100 g of an ideal gas is kept in a cylinder of 416 L volume

Question

100 g of an ideal gas is kept in a cylinder of 416 L volume at 27 $^\circ$ C under 1.5 bar pressure. The molar mass of the gas is __________ g mol^{$-$ 1}. (Nearest integer)

(Given : R = 0.083 L bar K^{$-$ 1} mol^{$-$ 1})

DivineJEE · Accepted Answer

Given, Mass of ideal gas = 100 gm

Let the molar mass of ideal gas = M

\therefore

Number of moles of gas (n) =

{{100} \over M}

Volume of cylinder (V) = 416 L

Temperature (T) = (27 + 273)K = 300 K

Pressure (P) = 1.5 bar

R = 0.083 L bar K

-

1 mol^{$-$
1}

Using ideal gas equation,

PV = nRT

\Rightarrow 1.5 \times 416 = {{100} \over M} \times 0.083 \times 300

\Rightarrow

M = 4

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