q = mcΔT
Choose what to solve for
Specific heats from the workbook reference (water 4.184 J·g⁻¹·°C⁻¹). Methodology & sources →
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q is the heat transferred. A positive value means the substance absorbed heat (it warmed up); a negative value means it released heat. The specific heat c tells you how much energy one gram needs to change by one degree — water's high value (4.184 J·g⁻¹·°C⁻¹) is why it resists temperature change. In coffee-cup calorimetry the heat of reaction is the opposite of the heat gained by the solution: q_rxn = −q_solution.
Worked Example — Heat of Solution from Calorimetry Data
Question: 0.205 g of KOH is dissolved in 55.9 g of water in a coffee-cup calorimeter. The temperature rises from 23.5°C to 24.4°C. Find ΔHsoln in kJ/mol. Assume cp = 4.184 J g⁻¹ °C⁻¹.
Step 1 — heat absorbed by the solution: qsoln = mcΔT = (55.9 + 0.205) × 4.184 × (24.4 − 23.5) = 210.9 J
Step 2 — heat of reaction: qrxn = −qsoln = −210.9 J (the dissolution releases heat into the solution)
Step 3 — moles of KOH (M = 56.11 g/mol): n = 0.205 ÷ 56.11 = 3.65 × 10⁻³ mol
Step 4 — molar enthalpy: ΔHsoln = qrxn ÷ n = −210.9 ÷ 3.65×10⁻³ = −57,700 J/mol = −57.7 kJ/mol
Answer: ΔHsoln = −57.7 kJ/mol (exothermic, since the temperature rose).
Common Mistakes
- Sign convention. A temperature rise means the reaction released heat into the solution — so qrxn is negative (exothermic), even though qsoln (heat gained by the solution) is positive. They are equal in size and opposite in sign.
- Which mass to use. Use the total mass of the resulting solution (solute + solvent) in q = mcΔT, not just the solvent — though for dilute solutions the solute mass is often small enough to be a minor correction.
- J vs. kJ. q = mcΔT gives joules when cp is in J g⁻¹°C⁻¹. Divide by 1000 to report ΔH in kJ/mol, and divide by n after converting, or be consistent throughout.
Frequently Asked Questions
Heat (q) equals mass (m) × specific heat (c) × temperature change (ΔT). Positive q is heat absorbed, negative q is heat released.
4.184 J·g⁻¹·°C⁻¹. Presets for ice, steam, aluminium, iron, copper and gold are in the dropdown.
Energy is conserved: heat that leaves the chemical reaction (qrxn, if exothermic) is the same heat that enters the surrounding solution (qsoln). Since one is heat leaving and the other is heat arriving, they have equal magnitude but opposite sign — this is the basic assumption behind calorimetry.
For dilute aqueous solutions, cₐ of pure water (4.184 J g⁻¹ °C⁻¹) is the standard approximation, since water dominates the mass and heat capacity of the mixture. For concentrated solutions or non-aqueous solvents, a different, measured specific heat should be used if known.