Question

relationships involving $delta h_{rxn}$, hess’s law (sample)
example 1: calculate the $delta h^{circ}$ for the reaction below:
c (s) + h₂o (g) → co (g) + h₂ (g) $delta h_{rxn}=???$
given the following information:
c(s) + o₂(g) → co₂(g) $delta h=-393.5$ kj
2 co(g) + o₂(g) → 2 co₂(g) $delta h=-566.0$ kj
2 h₂(g) + o₂(g) → 2 h₂o(g) $delta h=-483.6$ kj

Explanation:

Step1: Manipulate the given equations

We want to get the target reaction $C(s)+H_2O(g)
ightarrow CO(g) + H_2(g)$.
The first - given equation is $C(s)+O_2(g)
ightarrow CO_2(g)\quad\Delta H_1=- 393.5\ kJ$.
The second - given equation $2CO(g)+O_2(g)
ightarrow 2CO_2(g)\quad\Delta H_2 = - 566.0\ kJ$ can be rewritten as $CO_2(g)
ightarrow CO(g)+\frac{1}{2}O_2(g)\quad\Delta H_{2}^{'}=\frac{566.0}{2}\ kJ = 283.0\ kJ$ (reverse and divide by 2).
The third - given equation $2H_2(g)+O_2(g)
ightarrow 2H_2O(g)\quad\Delta H_3=-483.6\ kJ$ can be rewritten as $H_2O(g)
ightarrow H_2(g)+\frac{1}{2}O_2(g)\quad\Delta H_{3}^{'}=\frac{483.6}{2}\ kJ = 241.8\ kJ$ (reverse and divide by 2).

Step2: Add the manipulated equations

Adding $C(s)+O_2(g)
ightarrow CO_2(g)$, $CO_2(g)
ightarrow CO(g)+\frac{1}{2}O_2(g)$ and $H_2O(g)
ightarrow H_2(g)+\frac{1}{2}O_2(g)$ together:
$C(s)+O_2(g)+CO_2(g)+H_2O(g)
ightarrow CO_2(g)+CO(g)+\frac{1}{2}O_2(g)+H_2(g)+\frac{1}{2}O_2(g)$
After canceling out the common terms ($CO_2(g)$ and $O_2(g)$ on both sides), we get the target reaction $C(s)+H_2O(g)
ightarrow CO(g)+H_2(g)$.

Step3: Calculate $\Delta H_{rxn}$

According to Hess's law, $\Delta H_{rxn}=\Delta H_1+\Delta H_{2}^{'}+\Delta H_{3}^{'}$.
$\Delta H_{rxn}=-393.5 + 283.0+241.8$.
$\Delta H_{rxn}=131.3\ kJ$.

Answer:

$131.3\ kJ$