By John Brennan, Updated Mar 24, 2022

Image credit: tonuacatic/iStock/GettyImages

Calorimetry is a cornerstone of experimental thermochemistry, allowing scientists to determine reaction enthalpies and heat capacities. While many students are comfortable measuring the final temperature (T_f) of a calorimeter experiment, a common classroom challenge is predicting T_f when the reaction enthalpy (ΔH_rxn) and the heat capacities of all components are known. This article walks through that calculation in a clear, systematic way.

Step 1 – Identify the Given Data

Carefully read the problem statement. You’ll typically find:

• ΔH_rxn for the reaction (kJ)
• Heat capacity of the reaction mixture, C_p,contents (kJ g⁻¹ K⁻¹)
• Total mass of the reaction products, m_contents (g)
• Calorimeter constant, C_cal (kJ K⁻¹)
• Initial temperature, T_i (°C)

Step 2 – Assume a Perfect Calorimeter

In an ideal, adiabatic calorimeter, no heat is lost to the surroundings. All heat released by the reaction is absorbed by the calorimeter and its contents.

Step 3 – Set Up the Energy Balance

Because the calorimeter and its contents reach the same final temperature, the heat released equals the heat absorbed:

ΔH_rxn = [C_p,contents × m_contents + C_cal] × (T_i – T_f)

Note the subtraction order: (T_i – T_f). Reaction enthalpies are negative for exothermic processes, so this sign convention keeps the algebra straightforward.

Step 4 – Solve for T_f

Rearrange the equation:

ΔH_rxn / [C_p,contents × m_contents + C_cal] = T_i – T_f

Flip the sign and add T_i:

T_f = T_i – ΔH_rxn / [C_p,contents × m_contents + C_cal]

Step 5 – Plug in the Numbers

Example: ΔH_rxn = –200 kJ, C_p,contents = 0.00418 kJ g⁻¹ K⁻¹, m_contents = 200 g, C_cal = 2 kJ K⁻¹, T_i = 25 °C.

T_f = 25 – [–200 / (0.00418 × 200 + 2)]
    = 25 – [–200 / 2.836]
    = 25 + 70.5
    = 95.5 °C

The final temperature is 95.5 °C.

Things Needed

• Pencil and paper for scratch work
• Scientific calculator (or spreadsheet) for arithmetic

References

• Chemical Principles: The Quest for Insight, Peter Atkins et al., 2008