Thermochemical Equations Versus ∆H Notation

There are two ways to express the ∆H value associated with a balanced chemical equation.

A thermochemical equation includes the energy change as an integral part of the equation.

In an endothermic reaction, the energy absorbed by the reactants to form the products appears on the reactant side of the equation as though the energy itself is a reactant. Of course, energy is not a form of matter, so this cannot be strictly true.

Energy (enthalpy) changes are extensive properties. These are properties that depend on the quantity of material reacting and forming in a reaction. For this reason, the unit for an enthalpy change is kJ/mol. Consequently, if twice as many species react, the magnitude of the enthalpy change should be doubled. In a thermochemical equation, the mole in the denominator of the enthalpy unit actually refers to a mole of the reaction. The following equation shows the decomposition of water:

572 kJ/mol + 2 H2O(l) ➝ 2 H2(g) + O2(g)

It indicates that 572 kJ of energy are required per mole of this reaction. A mole of this reaction involves the decomposition of 2 mol of H2O(l) to form 2 mol of H2(g) and 1 mol of O2(g). Consequently, if 1 mol of water is decomposed, the energy requirement will be half as much, as represented in the following thermochemical equation.

286 kJ/mol + H2O(l) ➝ H2(g) + ½ O2(g)

In an exothermic reaction, the energy released by the reactants as the products are formed appears on the product side of the equation. According to what we’ve learned about bond energy, it should come as no surprise that the equation for the formation of water is simply the reverse of that for the decomposition, including the same magnitude of the heat change.

2 H2(g) + O2(g) ➝ 2 H2O(l) + 572 kJ/mol

The energy released by this reaction is exploited in fuel cells (Figure 4.4.3). The prototype fuel cell was used in the Apollo spacecrafts. These cells were continuously fed with hydrogen and oxygen gas and had the unique advantage of producing drinking water along with energy. The International Space Station continues to rely on fuel cells for energy production in space today.

∆H notation requires the energy change to be specified along with the equation, but written separately following a “∆H =” symbol at the end of the equation.

Endothermic reactions are expressed with a positive ∆H value. Exothermic reactions are, of course, negative. If no sign is shown in front of a ∆H value, it is assumed to be positive.

Decomposition of water: 2 H2O(l) ➝ 2 H2(l) + O2(g) ∆H = +572 kJ/mol

Formation of water: 2 H2(l) + O2(g) ➝ 2 H2O(l) ∆H = –572 kJ/mol

Sample Problem — ∆H Notation and Thermochemical Equations

Given the following ∆H value, write a balanced thermochemical equation and an equation using ∆H notation with the smallest possible whole number coefficients given

∆Hdecomposition of NO2(g) = +33.9 kJ/mol.

What to Think about

1. The decomposition of a binary compound implies the formation of its elements in their standard states (phases they are found in under room conditions). The compound NO2(g) decomposes into nitrogen and oxygen gas, both of which are diatomic.

2. This reaction involves decomposition, hence there is likely more energy required to break reactant bonds than energy is released during the formation of product bonds. This is an endothermic reaction. An endothermic reaction shows the heat of reaction as a reactant. In its unbalanced form, there are 33.9 kJ required for each mole of reactant decomposed.

3. Once this equation is balanced, there are 2 mol of nitrogen dioxide decomposed and hence twice as much heat of reaction.

4. The ∆H notation for an endothermic reaction results in a positive ∆H value. The ∆H notation shows a positive ∆H value adjusted for 2 mol of reactant.

How to Do It

Practice Problems — Representing Exothermic and Endothermic Changes

Given the following ∆H values, write a balanced thermochemical equation and an equation using ∆H notation with the smallest possible whole number coefficients for each of the following chemical changes:

1. ∆Hcombustion of C2H6(g) = –1428.5 kJ/mol

2. ∆Hdecomposition of NH3(g) = 46.1 kJ/mol

3. ∆Hformation of HBr(g) = –36.1 kJ/mol