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Question
The density of an ideal gas is 1.25 × 10−3 g cm−3 at STP. Calculate the molecular weight of the gas.
Use R=8.31J K-1 mol-1
Solution
Let:
m = Mass of the gas
M = Molecular mass of the gas
Now,
Density of ideal gas,\[\rho\]= 1.25 × 10−3 gcm−3 =1.25 kgm−3
Pressure, P = 1.01325\[\times\]105 Pa (At STP)
Temperature, T = 273 K (At STP)
Using the ideal gas equation, we get
\[PV = nRT . . . (1)\]
\[n = \frac{m}{M} . . . (2)\]
\[ \therefore PV = \frac{m}{M}RT\]
\[ \Rightarrow M = \frac{m}{V}\frac{RT}{P}\]
\[ \Rightarrow M = \rho\frac{RT}{P}\]
\[ \Rightarrow M = 1 . 25 \times \frac{8 . 31 \times 273}{{10}^5}\]
\[ \Rightarrow M = 2 . 83 \times {10}^{- 2} \]
\[ = 28 . 3 g - {\text { mol }}^{- 1} \]
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