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The mass of 0.5 dm^(3) of hydrogen at a ...

The mass of `0.5 dm^(3)` of hydrogen at a pressure of 1 bar of Hg and at a temperature of `300 K` was found to be `4.0 xx 10^(-2) g`. Calculate the molar mass of hydrogen.

Text Solution

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Step I. Calculate of no. Of moles of hydrogen
`P = 1` bar , `V = 0.5 dm^(3)`
`T = 300 K` , `R = 083 "bar" dm^(3) K^(-1) mol^(-1)`
According to ideal gas equation, `PV = nRT`
`n = (PV)/(RT) = ((1 "bar") xx (0.5 dm^(3)))/((0.083 "bar" dm^(3) K^(-1) mol^(-1)) xx (300 K)) = 2.0 xx 10^(-2) mol`.
Step II. Calculation of molar mass of hydrogen
Mass of hydrogen `(m) = 4.0 xx 10^(-2) g`.
No. of mass of hydrogen `(n) = 2.0 xx 10^(-2) mol`.
Molar mass of hydrogen `(M) = ("Mass of hydrogen")/("No. of moles of hydrogen ") = ((4.0 xx 10^(-2)g))/((2.0 xx 10^(-2) mol)) = 2.0 g mol^(-1)`
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