How do you perform a constant-pressure energy balance for a single-reactant, single-product reacting system to determine heat of reaction?

• A. Q_p = ΔHrxn × ξ (per chosen basis)
• B. Q_p = ΔUrxn × ξ
• C. Q_p = ΔHrxn / ξ
• D. Q_p = ξ / ΔHrxn

Answer: (A)

At constant pressure, the heat flowing into or out of the reacting system equals the enthalpy change of the reaction. For a single-reaction system progressing by an extent of reaction ξ, the total enthalpy change is the reaction enthalpy change per unit progress, ΔHrxn, times ξ. So the heat at constant pressure is Q_p = ΔHrxn × ξ. This aligns with the sign convention: if the reaction is exothermic (ΔHrxn negative) and ξ increases, heat is released (Q_p negative); if endothermic, heat is absorbed (Q_p positive).

The other forms mix up this relationship: using ΔUrxn would apply to a constant-volume scenario, not constant pressure, and dividing or inverting by ξ would misscale the enthalpy change with the reaction extent.