Answer
a. $5.65\times10^{-21}J$
b. 3700 J
Work Step by Step
a. The average translational kinetic energy of a gas molecule is $\frac{3}{2}kT$.
$$\frac{3}{2}kT=\frac{3}{2}(1.38\times10^{-23}J/K)(273K)=5.65\times10^{-21}J$$
b. The total translational KE is the average kinetic energy of each molecule, multiplied by the number of molecules. One mole of gas contains Avogadro’s number of molecules.
$$N_A\frac{3}{2}kT=(6.02\times10^{23})\frac{3}{2}(1.38\times10^{-23}J/K)(298K)=3700J$$