D20.2 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, so Δ_rH 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 Δ_rH°, the standard-state reaction enthalpy change, and a temperature. The subscript “r” in Δ_rH° indicates that the enthalpy change is for a chemical reaction.

The standard-state reaction enthalpy change, Δ_rH°, 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 older 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 Δ_rH° 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 “Δ_rH°_{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, Δ_rH° 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 Δ_rH° = −483.6 kJ/mol.

The following conventions apply to thermochemical expressions:

• In a thermochemical expression, the listed Δ_rH° value indicates the heat transfer of energy for the coefficients in the chemical equation. If the coefficients are multiplied by some factor, Δ_rH° must be multiplied by that same factor. (The “per mol” in the units of Δ_rH° 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

• Δ_rH° 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 Δ_rH°.
• A negative Δ_rH° indicates an exothermic reaction; a positive Δ_rH° indicates an endothermic reaction. If the direction of a chemical equation is reversed, the arithmetic sign of its Δ_rH° is changed. (A process that is endothermic when reactants change into products is exothermic when products change into reactants.)