Question

c (s) + o₂ (g) → co₂ (g) δh₁ = -393.5kj
2co (g) + o₂ (g) → 2co₂ (g) δh₂ = -566.0kj
2h₂o (g) → 2h₂ (g) + o₂ (g) δh₃ = 483.6kj
the overall chemical equation is c (s) + h₂o (g) → co (g) + h₂ (g). to calculate the final enthalpy of the overall chemical equation, which step must occur?
divide the third equation by two, and double the enthalpy. then, add.
reverse the second equation, and change the sign of the enthalpy. then, add.
multiply the first equation by three, and triple the enthalpy. then, add.
reverse the first equation, and change the sign of the enthalpy. then, add.

Explanation:

Step1: Match target reactants/products

Target: $\text{C (s)} + \text{H}_2\text{O (g)}
ightarrow \text{CO (g)} + \text{H}_2\text{ (g)}$
Keep 1st equation as-is:
$\text{C (s)} + \text{O}_2\text{ (g)}
ightarrow \text{CO}_2\text{ (g)} \quad \Delta H_1 = -393.5\text{kJ}$

Step2: Reverse and halve 2nd equation

Get $\text{CO}_2\text{ (g)}
ightarrow \text{CO (g)} + \frac{1}{2}\text{O}_2\text{ (g)}$
$\Delta H = \frac{566.0}{2} = 283.0\text{kJ}$

Step3: Halve 3rd equation

Get $\text{H}_2\text{O (g)}
ightarrow \text{H}_2\text{ (g)} + \frac{1}{2}\text{O}_2\text{ (g)}$
$\Delta H = \frac{483.6}{2} = 241.8\text{kJ}$

Step4: Identify required step

Halving the 3rd equation (divide by 2, adjust enthalpy) is needed.

Answer:

Divide the third equation by two, and double the enthalpy. Then, add.