$2-$ Ammonia $(N{H}_3)$ is a crucial compound in the chemical industry, primarily used for fertilizer production. Its synthesis involves combining nitrogen $(N_2)$ and hydrogen $(H_2)$ gases. Consider a process where you have to separate ammonia from a mixture of nitrogen and hydrogen.

$($a$)$ The mole percentage of $N{H}_3$ in the mixture after the reaction is approximately $15\%.$ Calculate the minimum theoretical energy penalty $($in $kJ)$ for separating $1kg$ of $N{H}_3$ from this mixture, assuming ideal gas behavior and room temperature $(298$ K$).$

$($b$)$ Industrial processes for ammonia separation quote an energy penalty of $20M\frac{J}{k}gN{H}_3.$ Calculate the energy efficiency of these industrial processes based on the theoretical energy penalty you computed.