Answer: The molar mass of the unknown gas is 9 g/mol
Explanation:
From Graham's law of effusion rates, the rate of effusion of a gas is inversely proportional to the square root of its molar mass.
[tex]\frac{rate_1}{rate_2}=\sqrt{\frac{M_2}{M_1}} [/tex]
[tex]rate=\frac{volume}{time} [/tex]
Rate is volume effused per unit time. Since, the volumes are same, the formula could be written as:
[tex]\frac{t_B}{t_A}=\sqrt{\frac{M_B}{M_A}}[/tex]
Putting the values in the formula:
[tex]\frac{2.42min}{11.1min}=\sqrt{\frac{M_{H_2}}{M_A}} [/tex]
[tex]\frac{2.42min}{11.1min}=\sqrt{\frac{2}{M_A}} [/tex]
Squaring both sides:
[tex]\frac{2}{M_A}=0.218[/tex]
[tex]M_A=9g/mol[/tex]
The molar mass of the unknown gas is 9 g/mol
