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

Hint: 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.