49.2 mol of helium is confined to a 19 L vessel at a pressure of 2 atm. Find the average kinetic energy of a helium molecule of mass 5.34 × 10−26 kg. Answer in units of J.

Question

Boltzmann’s constant is 1.38 × 10−23 J/K, and the universal gas constant is 8.31 J/K.

Answer 1

E_K = 3/2 kT. You need only get T from rearranging the ideal gas law: T = PV/nR . You have all the variables in the appropriate units for R = .0821 liter-atm/mole-K. I would use that: you get Kelvin for T, so you're good to go for the kinetic energy expression as k has units of J/K and you get Joules. If you must use R = 8.314, you have to convert atm to Pa, and liters to m³ before you can substitute into the IGL.

Good luck!