A sample of oxygen gas diffuses through a porous barrier in 50 seconds. How long would it take for an equal volume of methane gas to diffuse through the same barrier under identical conditions?

• Molar mass of Oxygen ($O_2$): $2 \times 16 \text{ g/mol} = 32 \text{ g/mol}$
• Molar mass of Methane ($CH_4$): $12 \text{ g/mol} + (4 \times 1 \text{ g/mol}) = 16 \text{ g/mol}$

Graham's Law can be expressed as:

Where Rate is the volume diffused per unit time ($\frac{V}{t}$).
Let oxygen be gas 1 and methane be gas 2.

Given:

• $V_{O_2} = 200 \text{ cm}^3$
• $t_{O_2} = 50 \text{ s}$
• $V_{CH_4} = 80 \text{ cm}^3$
• $t_{CH_4} = ?$
• $M_{O_2} = 32 \text{ g/mol}$
• $M_{CH_4} = 16 \text{ g/mol}$

To rationalize the denominator:

The time it will take for 80 cm$^3$ of methane to diffuse is: