D21.2 Standard-state Reaction Enthalpy Change
We said previously that bond enthalpies apply only to gas-phase reactions and bond enthalpies are averages over many different molecules. Therefore, ΔrH values calculated from bond enthalpies are not exact. More accurate values of enthalpy changes can be determined using calorimetric measurements and tabulating the results. For a given chemical reaction, such measurements are summarized in a thermochemical expression, a balanced chemical equation together with the value 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.
The standard state does not specify a temperature. (Because it is possible for ΔrH° to vary slightly with temperature, temperature is typically specified as part of the 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.
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 because the strength of intermolecular attractions changes, so a reactant or a product in a different physical state results 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.)
Exercise: Standard Reaction Enthalpy
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