For which one of the following system $\Delta E<\Delta H$

The first law of thermodynamics represents the conservation of energy which states that energy can neither be created nor be destroyed it can only change forms.

We know, $\Delta H=\Delta E+\Delta nRT$

Where, $\Delta H$ is the enthalpy change, $\Delta E$ is the internal energy change and $\Delta n$ is the number of gaseous moles of product - number of gaseous moles of reactant.

When $\Delta n>0,\Delta H>\Delta E$

And when $\Delta n<0,\Delta H<\Delta E$

Considering the equation, $2{\mathrm{NH}}_{3\left(g\right)}\to {\mathrm{N}}_{2\left(g\right)}+3{\mathrm{H}}_{2\left(g\right)}$

Here, $\Delta n=3+1-2=2$ which is> 0 .

Hence, $\Delta E<\Delta H$ is this reaction.

Therefore, option (C) is correct.