A) 1:3
B) 1:1
C) 2:1
D) 3:1
Correct Answer: A
Solution :
[a] From ideal gas equation, \[PV=nRT\] \[PV\left( \frac{m}{M} \right)RT\,or\,M=m\frac{RT}{PV}\] Let the molecular wt. of A and B be \[{{M}_{A}}\] and \[{{M}_{B}}\] respectively. Then \[{{M}_{A}}=2\times \frac{RT}{1\times V};\,{{M}_{B}}=\frac{3\times RT}{0.5\times V}\] \[\therefore \frac{{{M}_{A}}}{{{M}_{B}}}=\frac{2RT}{V}\times \frac{0.5V}{3RT}=\frac{2\times 0.5}{3}=\frac{1}{3}\] Therefore, the ratio \[{{M}_{A}}:{{M}_{B}}=1:3\]
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