Chapter 10, Problem 35A

Interpretation Introduction

Interpretation:For the given reaction $\Delta \text{H}°$ is to becalculated. 

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

Concept introduction:According to Hess' law for any process, the change in enthalpy will not depend on the initial and final states and it is same whether a reaction takes place in one or more than one step.

Answer to Problem 35A

  $\Delta \text{H}°$ for the given reaction equation is -11kJ.

Explanation of Solution

The given equations are as follows:

  ${\text{Fe}}_{\text{2}}{\text{O}}_{\text{3}}\left(s\right)+3\text{CO}\left(g\right)\to 2\text{Fe}\left(s\right){\text{+3CO}}_{\text{2}}\left(g\right)\Delta \text{H}°\text{=}-23\text{kJ}$ …… (1)

  ${\text{3Fe}}_{\text{2}}{\text{O}}_{\text{3}}\left(s\right)+\text{CO}\left(g\right)\to 2{\text{Fe}}_{\text{3}}{\text{O}}_{\text{4}}\left(s\right){\text{+CO}}_{\text{2}}\left(g\right)\Delta \text{H}°\text{=}-39\text{kJ}$ …… (2)

  ${\text{Fe}}_3{\text{O}}_4\left(s\right)+\text{CO}\left(g\right)\to 3\text{FeO}\left(s\right){\text{+CO}}_{\text{2}}\left(g\right)\Delta \text{H}°\text{=+18kJ}$ …… (3)

Multiplyreaction equation (1) with 3 is as follows:

  ${\text{3Fe}}_{\text{2}}{\text{O}}_{\text{3}}\left(s\right)+9\text{CO}\left(g\right)\to 6\text{Fe}\left(s\right){\text{+9CO}}_{\text{2}}\left(g\right)\Delta \text{H}°\text{=}-69\text{kJ}$ …… (4)

Reverse reaction equation (2) is as follows:

  $2{\text{Fe}}_{\text{3}}{\text{O}}_{\text{4}}\left(s\right){\text{+CO}}_{\text{2}}\left(g\right)\to {\text{3Fe}}_{\text{2}}{\text{O}}_{\text{3}}\left(s\right)+\text{CO}\left(g\right)\Delta \text{H}°\text{=+}39\text{kJ}$ …… (5)

Reverse reaction equation (3) and multiply with 2 is as follows:

  $6\text{FeO}\left(s\right){\text{+2CO}}_{\text{2}}\left(g\right)\to 2{\text{Fe}}_3{\text{O}}_4\left(s\right)+2\text{CO}\left(g\right)\Delta \text{H}°\text{=}-36\text{kJ}$ …… (6)

To get given reaction equation add the reactions that present in equation (4), (5) and (6) is as follows:

  $\text{6FeO}\left(s\right)+6\text{CO}\left(g\right)\to 6\text{Fe}\left(s\right)+6{\text{CO}}_{\text{2}}\left(g\right)\Delta \text{H°=}-66\text{kJ}$

Divide resultant reaction equation with 6 is as follows:

  $\text{FeO}\left(s\right)+\text{CO}\left(g\right)\to \text{Fe}\left(s\right)+{\text{CO}}_{\text{2}}\left(g\right)\Delta \text{H°=}-11\text{kJ}$

Thus, $\Delta \text{H}°$ for the given reaction equation is -11kJ.

Conclusion

Given overall equation is as follows:

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

For this reaction $\Delta \text{H}°$ is -11kJ.