Oxygen diffuses 300 cm³ in 73 s. How long would it take 600 cm³ of chlorine to diffuse under the same conditions?

We are given:

• Volume of oxygen ($V_{O_2}$) = 300 cm³
• Time for oxygen to diffuse ($t_{O_2}$) = 73 s
• Volume of chlorine ($V_{Cl_2}$) = 600 cm³
• Time for chlorine to diffuse ($t_{Cl_2}$) = ?

• Molar mass of Oxygen (O) = 16.00 g/mol
• Molar mass of $O_2$ ($M_{O_2}$) = $2 \times 16.00 = 32.00 \text{ g/mol}$
• Molar mass of Chlorine (Cl) = 35.45 g/mol
• Molar mass of $Cl_2$ ($M_{Cl_2}$) = $2 \times 35.45 = 70.90 \text{ g/mol}$

Graham's Law states that the rate of diffusion of a gas is inversely proportional to the square root of its molar mass. The rate of diffusion can be expressed as volume diffused per unit time ($V/t$).

Substituting the rate with volume and time:

First, simplify the right side:

Next, simplify the left side:

Rounding to three significant figures, the time taken for chlorine to diffuse is:

The time it will take for 600 cm³ of chlorine to diffuse through the same plug is approximately 217 s.