8.4 Stoichiometry Calculations Using Enthalpy
Learning Objective
1. Perform stoichiometry calculations using energy changes from thermochemical equations.
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 H_{2}(g) + O_{2}(g) → 2 H_{2}O(ℓ)
we recognized the equivalences
2 mol H_{2} ⇔ 1 mol O_{2} ⇔ 2 mol H_{2}O
where ⇔ is the mathematical symbol for “is equivalent to.” In our thermochemical equation, however, we have another quantity—energy change:
2H_{2}(g) + O_{2}(g) → 2H_{2}O(ℓ) ΔH = −570 kJ
This new quantity allows us to add another equivalence to our list:
2 mol H_{2} ⇔ 1 mol O_{2} ⇔ 2 mol H_{2}O ⇔ −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 H_{2} are related to −570 kJ, while 1 mol of O_{2} 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
H_{2}(g) + Cl_{2}(g) → 2 HCl(g) ΔH = −184.6 kJ
The equivalences for this thermochemical equation are
1 mol H_{2} ⇔ 1 mol Cl_{2} ⇔ 2 mol HCl ⇔ −184.6 kJ
Suppose we asked how much energy is given off when 8.22 mol of H_{2} react. We would construct a conversion factor between the number of moles of H_{2} and the energy given off, −184.6 kJ:
The negative sign means that this much energy is given off.
Example 8
Given the thermochemical equation
N_{2}(g) + 3 H_{2}(g) → 2 NH_{3}(g) ΔH = −91.8 kJ
how much energy is given off when 222.4 g of N_{2} reacts?
Solution
The balanced thermochemical equation relates the energy change to moles, not grams, so we first convert the amount of N_{2} to moles and then use the thermochemical equation to determine the energy change:
Test Yourself
Given the thermochemical equation
N_{2}(g) + 3 H_{2}(g) → 2 NH_{3}(g) ΔH = −91.8 kJ
how much heat is given off when 1.00 g of H_{2} reacts?
Answer
−15.1 kJ
Like any stoichiometric quantity, we can start with energy and determine an amount, rather than the other way around.
Example 9
Given the thermochemical equation
N_{2}(g) + O_{2}(g) → 2 NO(g) ΔH = 180.6 kJ
if 558 kJ of energy are supplied, what mass of NO can be made?
Solution
This time, we start with an amount of energy:
Test Yourself
How many grams of N_{2} will react if 100.0 kJ of energy are supplied?
N_{2}(g) + O_{2}(g) → 2 NO(g) ΔH = 180.6 kJ
Answer
15.5 g
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) + Fe_{2}O_{3}(s) → Al_{2}O_{3}(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

Write the equivalences that this balanced thermochemical equation implies.
PCl_{3}(g) + Cl_{2}(g) → PCl_{5}(g) ΔH = −87.9 kJ

Write the equivalences that this balanced thermochemical equation implies.
2 SO_{3}(g) → 2 SO_{2}(g) + O_{2}(g) ΔH = 197.9 kJ

How many kilojoules are given off when 17.8 mol of CH_{4}(g) react?
CH_{4}(g) + 2 O_{2}(g) → CO_{2}(g) + 2 H_{2}O(ℓ) ΔH = −890.1 kJ

How many kilojoules are absorbed when 0.772 mol of N_{2}(g) reacts?
N_{2}(g) + 2 NO(g) → 2 N_{2}O(g) ΔH = 73.8 kJ

How many kilojoules are absorbed when 23.09 mol of C_{6}H_{6}(ℓ) are formed?
6 C(s) + 3 H_{2}(g) → C_{6}H_{6}(ℓ) ΔH = 49.0 kJ

How many kilojoules are given off when 8.32 mol of Mg react?
2 Mg(s) + O_{2}(g) → 2 MgO(s) ΔH = −1,213 kJ

Glucose is the main fuel metabolized in animal cells:
C_{6}H_{12}O_{6} + 6 O_{2} → 6 CO_{2} + 6 H_{2}O ΔH = −2,799 kJ
How much energy is given off when 100.0 g of C_{6}H_{12}O_{6} react?

Given the thermochemical equation
2 Al(s) + Fe_{2}O_{3}(s) → Al_{2}O_{3}(s) + 2 Fe(s) ΔH = −850.2 kJ
how much energy is given off when 288 g of Fe are produced?

Given the thermochemical equation
2 CO_{2}(g) → 2 CO(g) + O_{2}(g) ΔH = 566 kJ
how much energy is absorbed when 85.2 g of CO_{2} are reacted?

Given the thermochemical equation
2 Na^{+}(aq) + SO_{4}^{2−}(aq) → Na_{2}SO_{4}(s) ΔH = 819.8 kJ
how much energy is absorbed when 55.9 g of Na^{+}(aq) are reacted?

NaHCO_{3} decomposes when exposed to heat:
2 NaHCO_{3}(s) → Na_{2}CO_{3}(s) + CO_{2}(g) + H_{2}O(ℓ) ΔH = 91.5 kJ
What mass of NaHCO_{3} is decomposed by 256 kJ?

HgO decomposes when exposed to heat:
2 HgO(s) → 2 Hg(ℓ) + O_{2}(g) ΔH = 181.6 kJ
What mass of O_{2} can be made with 100.0 kJ?

For the thermochemical equation
Fe_{2}O_{3}(s) + 3 SO_{3}(g) → Fe_{2}(SO_{4})_{3} (s) ΔH = −570.2 kJ
what mass of SO_{3} is needed to generate 1,566 kJ?

For the thermochemical equation
H_{2}(g) + Br_{2}(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 PCl_{3} ⇔ 1 mol of Cl_{2} ⇔ 1 mol of PCl_{5} ⇔ −87.9 kJ
3.
15,800 kJ
5.
1,130 kJ
7.
1,554 kJ
9.
548 kJ
11.
470 g
13.
6.60 × 10^{2} g