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The following two reactions are known:
$Fe_2O_3(s) + 3CO(g) \rightarrow 2Fe(s) + 3CO_2(g)$; $\Delta H = -26.8$ kJ
$FeO(s) + CO(g) \rightarrow Fe(s) + CO_2(g)$; $\Delta H = -16.5$ kJ
The value of $\Delta H$ for the following reaction $Fe_2O_3(s) + CO(g) \rightarrow 2FeO(s) + CO_2(g)$ is
$Fe_2O_3(s) + 3CO(g) \rightarrow 2Fe(s) + 3CO_2(g)$; $\Delta H = -26.8$ kJ
$FeO(s) + CO(g) \rightarrow Fe(s) + CO_2(g)$; $\Delta H = -16.5$ kJ
The value of $\Delta H$ for the following reaction $Fe_2O_3(s) + CO(g) \rightarrow 2FeO(s) + CO_2(g)$ is
A
+10.3 kJ
B
−43.3 kJ
C
−10.3 kJ
D
+6.2 kJ
Detailed Solution
(1) $Fe_2O_3 + 3CO \rightarrow 2Fe + 3CO_2$; $\Delta H_1 = -26.8$ kJ
(2) $FeO + CO \rightarrow Fe + CO_2$; $\Delta H_2 = -16.5$ kJ
Reverse (2) and multiply by 2: $2Fe + 2CO_2 \rightarrow 2FeO + 2CO$; $\Delta H = +33.0$ kJ
Add this to (1): $Fe_2O_3 + 3CO + 2Fe + 2CO_2 \rightarrow 2Fe + 3CO_2 + 2FeO + 2CO$
Cancelling common species: $Fe_2O_3 + CO \rightarrow 2FeO + CO_2$
$\Delta H = \Delta H_1 - 2\Delta H_2 = -26.8 - 2(-16.5) = -26.8 + 33.0$
$\Delta H = +6.2$ kJ
(2) $FeO + CO \rightarrow Fe + CO_2$; $\Delta H_2 = -16.5$ kJ
Reverse (2) and multiply by 2: $2Fe + 2CO_2 \rightarrow 2FeO + 2CO$; $\Delta H = +33.0$ kJ
Add this to (1): $Fe_2O_3 + 3CO + 2Fe + 2CO_2 \rightarrow 2Fe + 3CO_2 + 2FeO + 2CO$
Cancelling common species: $Fe_2O_3 + CO \rightarrow 2FeO + CO_2$
$\Delta H = \Delta H_1 - 2\Delta H_2 = -26.8 - 2(-16.5) = -26.8 + 33.0$
$\Delta H = +6.2$ kJ