Question

An unknown gas effuses at a rate 0.797 times that of nitrogen at the same temperature. what is the molar mass of the unknown gas?

Answer 1

Answer: Molar mass of unknown gas=43.75
`gmol^(-1)`

Explanation: Graham's Law states that the rate of effusion of gas is inversely proportional to the square root of their atomic masses.

`{\text {Rate of effusion}}=\frac{1}{\sqrt\text {Molecular mass}}`

`(R_1)/(R_2)=\sqrt(M_2)/(M_1)`

`R_1`= rate of effusion of nitrogen = x

`R_2`= rate of effusion of unknown gas = 0.797x

`M_1`= Molecular mass of nitrogen
`(N_2)` = 28g

`M_2`= Molecular mass of unknown gas

`(x)/(0.797x)=\sqrt(M_2)/(28gmol^(-1))`

`M_2=43.75gmol^(-1)`

Answer 2

mass B/molar mass A = (rate A/rate B)^2. we know our unknown gas (A) effuses at .797 times our known gas (B) so rate A/rate B = .797 so 0.797^2 = 28 / molar mass A Molar mass A = 28 / 0.635 = 44.09 g / mole Molar mass is 44.09 g/mol