The molar heat of reaction is the heat change divided by the number of moles: (delta H) = Q / n, written negative for an exothermic reaction and positive for an endothermic one.
This page walks through heat of reaction per mole for SPM Chemistry, step by step: the formula you need, the units to watch, and a worked example.
When you use this
A heat change measured in the laboratory depends on how much reacted. To compare reactions fairly, and to quote a heat of neutralisation or combustion, SPM Chemistry asks for the heat released per mole, which is the molar heat of reaction.
The formula and units
(delta H) = Q / n
- Q is the heat change from Q = m x c x (theta), in J (or kJ).
- n is the number of moles of the substance the heat is defined per (the acid or water for neutralisation, the fuel for combustion).
- (delta H) is the molar heat of reaction, in kJ mol−1.
Sign. An exothermic reaction (temperature rises) has a negative (delta H); an endothermic reaction (temperature falls) has a positive (delta H). Always convert Q to kJ before dividing, and state the sign.
Worked example 1 (easy)
A reaction releases 5.04 kJ of heat when 0.10 mol of the reactant reacts. Find the molar heat of reaction.
- (delta H) = -Q / n = -5.04 / 0.10 = -50.4 kJ mol−1 (exothermic).
Worked example 2 (medium)
50 cm3 of 1.0 mol dm−3 hydrochloric acid is neutralised by 50 cm3 of 1.0 mol dm−3 sodium hydroxide. The temperature rises by 6.8 °C. Find the heat of neutralisation.
- m = 100 g, so Q = 100 x 4.2 x 6.8 = 2856 J = 2.856 kJ.
- n(water formed) = 1.0 x (50 / 1000) = 0.050 mol.
- (delta H) = -2.856 / 0.050 = -57.1 kJ mol−1 (exothermic).
Worked example 3 (SPM level)
Burning 0.020 mol of ethanol raises the temperature of 250 g of water by 26 °C. Find the heat of combustion of ethanol.
- Q = m x c x (theta) = 250 x 4.2 x 26 = 27300 J = 27.3 kJ.
- (delta H) = -Q / n = -27.3 / 0.020 = -1365 kJ mol−1 (exothermic).
The negative sign shows heat is given out, and dividing by the moles of ethanol gives the value per mole of fuel, which is how heats of combustion are compared in a data table.
Getting the sign and the “per mole of what” right
Two details decide full marks. First, the sign: read the temperature. A rise is exothermic and takes a minus sign; a fall is endothermic and takes a plus. Second, decide what the heat is per mole of. For neutralisation it is per mole of water formed; for combustion it is per mole of fuel burned. Using the correct n is what turns a raw joule figure into the standard molar quantity the exam wants.
Why the value is quoted per mole
A molar heat of reaction lets different reactions be compared fairly, which is why data tables list values per mole. Doubling the amounts of acid and alkali would double the heat released, yet the heat of neutralisation per mole stays the same, so it describes the reaction itself rather than the size of your sample. This is why the exam asks you to complete the molar step even when it has already given you the total heat change, and why quoting the value per mole lets you compare, say, the heats of combustion of a series of alcohols directly.
Common traps
- Dividing the wrong way. It is Q divided by n, never n divided by Q.
- Forgetting the sign. A heat of reaction without + or - is incomplete and loses a mark.
- Mixing J and kJ. Convert Q to kJ before dividing so the answer is in kJ mol−1.
- Using the wrong n. Count moles of the species the heat of reaction is defined per, not of everything present.
Our teachers have students state “exothermic, so negative” (or the reverse) in words before writing the value, so the sign is never an afterthought and the molar step is always shown in full.
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