83.6 mol of helium is confined to 14L vessel at a pressure of 8 atm. What is average kinetic energy of a helium molecule of mass 5.34×10^−26 kg.

Question

Boltz's constant is 1.38×10^−23 J/K,universal gas constant is 8.31 J/K

Answer in units of J.

Answer 1

Hi Justice D., The average kinetic energy of molecules in an ideal gas is given by K = 3/2*k*T, where k is Boltz's constant and T is temperature in Kelvin. You can use the ideal gas law to find the temperature.

PV = nRT, so T = PV/nR. Substituting into avg. kinetic energy eq. K = (3/2)kPV/nR. At this point you can use R equal to 0.0821, or, 8.31 if you change atm to N/m^2 and Volume of 14 Liters to 14E-3 m^3. Since you are given R = 8.31, 8 atm = 810600 N/m^2.

K = (1.5)*(1.38E-23)*(810600)*(14E-3)/(83.6*8.31) = 3.38E-22 Joules.

Or K = 1.5*(1.38E-23)*(8)*(14)/(83.6*.0821) = 3.38E-22 Joules as a check on conversions.

I hope this helps, Joe