8.4 Stoichiometry Calculations Using Enthalpy

In Chapter 6 “Stoichiometry and the Mole”, we related quantities of one substance to another in a chemical equation by performing calculations that used the balanced chemical equation; the balanced chemical equation provided equivalences that we used to construct conversion factors. For example, in the balanced chemical equation

2 H₂(g) + O₂(g) → 2 H₂O(ℓ)

we recognized the equivalences

2 mol H₂ ⇔ 1 mol O₂ ⇔ 2 mol H₂O

where ⇔ is the mathematical symbol for “is equivalent to.” In our thermochemical equation, however, we have another quantity—energy change:

2H₂(g) + O₂(g) → 2H₂O(ℓ) ΔH = −570 kJ

This new quantity allows us to add another equivalence to our list:

2 mol H₂ ⇔ 1 mol O₂ ⇔ 2 mol H₂O ⇔ −570 kJ

That is, we can now add an energy amount to the equivalences—the enthalpy change of a balanced chemical reaction. This equivalence can also be used to construct conversion factors so that we can relate enthalpy change to amounts of substances reacted or produced.

Note that these equivalences address a concern. When an amount of energy is listed for a balanced chemical reaction, what amount(s) of reactants or products does it refer to? The answer is that relates to the number of moles of the substance as indicated by its coefficient in the balanced chemical reaction. Thus, 2 mol of H₂ are related to −570 kJ, while 1 mol of O₂ is related to −570 kJ. This is why the unit on the energy change is kJ, not kJ/mol.

For example, consider the thermochemical equation

H₂(g) + Cl₂(g) → 2 HCl(g) ΔH = −184.6 kJ

The equivalences for this thermochemical equation are

1 mol H₂ ⇔ 1 mol Cl₂ ⇔ 2 mol HCl ⇔ −184.6 kJ

Suppose we asked how much energy is given off when 8.22 mol of H₂ react. We would construct a conversion factor between the number of moles of H₂ and the energy given off, −184.6 kJ:

The negative sign means that this much energy is given off.

Like any stoichiometric quantity, we can start with energy and determine an amount, rather than the other way around.

Chemistry Is Everywhere: Welding with Chemical Reactions

One very energetic reaction is called the thermite reaction. Its classic reactants are aluminum metal and iron(III) oxide; the reaction produces iron metal and aluminum oxide:

2 Al(s) + Fe₂O₃(s) → Al₂O₃(s) + 2 Fe(s) ΔH = −850.2 kJ

When properly done, the reaction gives off so much energy that the iron product comes off as a liquid. (Iron normally melts at 1,536°C.) If carefully directed, the liquid iron can fill spaces between two or more metal parts and, after it quickly cools, can weld the metal parts together.

Thermite reactions are used for this purpose even today. For civilian purposes, they are used to reweld broken locomotive axles that cannot be easily removed for repair. They are used to weld railroad tracks together. Thermite reactions can also be used to separate thin pieces of metal if, for whatever reason, a torch doesn’t work.

Thermite reactions are also used for military purposes. Thermite mixtures are frequently used with additional components as incendiary devices—devices that start fires. Thermite reactions are also useful in disabling enemy weapons: a piece of artillery doesn’t work so well when it has a hole melted into its barrel because of a thermite reaction!

Key Takeaway

• The energy change of a chemical reaction can be used in stoichiometry calculations.

Exercises

1. Write the equivalences that this balanced thermochemical equation implies.

   PCl₃(g) + Cl₂(g) → PCl₅(g) ΔH = −87.9 kJ

2. Write the equivalences that this balanced thermochemical equation implies.

   2 SO₃(g) → 2 SO₂(g) + O₂(g) ΔH = 197.9 kJ

3. How many kilojoules are given off when 17.8 mol of CH₄(g) react?

   CH₄(g) + 2 O₂(g) → CO₂(g) + 2 H₂O(ℓ) ΔH = −890.1 kJ

4. How many kilojoules are absorbed when 0.772 mol of N₂(g) reacts?

   N₂(g) + 2 NO(g) → 2 N₂O(g) ΔH = 73.8 kJ

5. How many kilojoules are absorbed when 23.09 mol of C₆H₆(ℓ) are formed?

   6 C(s) + 3 H₂(g) → C₆H₆(ℓ) ΔH = 49.0 kJ

6. How many kilojoules are given off when 8.32 mol of Mg react?

   2 Mg(s) + O₂(g) → 2 MgO(s) ΔH = −1,213 kJ

7. Glucose is the main fuel metabolized in animal cells:

   C₆H₁₂O₆ + 6 O₂ → 6 CO₂ + 6 H₂O ΔH = −2,799 kJ

   How much energy is given off when 100.0 g of C₆H₁₂O₆ react?

8. Given the thermochemical equation

   2 Al(s) + Fe₂O₃(s) → Al₂O₃(s) + 2 Fe(s) ΔH = −850.2 kJ

   how much energy is given off when 288 g of Fe are produced?

9. Given the thermochemical equation

   2 CO₂(g) → 2 CO(g) + O₂(g) ΔH = 566 kJ

   how much energy is absorbed when 85.2 g of CO₂ are reacted?

10. Given the thermochemical equation

    2 Na⁺(aq) + SO₄²⁻(aq) → Na₂SO₄(s) ΔH = 819.8 kJ

    how much energy is absorbed when 55.9 g of Na⁺(aq) are reacted?

11. NaHCO₃ decomposes when exposed to heat:

    2 NaHCO₃(s) → Na₂CO₃(s) + CO₂(g) + H₂O(ℓ) ΔH = 91.5 kJ

    What mass of NaHCO₃ is decomposed by 256 kJ?

12. HgO decomposes when exposed to heat:

    2 HgO(s) → 2 Hg(ℓ) + O₂(g) ΔH = 181.6 kJ

    What mass of O₂ can be made with 100.0 kJ?

13. For the thermochemical equation

    Fe₂O₃(s) + 3 SO₃(g) → Fe₂(SO₄)₃ (s) ΔH = −570.2 kJ

    what mass of SO₃ is needed to generate 1,566 kJ?

14. For the thermochemical equation

    H₂(g) + Br₂(ℓ) → 2 HBr(g) ΔH = −72.6 kJ

    what mass of HBr will be formed when 553 kJ of energy are given off?

Answers

1.

1 mol of PCl₃ ⇔ 1 mol of Cl₂ ⇔ 1 mol of PCl₅ ⇔ −87.9 kJ

3.

15,800 kJ

5.

1,130 kJ

7.

1,554 kJ

9.

548 kJ

11.

470 g

13.

6.60 × 10² g