Answer:
[tex]\large \boxed{\text{45.1 g/mol}}[/tex]
Explanation:
Graham’s Law applies to the diffusion of gases:
The rate of diffusion (r) of a gas is inversely proportional to the square root of its molar mass (M).
[tex]r \propto \dfrac{1}{\sqrt{M}}[/tex]
If you have two gases, the ratio of their rates of diffusion is
[tex]\dfrac{r_{2}}{r_{1}} = \sqrt{\dfrac{M_{1}}{M_{2}}}[/tex]
The time for diffusion is inversely proportional to the rate.
[tex]\dfrac{t_{2}}{t_{1}} = \sqrt{\dfrac{M_{2}}{M_{1}}}[/tex]
Data:
t₂ = 222 s
t₁ = 175 s
M₁ = 28.01
Calculation :
[tex]\begin{array}{rcl}\dfrac{222}{175} & = & \sqrt{\dfrac{M_{2}}{28.01}}\\\\1.269 & = & \sqrt{\dfrac{M_{2}}{28.01}}\\\\1.609 & = & \dfrac{M_{2}}{28.01}\\\\M_{2} & = & 1.609 \times 28.01\\ & = & \textbf{45.1 g/mol}\\\end{array}\\\text{The molar mass of the unknown gas is $\large \boxed{\textbf{45.1 g/mol}}$}[/tex]
