D17.6 Standard-state Reaction Enthalpy Change
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.
A standard state is a commonly accepted set of conditions used as a reference point. For chemists, the standard state refers to gases at a pressure of 1 bar, solutions at a concentration of 1 mol/L (1 M), pure solids, or pure liquids. (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 it is possible for ΔrH° to 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:
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 moles of H2(g) reacting with 1 mole of O2(g) to give 2 moles of H2O(g). The heat transfer of energy to the surroundings is then:
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).
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