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Standard XII

Chemistry

Ideal Gas Equation

When 2 g of a...

Question

When $2 g$ of a gas A is introduced into an evacuated flask kept at $25^{\circ} C$ , the pressure is found to be $1 a t m$ . If $3 g$ of another gas B is then added to the same flask at the same temperature, the total pressure becomes $1.5 a t m$ . Assuming ideal gas behaviour, the value of $\frac{M_{B}}{M_{A}}$ to the nearest integer is :

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Solution

From ideal gas equation,
$P V = n R T$
$P V = (\frac{m}{M}) R T ∴ M = \frac{m R T}{P V}$
Where m and M are given mass and the molar mass respectively.

After adding B the pressure in the flask increases by 0.5 atm.
On applying ideal gas equation for the gases A and B taking volume and temperature to be same for both,
$M_{A} = \frac{2 \times R T}{1 \times V}; M_{B} = \frac{3 \times R T}{0.5 \times V}$

$∴ \frac{M_{A}}{M_{B}} = \frac{2 R T}{V} \times \frac{0.5 V}{3 R T} = \frac{2 \times 0.5}{3} = \frac{1}{3}$
Therefore, the ratio $M_{A} : M_{B} = 1 : 3$
$\frac{M_{B}}{M_{A}} = 3$

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Ideal Gas Equation

Standard XII Chemistry

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