Chapter 4, Problem 4.1CP

In calculating $\Delta H_R^{°}$ at 285.15 K, only the $\Delta H_f^{°}$ of the compounds that take part in the reactions listed in Tables 4.1 and 4.2 (Appendix A, Data Tables) are needed. Is this statement also true if you want to calculate $\Delta H_R^{°}$ at 500. K?

Interpretation Introduction

Interpretation: Whether the given statement is true for the calculation of standard enthalpy change of the reaction at 500 K or not needs to be determined.

Concept Introduction:

Enthalpy change of a reaction is the amount of heat absorbed or evolved during the reaction which takes place at constant pressure conditions The standard enthalpy change for a reaction ${\text{ΔH}}_{\text{R}}^{\text{0}}$ is given in terms of the difference in the standard enthalpy of formation of the products and that of reactants.

i.e. ${\text{ΔH}}_{\text{R}}^{\text{0}}\text{ = }{\displaystyle \sum {\text{n}}_{\text{p}}{\text{ΔH}}_{\text{f}}^{\text{0}}}\text{(products) - }{\displaystyle \sum {\text{n}}_{\text{r}}{\text{ΔH}}_{\text{f}}^{\text{0}}}\text{(reactants) ------(1)}$

Here,n_p and n_r are the number of moles of the products and reactants

Answer to Problem 4.1CP

The given statement is not true, since heat capacities of the substances involved in the reaction needs to be included at T = 500K

Explanation of Solution

Based on Kirchhoff's law the change in enthalpy (ΔH) of a reaction is directly proportional to the change in temperature (ΔT) i.e.

  $\begin{array}{l}\text{ΔH α ΔT}\\ {\text{ΔH = C}}_{\text{p}}\text{ΔT}\end{array}$

Where C_p is the heat capacity at constant pressure.

Equation (1) holds true only if the reaction takes place at 298K. At any other temperature, the heat capacities of the products and reactants need to be included. As a result, the net equation becomes:

  ${\text{ΔH}}_{\text{f}}^{\text{0}}{\text{(500 K) = ΔH}}_{\text{f}}^{\text{0}}\text{(298 K) + }{\displaystyle \underset{\text{298}}{\overset{\text{500}}{\int }}{\text{ΔC}}_{\text{p}}}\text{dT ------(2)}$

  ${\text{ΔC}}_{\text{p}}={\displaystyle \sum {\text{C}}_{\text{p}}}\text{(products)}-{\displaystyle \sum {\text{C}}_{\text{p}}}\text{(reactants) }$

Where ΔC_p is the difference in the heat capacities of the products and reactants

Conclusion

In order to calculate the enthalpy change of the reaction at 500 K (or any temperature other than 298 K), heat capacities of the substances involved in the reaction needs to be included.