Question

For which of the following reactions, $\Delta$H ˂ $\Delta$E?
A. ${{N}_{2}}+3{{H}_{2}}\xrightarrow[{}]{}2N{{H}_{3}}$
B. $A{{g}_{2}}O\xrightarrow[{}]{}2Ag+\dfrac{1}{2}{{O}_{2}}$
C. $CO+\dfrac{1}{2}{{O}_{2}}\to C{{O}_{2}}$
D. $C+{{O}_{2}}\to C{{O}_{2}}$

Answer 1

We should know the relation between $\Delta$H and $\Delta$E. The relation between $\Delta$H and $\Delta$E is as follows.
$\Delta$H = $\Delta$E + $\Delta$nRT
$\Delta$H= Change in enthalpy, $\Delta$E = internal energy change, $\Delta$n = change in number of gas moles, R = universal gas constant, T= temperature.

Complete step by step answer:
Now, we have to calculate $\Delta$H for all the given options.
a) Coming to options, option A, ${{N}_{2}}+3{{H}_{2}}\xrightarrow[{}]{}2N{{H}_{3}}$
For option A, $\Delta$n = number of moles of products – number moles of reactants.
$\Delta$n = 2-4
$\Delta$n = -2
Substitute Δn value in $\Delta$H = $\Delta$E + $\Delta$nRT
$\Delta$H = $\Delta$E -2 RT (for option-A)
b) Coming to option B,$A{{g}_{2}}O\xrightarrow[{}]{}2Ag+\dfrac{1}{2}{{O}_{2}}$.
$\Delta$n = number of moles of products – number moles of reactants.
$\Delta$n = 2.5- 1
= 1.5
Substitute Δn value in $\Delta$H = $\Delta$E + $\Delta$nRT
$\Delta$H = $\Delta$E +1.5 RT (for option-B)
c) Coming to option C, $CO+\dfrac{1}{2}{{O}_{2}}\to C{{O}_{2}}$
$\Delta$n = number of moles of products – number moles of reactants.
$\Delta$n = 1- 1.5
= -0.5
Substitute Δn value in $\Delta$H = $\Delta$E + $\Delta$nRT
$\Delta$H = $\Delta$E - 0.5 RT (for option-C)
d) Coming to option D, $C+{{O}_{2}}\to C{{O}_{2}}$
$\Delta$n = number of moles of products – number moles of reactants.
$\Delta$n = 1- 2
= -1
Substitute Δn value in $\Delta$H = $\Delta$E + $\Delta$nRT
$\Delta$H = $\Delta$E - RT (for option-D)
By observing all the options, $\Delta$H˂ $\Delta$E is for option A.

So, the correct option is A.

Note: Don’t be confused with the symbols $\Delta$H and $\Delta$E.
$\Delta$H = change in enthalpy.
$\Delta$E = change in internal energy.