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Question: The difference between heats of reaction at constant pressure and constant volume for the reaction: ...

The difference between heats of reaction at constant pressure and constant volume for the reaction:
2C6H6(l)+15O2(g)→12CO2(g)+6H2O(l)2{C_6}{H_6}(l) + 15{O_2}(g) \to 12C{O_2}(g) + 6{H_2}O(l) at 25∘C{25^ \circ }C in KJKJ is:
A: −7.43 - 7.43
B: +3.72 + 3.72
C: −3.72 - 3.72
D: +7.43 + 7.43

Explanation

Solution

In this question, we have to calculate the difference between heat of reaction at constant pressures and at constant volume. So, the difference between the sum of enthalpies of a product and the sum of enthalpies of reactants at a given temperature and constant pressure is called the heat of reaction. It is denoted by ΔH\Delta H.

Complete step by step answer:
Basically, the heat of reaction at constant pressure is ΔH\Delta H and at constant volume is ΔU\Delta U.
Since, for any reaction the relation between this heat is given by the following equation.
ΔH=ΔU+9(Δng)RT\Delta H = \Delta U + 9(\Delta {n_g})RT
As we have to calculate the difference,
Therefore,
ΔH−ΔU=9(Δng)RT\Delta H - \Delta U = 9(\Delta {n_g})RT
Where (Δng)(\Delta {n_g})= change in number of gaseous moles in any reaction.
While as the given reaction is:
2C6H6(l)+15O2(g)→12CO2(g)+6H2O(l)2{C_6}{H_6}(l) + 15{O_2}(g) \to 12C{O_2}(g) + 6{H_2}O(l)
Since in the above reaction, the only gaseous species are CO2C{O_2} and O2{O_2}. So
(Δng)=12−15(\Delta {n_g}) = 12 - 15 which is equal to −3. - 3.
Hence,
By using ΔH−ΔU=(Δng)RT.\Delta H - \Delta U = \left( {\Delta {n_g}} \right)RT.
Therefore,
By substituting the value of (Δng)(\Delta {n_g}), RR and TT
ΔH−ΔU=(−3)×8.314×2.98.15 J.\Delta H - \Delta U = \left( { - 3} \right) \times 8.314 \times 2.98.15{\text{ J}}{\text{.}}
By solving the above values.
ΔH−ΔU=−7.43 KJ\Delta H - \Delta U = - 7.43{\text{ KJ}}

So, the correct answer is Option A.

Note: At constant volume, the heat of reaction is equal to the change in the internal energy of the system. At constant pressure, the heat of reaction is equal to the enthalpy change of the system.
If ΔH>0⇒\Delta H > 0 \Rightarrow Therefore, the change in the enthalpy is positive which means that energy is being absorbed, this is called an endothermic reaction.
If ΔH<0⇒\Delta H < 0 \Rightarrow The change in enthalpy is negative which means that energy is being expelled, this is called an exothermic reaction.