Chemistry · General chemistry I · Worked example
Find ΔHf° of magnesium oxide with Hess’s law
A student measures ΔH₁ = −467 kJ for Mg(s) + 2HCl(aq) → MgCl₂(aq) + H₂(g) and ΔH₂ = −151 kJ for MgO(s) + 2HCl(aq) → MgCl₂(aq) + H₂O(l). With ΔH₃ = −285.83 kJ for H₂(g) + ½O₂(g) → H₂O(l), find ΔH for Mg(s) + ½O₂(g) → MgO(s).
Line the steps up with the target
The target has Mg(s) and ½O₂(g) on the left and MgO(s) on the right. Equation 1 has Mg(s) on the left, so it is used as written. Equation 2 has MgO(s) on the left, so it is reversed. Equation 3 supplies the O₂(g).
| Step | Used | ΔH (kJ) |
|---|---|---|
| 1: Mg(s) + 2HCl(aq) → MgCl₂(aq) + H₂(g) | as written | −467 |
| 2: MgO(s) + 2HCl(aq) → MgCl₂(aq) + H₂O(l) | reversed | +151 |
| 3: H₂(g) + ½O₂(g) → H₂O(l) | as written | −285.83 |
Reverse equation 2
Running it backward puts MgO(s) on the product side and changes ΔH₂ = −151 kJ to +151 kJ.
Add the equations and cancel
2HCl(aq), MgCl₂(aq), H₂(g) and H₂O(l) each appear once on each side, in the same state, so they cancel. What is left is the target.
Add the enthalpies
The ΔH values add the same way. −467 and +151 are known to the ones place, so the sum is too.
Read the result
The target makes one mole of MgO(s) from its elements in their standard states, so it is the formation equation: ΔHf°(MgO) ≈ −602 kJ/mol. The two measurements were made near room temperature, so the result approximates the standard value at 25 °C.
Result
ΔH = −602 kJ for Mg(s) + ½O₂(g) → MgO(s), so ΔHf°(MgO) ≈ −602 kJ/mol.
Your turn
Using ΔHf°(MgO) = −602 kJ/mol, find ΔH for MgO(s) → Mg(s) + ½O₂(g) and for 2Mg(s) + O₂(g) → 2MgO(s).
Show the answer and explanation
+602 kJ and −1.20 × 10³ kJ.
The first is the formation equation reversed, so the sign flips: +602 kJ. The second is the formation equation doubled: 2 × (−602 kJ) = −1204 kJ, which is −1.20 × 10³ kJ to the three significant figures of 602.
Keep exploring
In Hess law & thermodynamics, change equation 2’s multiplier from −1 to +1. The studio reports that the steps no longer add up to the target: MgO(s) stays on the left and the HCl(aq), MgCl₂(aq) and water no longer cancel.
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