The temperature of 7.10 mol of an ideal monatomic gas is raised 15.0 K in an adiabatic process. what is the change ÄK in the average kinetic energy per atom?

No matter how the temperature is raised, the average kinetic energy is (3/2) k T, where k = Boltzmann constant = 1.38*10^-23 J/K

Use that fact to compute the change in average KE per atom. It will be just
(3/2)k(delta T)

The number of moles will not affect the average.