Library / Foundations: Chemistry / FCH-16

Foundations: Chemistry

Enthalpy change from calorimetry

Heat of reaction from the temperature rise of a solution.

Ref: FCH-16
Rev: v1
Field: Foundations: Chemistry
Result: ΔH [kJ/mol]

Q = m c Δ T, Δ H = - \frac{Q}{n}

Q is the heat absorbed by the solution (in J), m its mass in g, c its specific heat capacity (4.18 J g⁻¹ K⁻¹ for water) and n the moles of the limiting reagent. The minus sign makes a temperature rise give a negative (exothermic) ΔH.

A reaction that warms the water has given out energy. The temperature rise tells you how much, and dividing by the moles gives the energy per mole.

Calculator

Solve for

ΔHEnthalpy changeComputed

kJ/mol

mMass of solution

5500

cSpecific heat capacity

J/(g K)

0.110

ΔTTemperature rise

0.150

nMoles of limiting reagent

mol

0.0011

Heat absorbed by the solution1.359 kJ
Heat per gram of solution27.17 J/g

What drives the result

Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.

Enthalpy change (kJ/mol) current value −54.34 kJ/mol

nMoles of limiting reagentKey driver

−1,360−1.36

mMass of solution

−543−5.43

ΔTTemperature rise

−418−0.836

cSpecific heat capacity

−130−1.3

Neutralisation of a strong acid with a strong alkali gives about −57 kJ/mol; polystyrene cup losses make the measured value a little lower.
Heat lost to the surroundings is the main source of error, so insulate the cup and use a lid.

Chart data as tables

Ranked variables

Variable	Typical range	Lowest result	Highest result	Swing (kJ/mol)	Local step	Change in result
n Moles of limiting reagent	0.001 to 1 mol	−1,359	−1.359	1,357	+10%	−9.09 %
m Mass of solution	5 to 500 g	−543.4	−5.434	538	+10%	+10 %
ΔT Temperature rise	0.1 to 50 K	−418	−0.836	417.2	+10%	+10 %
c Specific heat capacity	0.1 to 10 J/(g K)	−130	−1.3	128.7	+10%	+10 %

Sweep of Temperature rise

Temperature rise (K)	Enthalpy change (kJ/mol)
0.1	−0.836
6.337	−52.98
12.57	−105.1
18.81	−157.3
25.05	−209.4
31.29	−261.6
37.52	−313.7
43.76	−365.9
50	−418

Sweep one variable

Vary

Enthalpy change (kJ/mol)Hover, touch, or use the arrow keys on the chart

Variables and how each one contributes

ΔH

Enthalpy change

Result · kJ/mol

What the equation gives you. Everything else feeds it.

Mass of solution

g · typical 5 to 500

Mass of solution heated (1 cm³ of water ≈ 1 g). Directly proportional to Q.

Specific heat capacity

J/(g K) · typical 0.1 to 10

4.18 for water-based solutions. Directly proportional to Q.

ΔT

Temperature rise

K · typical 0.1 to 50

Rise in temperature of the solution. Directly proportional to Q.

Moles of limiting reagent

mol · typical 0.001 to 1

Moles of the reagent that is used up. Inversely proportional.

Worked example with the values above

Q = m c ΔT = 50 × 4.18 × 6.5 = 1,359 J = 1.359 kJ.
Divide by the moles: 1.359 / 0.025.
ΔH = −54.34 kJ/mol (negative: exothermic).

Assumptions and limits

Solution has the properties of water.
No heat lost to the surroundings.

Common mistakes

Dividing by the mass of reactants instead of the moles.
Giving the wrong sign.

Statistics and uncertainty

Heat loss and thermometer reading error (±0.5 K on 6.5 K is 8%) make ΔH from a simple cup experiment uncertain by 5–10%.

Where it is used

Measuring energy of fuels and reactions.
Checking neutralisation heats.

Maths you need

Specific heat capacity: Q = m c ΔT
Moles: n = c V

Related formulas

Practise this formula