The mean free path of a molecule is 2.25 $\times$ 10^-7 m in an ideal gas at standard temperature and pressure.What is the mean free path when the diameter of the molecule is doubled and the temperature of the gas is doubled? A) 0.75 $\times$ 10^-7m B) 1.13 $\times$ 10^-7m C) 2.25 $\times$ 10^-7m D) 3.00 $\times$ 10^-7m E) 3.75 $\times$ 10^-7m

Question

Quizplus · Accepted Answer

The mean free path of a molecule is directly proportional to the temperature and inversely proportional to the diameter of the molecule.

If the temperature is doubled, the mean free path is also doubled.

If the diameter of the molecule is doubled, the mean free path is halved.

Thus, if we double the diameter and double the temperature, the overall effect on the mean free path will cancel out, resulting in the same value as before:

mean free path = (2.25 x 10^-7 m) / 2 = 1.125 x 10^-7 m = 1.13 x 10^-7 m

Therefore, the best choice is B.

The Mean Free Path of a Molecule Is 2 ×\times× 10-7 M in an Ideal Gas at Standard Temperature and 10-7

The Mean Free Path of a Molecule Is 2 $\times$ 10^-7 M in an Ideal Gas at Standard Temperature and 10^-7