Two vessels separately contain two ideal gases A and B at the same temperature, the pressure of A being twice that of B . Under such conditions, the density of A is found to be 1.5 times the density of B . The ratio of

Correct answer: A. (3)/(4) P _ A = ρ _ A RT MA , P _ B = ρ _ B RT MB ⇒ (PA)/(PB) = (ρA)/(ρB)(MB)/(MA) = 2 ⇒ (3)/(2)(MB)/(MA) = 2 So, (MA)/(MB) = (3)/(4)

NTA Abhyas 2020

Exam: NTA Abhyas
Year: 2020
Subject: Physics
Chapter: Kinetic Theory of Gases

NTA Abhyas 2020 · Physics · Kinetic Theory of Gases

Two vessels separately contain two ideal gases A and B at the same...

Two vessels separately contain two ideal gases

\text{A}

and

\text{B}

at the same temperature, the pressure of

A

being twice that of

\text{B}

. Under such conditions, the density of

\text{A}

is found to be

\text{1.5}

times the density of

\text{B}

. The ratio of molecular weights of

\text{A}

and

\text{B}

Options

A $\dfrac{3}{4}$
B $2$
C $\dfrac{1}{2}$
D $\dfrac{2}{3}$

Correct answer

A. $\dfrac{3}{4}$

Step-by-step solution

${P}_{A} = \dfrac{{ρ}_{A}RT}{MA}, {P}_{B} = \dfrac{{ρ}_{B}RT}{MB}$

$⇒ \dfrac{PA}{PB} = \dfrac{ρA}{ρB}\dfrac{MB}{MA} = 2$

$⇒ \dfrac{3}{2}\dfrac{MB}{MA} = 2$
So, $\dfrac{MA}{MB} = \dfrac{3}{4}$

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