Question

The difference between heat of combustion of liquid benzene at constant pressure and at constant volume at 300 K is \[\left( {R = 8.314\,J\dfrac{K}{{ml}}} \right)\]
A.-3741 J
B.3741 J
C.37.41 KJ
D.-37.41 KJ

Answer 1

Hint: The equation for combustion of liquid benzene is given by,
 ${C_6}{H_6}\left( l \right) + \dfrac{{15}}{2}{O_2}\left( g \right) \to 6C{O_2}\left( g \right) + 3{H_2}O\left( l \right)$
Since, the temperature is given in the question. So further we can calculate the no of moles. We know that \[(\Delta H-\Delta U)\] is the difference between heat of combustion at constant pressure and at constant volume. So, we can substitute the values in the equation \[\Delta H = \Delta U + \Delta {n_g}RT\] and calculate \[(\Delta H-\Delta U)\].

Complete step by step answer:
Given in the question is,
Temperature, \[T = 300K\]
Combustion of benzene-
 ${C_6}{H_6}\left( l \right) + \dfrac{{15}}{2}{O_2}\left( g \right) \to 6C{O_2}\left( g \right) + 3{H_2}O\left( l \right)$
 $\Delta {n_g} = {n_p}-{n_r} = 6 - \dfrac{{15}}{2} = \dfrac{{ - 3}}{2}$
We know,
The relation between \[\Delta H\] and \[\Delta E\] is given by,
 \[\Delta H = \Delta U + \Delta {n_g}RT\]
$\Rightarrow$ \[\Delta H-\Delta U = \Delta {n_g}RT\]
$\Rightarrow$ \[\Delta H-\Delta U\] is the difference between heat of combustion at constant pressure and at constant volume

Substituting the values in the above equation,
 \[\Delta H-\Delta U = \Delta {n_g}RT\]
$\Rightarrow$ $\Delta H-\Delta U = \dfrac{{ - 3}}{2} \times 8.314 \times 300$ (Since, \[R = 8.314\,J\dfrac{K}{{ml}}\] )
$\Rightarrow$ \[\Delta H-\Delta U = - 3741\,J\]

Therefore, the correct answer is option (A).

Note: The change in the internal energy of a system is the sum of the heat transferred and work done. At constant pressure, heat flow and the internal energy are related to the system’s enthalpy. The heat flow is equal to the change in the internal energy of the system plus the PV work done. When the volume of a system is constant, changes in its internal energy can be calculated by substituting the ideal gas law into the equation for \[\Delta U\].