Answer
We can rank the gases in order of total translational kinetic energy, from highest to lowest:
$b \gt a = c = d \gt e = f$
Work Step by Step
The total translational kinetic energy is the number of molecules $N$ multiplied by the average translational kinetic energy of the molecules $\overline{KE}$. We can write an expression for the total translational kinetic energy:
$N\times~\overline{KE} = \frac{3}{2}~NkT$
$KE = \frac{3}{2}~PV$
Let $P_0 = 50~kPa$
Let $V_0 = 2~L$
We can find an expression for the total translational kinetic energy in each case.
(a) $KE= \frac{3}{2}~(2P_0)~(2V_0) = 4\times \frac{3}{2}~P_0~V_0$
(b) $KE= \frac{3}{2}~(4P_0)~(2V_0) = 8\times \frac{3}{2}~P_0~V_0$
(c) $KE= \frac{3}{2}~(P_0)~(4V_0) = 4\times \frac{3}{2}~P_0~V_0$
(d) $KE= \frac{3}{2}~(2P_0)~(2V_0) = 4\times \frac{3}{2}~P_0~V_0$
(e) $KE= \frac{3}{2}~(2P_0)~(V_0) = 2\times \frac{3}{2}~P_0~V_0$
(f) $KE= \frac{3}{2}~(P_0)~(2V_0) = 2\times \frac{3}{2}~P_0~V_0$
We can rank the gases in order of total translational kinetic energy, from highest to lowest:
$b \gt a = c = d \gt e = f$
