5.9: Stoichiometry Calculations Using Enthalpy

Previously, 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 equivalents 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 equivalents:

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:

2 H₂ (g) + O₂ (g) → 2 H₂O (ℓ) ΔH = -570 kJ

This new quantity allows us to add another equivalent 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 equivalents—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 equivalents 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 it 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:

2 H₂ (g) + O₂ (g) → 2 H₂O (ℓ) ΔH = −570 kJ

The equivalencies for this thermochemical equation are:

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

Suppose we are 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:

[latex]8.22~\bcancel{mol~H_2}[/latex] x [latex]\frac{-184.6~kJ}{1~\bcancel{mol~H_2}}[/latex] = [latex]-1520~kJ[/latex]

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 = −850.2kJ

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 also 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 does not work when it has a hole melted into its barrel as a result of a thermite reaction!