If a molecule of O3 diffuses a certain distance in 3500 s, how long (s) would it take a molecule of Cl2 to diffuse the same distance at the same temperature and under the same conditions?

(1/3500/1/x) = sqrt(molar mass Cl2/molar mass O3).

Solve for x.

To determine the time it would take for a molecule of Cl2 to diffuse the same distance as a molecule of O3 under the same conditions, we need to consider the relationship between diffusivity and time. Diffusivity is a measure of how quickly a substance spreads or diffuses through a medium.

The diffusivity of a substance is directly proportional to the square root of its molar mass and inversely proportional to the viscosity of the medium. Since both O3 and Cl2 are diatomic molecules and have similar molar masses, we can assume that their diffusivities are comparable.

Given that O3 took 3500 seconds to diffuse a certain distance, we can use the square root of the ratio of the molar masses to determine the time it would take for Cl2.

First, we need to find the ratio of the molar masses of Cl2 to O3. The molar mass of Cl2 is approximately (2 * 35.45) = 70.90 g/mol, and the molar mass of O3 is approximately (3 * 16.00) = 48.00 g/mol).

The ratio of the molar masses is: (70.90 g/mol) / (48.00 g/mol) = 1.477

Since the diffusivity is directly proportional to the square root of the molar mass, the square root of the ratio of the molar masses is: sqrt(1.477) = 1.215

Therefore, the time it would take for a molecule of Cl2 to diffuse the same distance as a molecule of O3 would be approximately 1.215 times the time taken by O3.

Thus, the time taken by the molecule of Cl2 would be: 3500 s * 1.215 ≈ 4252.5 s

Hence, it would take approximately 4252.5 seconds (s) for a molecule of Cl2 to diffuse the same distance under the same conditions.