Question

The molar heat capacities at constant pressure (assume constant with respect to temperature) of A, B and C are in the ratio of $1.5:3.0:2.0$ .
If enthalpy change for the exothermic reaction $A + 2B \to 3C$ at 300K is -10kJ/mol & ${C_{p,m}}$ (B) is 300J/mol then enthalpy change at 310K is:
A.-8.85 kJ/mol
B.8.5 kJ/mol
C.-11.5 kJ/mol
D.None of these

Answer 1

At constant pressure, that the heat capacity is equal to change in temperature. The heat capacity of an object depends on mass and composition. Molar heat capacity is the amount of heat energy required to raise the temperature of 1 mole of a substance. The difference of enthalpy is defined by the difference of temperature.

Complete step by step answer:
Here we find out the change in enthalpy by given formula,
$\vartriangle H = n{C_p}\vartriangle T$ and
${C_{p,m}}$ (B) is 300J/mol so by their ratio
${C_{p,m}}$ (C) is 200J/mol and ${C_{p,m}}$ (A) is 150J/mol.

$$\vartriangle {H_{300K}} = - 10KJ \\\ \vartriangle {H_{310K}} - \vartriangle {H_{300K}} = (3 \times 200 - 2 \times 300 - 1 \times 150)\vartriangle T = - 1500 = - 1.5\dfrac{{kJ}}{{mole}} \\\$$

So, for reaction enthalpy change at 310K is:
$\Delta {H_{310K}} = - 1.5 - 10 = - 11.5\dfrac{{kJ}}{{mole}}$ .

Hence, option (C) is the correct answer.

Additional information:
The heat capacity at constant pressure is greater than the heat capacity at constant volume. Enthalpy can be expressed by molar enthalpy by dividing the enthalpy or change in enthalpy by the number of moles which is a state function.

Note: Evolution of enthalpy in Chemical Reactors Enthalpy in energy balance can be solved. When the temperature increases, the amount of molecular interactions also increases. When the number of interactions increase, then the enthalpy system rises. Here we see the given reaction is an exothermic reaction by the change in enthalpy.