}$

Substituting volume and moles in the Ideal Gas Law

P $\frac{Mass}{Density\\}$   =  $\frac{Given Mass}{Molar mass}$ x RT

Density (ρ) =  $\frac{PM}{RT}$

ρ₁ = $\frac{P1 M1}{RT}$

ρ₂ = $\frac{P2M2}{RT}$

ρ₁ / ρ₂ = $\frac{P1M1}{P2M2}$

$\frac{2.5}{5}$   = $\frac{P1}{P2}$ x $\frac{2M2}{M2}$                    Since, M₁ = 2M₂

$\frac{1}{2}$    =  $\frac{P1}{P2}$  x 2

$\frac{P1}{P2}$  = $\frac{1}{4}$

Therefore, the ratio of pressure exerted by gases A and B is in the ratio 1:4.