QJEEM17Ch5fe8: JEE Main 2017 Chemistry - Class 11 JEEM17Ch5fe8 Solution: At 300 K, the density of a certain gaseous molecule at 2 bar is …

Question

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At 300 K, the density of a certain gaseous molecule at 2 bar is double to that of dinitrogen (N₂ ) at 4 bar. The molar mass of gaseous molecule is :

Accepted Answer

Density =

\frac{M a s s}{V o l u m e}

PV = RT

\Rightarrow

V =

\frac{R T}{P}

So, Density(d) =

\frac{M P}{R T}

Now, d₁ = x, P₁ = 4, M₁ = 28, d₂ = 2x, P₂ = 2, M₂ = ?

∴

\frac{d_{1}}{d_{2}} = \frac{M_{1} P_{1}}{R T_{1}} \times \frac{R T_{2}}{M_{2} P_{2}} = \frac{M_{1} P_{1}}{M_{2} P_{2}}

[As T₁ = T₂ ]

\Rightarrow

M₂ =

\frac{M_{1} P_{1} d_{2}}{d_{1} P_{2}}

=

\frac{2 x \times 28 \times 4}{2 \times x}

= 112 g mol^-1

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