Chapter 10, Problem 33A

Interpretation Introduction

Interpretation:

The enthalpy change of the given reaction needs to be determined.

  $\text{2C}\left(\text{s}\right)\text{+}{\text{H}}_{\text{2}}\left(\text{g}\right)\to {\text{C}}_{\text{2}}{\text{H}}_{\text{2}}\left(\text{g}\right)$

Concept Introduction:

The enthalpy change for the overall reaction is sum of the enthalpy change of the steps in the reaction is known as Hess’s law.

Answer to Problem 33A

ΔH for the reaction is 226 kJ

Explanation of Solution

The given reaction is shown below:

  ${\text{C}}_{\text{2}}{\text{H}}_{\text{2}}\left(\text{g}\right)\text{+}\frac{\text{5}}{\text{2}}{\text{O}}_{\text{2}}\left(\text{g}\right)\to {\text{2CO}}_{\text{2}}\left(\text{g}\right)\text{+}{\text{H}}_{\text{2}}\text{O}\left(\text{l}\right)\text{ΔH}\text{=}\text{-1300}\text{kJ}$ ………(i)

  $\text{C}\left(\text{s}\right)\text{+}{\text{O}}_{\text{2}}\left(\text{g}\right)\to {\text{CO}}_{\text{2}}\left(\text{g}\right)\text{ΔH}\text{=}\text{-394}\text{kJ}$ ……. (ii)

  ${\text{H}}_{\text{2}}\left(\text{g}\right)\text{+}\frac{\text{1}}{\text{2}}{\text{O}}_{\text{2}}\left(\text{g}\right)\to {\text{H}}_{\text{2}}\text{O}\left(\text{l}\right){\text{ΔH}}_3\text{=}\text{-286}\text{kJ}$ ……. (iii)

Reverse the Equation (i) which is shown below:

  ${\text{2CO}}_{\text{2}}\left(\text{g}\right)\text{+}{\text{H}}_{\text{2}}\text{O}\left(\text{l}\right)\to {\text{C}}_{\text{2}}{\text{H}}_{\text{2}}\left(\text{g}\right)\text{+}\frac{\text{5}}{\text{2}}{\text{O}}_{\text{2}}\left(\text{g}\right){\text{ΔH}}_1\text{=}\text{1300}\text{kJ}$ ………(iv)

Multiply the equation(ii) by 2 which is shown below:

  $\text{2C}\left(\text{s}\right)\text{+}2{\text{O}}_{\text{2}}\left(\text{g}\right)\to 2{\text{CO}}_{\text{2}}\left(\text{g}\right){\text{ΔH}}_2\text{=}\text{-788}\text{kJ}$ ……. (v)

Add equation (iii), (iv) and (v) to get the overall equation as follows:

  ${\text{2CO}}_{\text{2}}\left(\text{g}\right)\text{+}{\text{H}}_{\text{2}}\text{O}\left(\text{l}\right)\to {\text{C}}_{\text{2}}{\text{H}}_{\text{2}}\left(\text{g}\right)\text{+}\frac{\text{5}}{\text{2}}{\text{O}}_{\text{2}}\left(\text{g}\right)$

  $\text{2C}\left(\text{s}\right)\text{+}2{\text{O}}_{\text{2}}\left(\text{g}\right)\to 2{\text{CO}}_{\text{2}}\left(\text{g}\right)$

  ${\text{H}}_{\text{2}}\left(\text{g}\right)\text{+}\frac{\text{1}}{\text{2}}{\text{O}}_{\text{2}}\left(\text{g}\right)\to {\text{H}}_{\text{2}}\text{O}\left(\text{l}\right)$

  $\text{2C}\left(\text{s}\right)\text{+}{\text{H}}_{\text{2}}\left(\text{g}\right)\to {\text{C}}_{\text{2}}{\text{H}}_{\text{2}}\left(\text{g}\right)$

The calculation of change in enthalpy of the reaction is shown below:

  $\begin{array}{c}\text{ΔH}\text{=}{\text{ΔH}}_{\text{1}}\text{+}{\text{ΔH}}_{\text{2}}\text{+}{\text{ΔH}}_{\text{3}}\\ \text{=}\text{1300}\text{kJ}\text{+}\left(\text{-788}\text{kJ}\right)\text{+}\left(\text{-286}\text{kJ}\right)\\ \text{=}\text{226}\text{kJ}\end{array}$

Conclusion

ΔH for the reaction is 226 kJ