The heat change is Q = m x c x (theta): mass of solution times specific heat capacity (4.2 J g-1 °C-1) times the temperature change; a temperature rise means an exothermic reaction.
This page walks through heat change of a reaction for SPM Chemistry, step by step: the formula you need, the units to watch, and a worked example.
When you use this
Thermochemistry experiments in SPM Chemistry measure a temperature change and ask for the heat energy involved. Whether it is neutralisation, displacement or dissolving, the heat released or absorbed by the solution is found the same way.
The formula and units
Q = m x c x (theta)
- Q is the heat change, in joules (J).
- m is the mass of the solution, in grams (g). Because dilute solutions have a density close to 1 g cm−3, the mass in grams equals the volume in cm3.
- c is the specific heat capacity, taken as that of water, 4.2 J g-1 °C-1.
- (theta) is the temperature change, in degrees Celsius (°C).
Units. Multiply g by J g-1 °C-1 by °C to get J; divide by 1000 for kilojoules (kJ). A temperature rise means heat is released (exothermic); a temperature fall means heat is absorbed (endothermic).
Worked example 1 (easy)
100 cm3 of water is warmed and its temperature rises by 12 °C. Find the heat absorbed by the water.
- m = 100 g (since 100 cm3 of water has mass 100 g).
- Q = 100 x 4.2 x 12 = 5040 J = 5.04 kJ.
Worked example 2 (medium)
50 cm3 of acid is mixed with 50 cm3 of alkali. The temperature of the mixture rises by 6.8 °C. Find the heat released by the neutralisation.
- Total volume = 100 cm3, so m = 100 g.
- Q = 100 x 4.2 x 6.8 = 2856 J = 2.856 kJ (exothermic).
Worked example 3 (SPM level)
Excess zinc powder is added to 50 cm3 of copper(II) sulfate solution. The temperature rises from 28.5 °C to 40.2 °C. Find the heat released by this displacement reaction.
- (theta) = 40.2 - 28.5 = 11.7 °C.
- m = 50 g (the mass of the solution, not the zinc).
- Q = 50 x 4.2 x 11.7 = 2457 J = 2.457 kJ (exothermic).
Which mass and which value of c
The single most important decision is what mass to use. You use the mass of the solution being heated, found from its volume and a density of 1 g cm−3, not the mass of the metal or solid added. The specific heat capacity is always taken as 4.2 J g-1 °C-1, the value for water, because the solution is mostly water. These two assumptions are stated in the syllabus and are expected in every calculation; getting them right is where the method marks sit.
Exothermic or endothermic?
The direction of the temperature change tells you the type of reaction, and this is often asked alongside the number. If the thermometer reading rises, the reaction gives out heat to the solution and is exothermic; if it falls, the reaction takes in heat and is endothermic. Neutralisation, combustion and most displacement reactions are exothermic, while dissolving certain salts such as ammonium nitrate is endothermic. Stating the type in words, with the temperature change as your evidence, earns the explanation mark that accompanies the calculation.
Common traps
- Using the mass of the solid. The heat warms the solution; use the solution’s mass, not the zinc or the metal.
- Forgetting the density step. Convert cm3 to g using 1 g cm−3 before multiplying.
- Leaving Q in joules when kilojoules are asked. Divide by 1000, and state the unit.
- Getting (theta) wrong. It is the difference between final and initial temperature, always taken as a positive size.
Our teachers have students write m, c and (theta) with their units before substituting, so the mass of solution is never confused with the mass of solid and no calculation loses its easy marks.
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