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NCERT Class XI Chemistry States of Matter Solutions

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Question : 18 of 23
Marks: +1, -0
2.9 g of a gas at 95°C occupied the same volume as 0.184 g of dihydrogen at 17°C, at the same pressure. What is the molar mass of the gas?
Solution:  
Let molar mass of gas = M
Moles of gas(n); = 2.9M\frac{2.9}{M} , T = 273 + 95 = 368 K ; Since PV = nRT
∴ V = nRTP\frac{nRT}{P} = 2.9×R×368M×P\frac{2.9 \times R \times 368}{M \times P} ... (1)
Moles of dihydrogen = 0.1842\frac{0.184}{2} = 0.092 ; T = 273 + 17 = 290 K
∴ Volume of dihydrogen = 0.092×R×290P\frac{0.092 \times R \times 290}{P} ... (2)
Since the volume is same, 2.9×R×368M×P\frac{2.9 \times R \times 368}{M \times P} = 0.092×R×290P\frac{0.092 \times R \times 290}{P}
∴ M = 2.9×3680.092×290\frac{2.9 \times 368}{0.092 \times 290} = 1067.926.68\frac{1067.9}{26.68} = 40
∴ Thus, molar mass of gas = 40
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