Question

the density of gas A is three times that of gas B. if the molecular weight of A is M the weight of B is a)3M b)root 3 M c)M/3 d) M/root3​

Answer 1

ANSWER:(c) M/3

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Answer 2

The molecular weight of B is $\frac{M}{3}$

Explanation:

Ideal gas law in terms of density:

$PV=nRT\\\\PV=\frac{w}{M}\times RT\\\\M=\frac{w}{V}\times \frac{RT}{P}\\\\M=\rho\times \frac{RT}{P}$

where,

P = pressure of the gas

V = volume of the gas

T = temperature of the gas  

n = number of moles of the gas

R = gas constant

M = molar mass of gas

w = mass of gas

$\rho$ = density

given: $\rho_{A}=3\times \rho_{B}$, $M_A=M$

$M_A=\rho_{A}\times \frac{RT}{P}$

$M=\rho_{A}\times \frac{RT}{P}$

Thus $M_B=\rho_{B}\times \frac{RT}{P}$

$M_B=\frac{\rho_{A}}{3}\times \frac{RT}{P}$

$M_B=\frac{M}{3}$

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