Answer : The unknown monoatomic gas is, argon.
Explanation :
According to the Graham's law, the rate of effusion of gas is inversely proportional to the square root of the molar mass of gas.
[tex]R\propto \sqrt{\frac{1}{M}}[/tex]
or,
[tex](\frac{R_2}{R_1})=\sqrt{\frac{M_1}{M_2}}[/tex] ..........(1)
where,
[tex]R_1[/tex] = rate of effusion of unknown gas = 2R
[tex]R_2[/tex] = rate of effusion of [tex]Br_2[/tex] gas = R
[tex]M_1[/tex] = molar mass of unknown gas = ?
[tex]M_2[/tex] = molar mass of [tex]Br_2[/tex] gas = 160 g/mole
Now put all the given values in the above formula 1, we get:
[tex](\frac{R}{2R})=\sqrt{\frac{M_1}{160g/mole}}[/tex]
[tex]M_1=40g/mol[/tex]
From the molar mass 40 g/mol we conclude that the unknown monoatomic gas will be, argon.
Therefore, the unknown monoatomic gas is, argon.
