Question

What is the diffusion coefficient of a gas (in cm²/s) at 25°C and 1 atm pressure if its root-mean-square velocity is 400 m/s and the gas constant R is 8.314 J/mol·K? The gas has a molar mass of 32 g/mol and a collision diameter of 3.5 Å.

Answer 1

To calculate the diffusion coefficient  D  of a gas, we can use the Chapman-Enskog equation:D =  3/16  *  1/ ^1/2  *  k * T ^3/2  /  P *  *  2 *  * M ^1/2  where:- k is the Boltzmann constant  R/N_A, where N_A is Avogadro's number, 6.022 x 10^23 mol^-1  - T is the temperature in Kelvin  25C = 298.15 K - P is the pressure in atm  1 atm -  is the collision diameter in cm  3.5  = 3.5 x 10^-8  cm - M is the molar mass in g/mol  32 g/mol First, let's calculate the Boltzmann constant  k :k = R / N_A = 8.314 J/molK /  6.022 x 10^23 mol^-1   = 1.381 x 10^-23  J/KNow, we can plug in the values into the Chapman-Enskog equation:D =  3/16  *  1/ ^1/2  *  1.381 x 10^-23  J/K * 298.15 K ^3/2  /  1 atm *  3.5 x 10^-8  cm  *  2 *  * 32 g/mol ^1/2  To convert pressure from atm to dynes/cm, we can use the conversion factor 1 atm = 1.01325 x 10^6 dynes/cm:D =  3/16  *  1/ ^1/2  *  1.381 x 10^-23  J/K * 298.15 K ^3/2  /  1.01325 x 10^6 dynes/cm *  3.5 x 10^-8  cm  *  2 *  * 32 g/mol ^1/2  Now, we can calculate the diffusion coefficient  D :D  0.660 cm/sSo, the diffusion coefficient of the gas at 25C and 1 atm pressure is approximately 0.660 cm/s.