Calorimetry Enthalpy Calculator
Inputs
| Solution Mass | 100 g |
|---|---|
| Specific Heat | 4,184 J/(kg·K) |
| Temperature Change | 5 °C |
| Moles Reacted | 0.05 mol |
Calorimetry Enthalpy Calculator
Find the reaction enthalpy (heat of reaction) from a coffee-cup calorimetry temperature change. Enter the solution mass, its specific heat, the temperature change, and the moles reacted to get the heat released q = mcΔT in joules and the molar enthalpy ΔH_rxn in kJ/mol.
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Enthalpy of reaction from calorimetry
In a constant-pressure (coffee-cup) calorimeter, a reaction runs in solution and the heat it releases or absorbs shows up as a temperature change in that solution. The heat exchanged with the solution is
q=mcΔT| Symbol | Quantity | Unit |
|---|---|---|
| q | Heat exchanged with the solution | J |
| m | Mass of solution | kg |
| c | Specific heat of solution | J·kg⁻¹·K⁻¹ |
| ΔT | Temperature change | K (= °C change) |
To get the enthalpy per mole of reaction, divide by the moles reacted and flip the sign. The heat gained by the solution was lost by the reacting system, so
ΔHrxn=−nqWhen the temperature rises, ΔT is positive, q is positive, and ΔH comes out negative — the hallmark of an exothermic reaction.
Worked example
A reaction is run in 100 g of dilute aqueous solution. Treating the solution as water gives a specific heat of c = 4184 J·kg⁻¹·K⁻¹. The temperature rises by 5 °C, and 0.05 mol of the limiting reactant is consumed. First find the heat absorbed by the solution, using the mass in kilograms (100 g = 0.1 kg):
q=mcΔT=0.1×4184×5=2092 JThen convert to a molar enthalpy and apply the sign convention:
ΔHrxn=−nq=−0.052092=−41840 J/mol=−41.84 kJ/molThe negative result confirms the reaction is exothermic, consistent with the temperature rise.
Watching the sign convention
The temperature change here is ΔT = T_final − T_initial. Because a degree Celsius and a kelvin are the same size, a change of 5 °C is a change of 5 K, so no temperature conversion is needed for ΔT. The only place the sign matters is the final step: heat flowing into the solution (a temperature rise) means heat flowing out of the reaction, which is why ΔH_rxn carries the opposite sign to q.
| Temperature change | Reaction type | Sign of ΔH |
|---|---|---|
| Solution warms (ΔT > 0) | Exothermic | negative |
| Solution cools (ΔT < 0) | Endothermic | positive |
What the simple model leaves out
This calculation assumes a perfectly insulated calorimeter where every joule goes into the solution, and that the solution behaves like its solvent so the mass and specific heat of water can stand in for the mixture. Real measurements lose some heat to the surroundings and to the cup, so careful work includes a calorimeter constant — the heat capacity of the apparatus itself — and corrects for heat lost during mixing. For a teaching-scale neutralisation or dissolution experiment, the water approximation is usually close enough to recover a meaningful molar enthalpy.
Frequently Asked Questions (FAQ)
How do you calculate enthalpy from calorimetry data?
First find the heat absorbed by the solution: q = m × c × ΔT, where m is the solution mass, c is its specific heat, and ΔT is the temperature change. Then divide by the moles of reactant consumed and flip the sign to get the molar enthalpy: ΔH_rxn = −q / n. The sign flip reflects that heat gained by the solution was lost by the reacting system. Dividing joules by moles gives J/mol, which is usually reported in kJ/mol.
What is a coffee-cup calorimeter?
A coffee-cup calorimeter is a simple constant-pressure calorimeter, often literally an insulated foam cup with a thermometer. A reaction is run in solution and the temperature change of that solution is measured. Because the experiment is open to the atmosphere at constant pressure, the heat measured equals the enthalpy change of the reaction. It is a standard teaching apparatus for measuring heats of neutralisation, dissolution, and other solution reactions.
Why is ΔH negative for an exothermic reaction?
When an exothermic reaction releases heat, that energy flows into the surrounding solution and its temperature rises, so ΔT is positive and q (heat gained by the solution) is positive. Enthalpy, though, is a property of the reacting system, which lost that energy. By convention ΔH_rxn = −q / n, so a positive temperature rise yields a negative ΔH. Endothermic reactions cool the solution, giving a negative ΔT and a positive ΔH.
What assumptions does this calculation make?
It assumes the calorimeter is perfectly insulated, so all the heat goes into the solution and none leaks to the surroundings or is absorbed by the cup itself. It also assumes the solution behaves like its solvent, so the specific heat and mass of water are used for dilute aqueous mixtures. More careful work adds the heat capacity of the calorimeter (its calorimeter constant) and corrects for heat loss during the measurement.
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