Two different ideal gases, X and Y, are kept in separate identical flasks at the exact same temperature and pressure. If the mean free path of the molecules of gas X is 9 times that of gas Y, what is the ratio of the molecular diameters of gas X to gas Y?

Step-by-step solution

For an ideal gas, the number density n is given by n = P k_B T . Since both gases are at the same pressure and temperature, their number densities are equal ( n_X = n_Y ). The mean free path is given by = 1 2 d^2 n . Since n is constant across both flasks, 1 d^2 . Therefore, _X _Y = ( d_Y d_X )^2 Given _X = 9 _Y , we have: 9 = ( d_Y d_X )^2 d_Y d_X = 3 d_X d_Y = 1 3 The ratio of their molecular diameters is 1:3 . Answer: 1:3