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Question
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
Volume (V) occupied by dihydrogen is given by,
`"V" = "m"/"M" "RT"/"P"`
`= 0.184/2 xx ("R" xx 290)/"p"`
Let M be the molar mass of the unknown gas. Volume (V) occupied by the unknown gas can be calculated as:
`"V" = "m"/"M" "RT"/"p"`
`= 2.9/"M" xx ("R"xx368)/"p"`
According to the question,
`0.184/2 xx ("R"xx290)/"p" = 2.9/"M" xx ("R"xx368)/"p"`
`=> (0.184xx290)/2 = (2.9 xx 368)/"M"`
`=> "M" = (2.9xx368xx2)/(0.184xx290)`
`= 40 " g mol"^(-1)`
Hence, the molar mass of the gas is 40 g mol–1.
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