Chapter 17, Problem 93A

Interpretation Introduction

Interpretation: The heat of the reaction is to be calculated.

Concept Introduction: Hess’s Law states that the overall change in enthalpy for the solution is the sum of all changes independent of the different phases or steps of a reaction.

Answer to Problem 93A

The heat of the reaction $\text{Ca(s)+C(s)+}\frac{\text{3}}{\text{2}}{\text{O}}_{\text{2}}\text{(g)}\to {\text{CaCO}}_{\text{3}}\text{(s)}$ is $\text{-1207}\text{.3kJ}$

Explanation of Solution

The chemical reaction for which enthalpy change is to be calculated

  $\text{Ca(s)+C(s)+}\frac{\text{3}}{\text{2}}{\text{O}}_{\text{2}}\text{(g)}\to {\text{CaCO}}_{\text{3}}\text{(s)}$ $(1)$

The thermochemical equations given are

  $\begin{array}{l}\text{Ca(s)+2C(s)}\to {\text{CaC}}_{\text{2}}\text{(s) }\Delta \text{H= -62}\text{.8 kJ (2)}\\ {\text{CO}}_{\text{2}}\text{(g)}\to {\text{C(s)+O}}_{\text{2}}\text{(g) }\Delta \text{H= 393}\text{.5 kJ (3)}\\ {\text{CaCO}}_3{\text{(s)+CO}}_{\text{2}}\text{(g)}\to {\text{CaC}}_{\text{2}}\text{(s)+}\frac{5}{\text{2}}{\text{O}}_{\text{2}}\text{(g) }\Delta \text{H= 1538 kJ (4)}\end{array}$

To get the required chemical reaction, first, we have to reverse the reaction $(4)$ which will change the sign of enthalpy.

  ${\text{CaC}}_{\text{2}}\text{(s)+}\frac{5}{\text{2}}{\text{O}}_{\text{2}}\text{(g)}\to {\text{CaCO}}_3{\text{(s)+CO}}_{\text{2}}\text{(g) }\Delta \text{H= -1538 kJ (5)}$

Now, add the three reactions $\text{(2)}$ , $(3)$ and $\text{(5)}$ , we get $(1)$ and the enthalpies also get added

  $\begin{array}{l}\text{Ca(s)+2C(s)}\to {\text{CaC}}_{\text{2}}\text{(s) }\Delta \text{H= -62}\text{.8 kJ (2)}\\ {\text{CO}}_{\text{2}}\text{(g)}\to {\text{C(s)+O}}_{\text{2}}\text{(g) }\Delta \text{H= 393}\text{.5 kJ (3)}\\ {\text{CaC}}_{\text{2}}\text{(s)+}\frac{5}{\text{2}}{\text{O}}_{\text{2}}\text{(g)}\to {\text{CaCO}}_3{\text{(s)+CO}}_{\text{2}}\text{(g) }\Delta \text{H= -1538 kJ (5)}\\ \overline{\underset{¯}{\text{Ca(s)+C(s)+}\frac{\text{3}}{\text{2}}{\text{O}}_{\text{2}}\text{(g)}\to {\text{CaCO}}_{\text{3}}\text{(s) }\Delta \text{H= -1207}\text{.3kJ}}}\end{array}$

The heat of the reaction $\text{Ca(s)+C(s)+}\frac{\text{3}}{\text{2}}{\text{O}}_{\text{2}}\text{(g)}\to {\text{CaCO}}_{\text{3}}\text{(s)}$ is $\text{-1207}\text{.3kJ}$