Heat effects of a chemical reaction are summarized in thermochemical expressions, balanced chemical equations together with values of ΔrH°, the standard-state reaction enthalpy change, and a temperature. The subscript “r” in ΔrH° indicates that the enthalpy change is for a chemical reaction.
The standard-state reaction enthalpy change, ΔrH°, is the standard-state enthalpy of pure, unmixed products minus the standard-state enthalpy of pure, unmixed reactants; that is, the enthalpy change for the reaction under standard-state conditions.
ΔrH° = H°(products) – H°(reactants)
A standard state is a commonly accepted set of conditions used as a reference point. For chemists, the standard state refers to substances under a pressure of 1 bar and solutions at a concentration of 1 mol/L (1 M). (Note that some thermochemical tables may list values with a standard state of 1 atm. Because 1 bar = 0.987 atm, thermochemical values are nearly the same under both sets of standard conditions; however, for accurate work the standard state should be checked.)
The standard state does not specify a temperature. Because ΔrH° can vary slightly with temperature, temperature is typically specified in a thermochemical expression.
We will include a superscript “º” to designate standard state. Thus, the symbol ΔrH°298 K indicates an enthalpy change for a reaction occurring under standard-state conditions and at 298 K.
For example, consider this thermochemical expression:
2 H2(g) + O2(g) ⟶ 2 H2O(g) ΔrH° = -8.031 × 10−22 kJ = −483.6 kJ/mol (25 °C)
This refers to reaction of two molecules of hydrogen with one molecule of oxygen to form two molecules of water, all in the gas phase at 1 bar pressure. If this reaction equation took place once, the two hydrogen molecules and the one oxygen molecule would react to form two water molecules and 8.031 × 10−22 kJ would be transferred to the surroundings.
Because we are interested in laboratory-scale reactions, where moles of reactants are involved, ΔrH° is always reported per mole of reaction rather than for a single reaction event. A mole of reaction involves a chemical reaction equation happening 6.022 × 1023 times; in this case that is 2 mol H2(g) reacting with 1 mol O2(g) to give 2 mol H2O(g). The heat transfer of energy to the surroundings is then:
(8.031 × 10−22 kJ) × (6.022 × 1023 mol−1) = 483.6 kJ/mol
Because the energy transfer is from reaction to surroundings, the sign is negative and ΔrH° = −483.6 kJ/mol.
The following conventions apply to thermochemical expressions:
- In a thermochemical expression, the listed ΔrH° value indicates the heat transfer of energy for the coefficients in the chemical equation. If the coefficients are multiplied by some factor, ΔrH° must be multiplied by that same factor. (The “per mol” in the units of ΔrH° means per mole of reaction as given by the chemical equation.) For example:
2 H2(g) + O2(g) ⟶ 2 H2O(g) ΔrH° = −483.6 kJ/mol two-fold increase: 4 H2(g) + 2 O2(g) ⟶ 4 H2O(g) ΔrH° = 2(−483.6 kJ/mol) = -967.2 kJ/mol two-fold decrease: H2(g) + ½ O2(g) ⟶ H2O(g) ΔrH° = ½(−483.6 kJ/mol) = -241.8 kJ/mol
- ΔrH° of a reaction depends on the physical state of the reactants and products (whether we have gases, liquids, solids, or aqueous solutions), so physical states must be shown.
- Energy is transferred to or from a substance when it changes phase, so a reactant or a product in a different physical state would result in a different ΔrH°.
- A negative ΔrH° indicates an exothermic reaction; a positive ΔrH° indicates an endothermic reaction. If the direction of a chemical equation is reversed, the arithmetic sign of its ΔrH° is changed. (A process that is endothermic when reactants change into products is exothermic when products change into reactants).
Be sure to take both stoichiometry and limiting reactants into account when determining the ΔrH° for a chemical reaction.