Question

5. The density of a gas at 25°C at 12 bar is the same as that of nitrogen gas at 30 bar. The
molar mass of the gas is :
(a) 14 g mot !
(b) 56 g mol
(C) 70 g mol-'
(d) 112 g mol-
​

Answer 1

Answer:

(b) . 56 is the molar mass of gas

Answer 2

Answer:

The molar mass of the gas is 70 g mol⁻¹ i.e.option(C).

Explanation:

The density of the gas is calculated as,

$\mathrm{\rho=\frac{PM}{RT} }$           (1)

Where,

ρ=density of the gas

P=pressure at which the gas is present

M=molar mass of the gas

R=universal gas constant

T=temperature in kelvin

From the question we have,

The pressure at which unknown gas is present(P₁)=12 bar

The pressure at which  Nitrogen is present (P₂)=30 bar

The molar mass of nitrogen gas(M₂)=28 gram

The pressure at which the gases are present(P)=12 bar

Since the density of both the gas is the same equation (1) can also be written as,

$\mathrm{\frac{P_!M_1}{RT} =\frac{P_2M_2}{RT}}$

$\mathrm{P_1M_1=P_2M_2}$         (2)

When we enter the values into equation (2), we obtain;

$\mathrm{12\times M_1=30\times 28}$

$\mathrm{M_1=70\ g\ mol^{-1}}$

Hence, the molar mass of the gas is 70 g mol⁻¹ i.e.option(C).

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