Lab: Coffee-Cup Calorimetry and Heat of Reaction

A coffee cup is open to the atmosphere, so the reaction happens at constant pressure. Under that condition the heat exchanged is equal to the enthalpy change, which is exactly the quantity thermochemical equations report.

The connection qp = ΔH assumes the pressure is effectively constant and the only work is pressure-volume work. For an electrical or electrochemical apparatus doing additional work, that short statement needs modification. In ordinary cup experiments, measure the temperature change of the solution and cup, then infer the chemical heat through conservation; the thermometer does not directly read a reaction enthalpy.

Measure total solution mass and ΔT; compute solution heat (and calibrated cup heat when supplied); use an energy balance to obtain reaction heat; then divide by the amount corresponding to the requested molar basis. For ν mol of limiting reactant per mole of reaction as written, ξ = n(limiting)/ν and ΔrH = q(reaction)/ξ. For 2 H₂ + O₂ → 2 H₂O, reacting 0.20 mol H₂ corresponds to 0.10 mol of reaction, not 0.20 mol. Dividing by moles of H₂ instead reports heat per mole H₂.

Suppose 50.0 mL of 1.00 M HCl reacts with 40.0 mL of 1.00 M NaOH. The supplied amounts are 0.0500 mol H⁺ and 0.0400 mol OH⁻, so 0.0400 mol water forms and acid remains in excess. With additive volumes, density 1.00 g/mL, c = 4.18 J/(g·°C), ΔT = 6.00 °C and Ccal = 10.0 J/°C, qsurroundings = (90.0)(4.18)(6.00) + (10.0)(6.00) = 2317.2 J. Thus qreaction = −2.3172 kJ and ΔH = −2.3172/0.0400 = −57.9 kJ/mol water. Dividing by the excess 0.0500 mol acid would assign heat to acid that did not react.

Dilute aqueous solutions are treated as having density 1.00 g/mL and specific heat 4.18 J/g C. The polystyrene cup is assumed to absorb negligible heat unless a calorimeter constant is supplied. Both assumptions are approximations and should be stated when reporting a result.

Both starting solutions should have known, preferably equal temperatures. If their temperatures differ, account for their thermal mixing before attributing the whole thermometer change to reaction. The water-like density and c approximations are most reasonable for dilute solutions; concentrated salts or acids can differ appreciably. Include all solution mass, but do not double-count the cup if the supplied calibration already represents the whole calorimeter assembly.

For an exothermic reaction, heat escaping to air or absorbed by an unaccounted cup can reduce the measured solution temperature rise, making the inferred molar enthalpy less negative. A concentration error has no universal direction: if reaction heat is held fixed, overestimating reacting moles reduces |q/n| and underestimating them increases it; in a real run the reaction extent and measured heat may also change. Trace each error through q and the chosen mole denominator separately.

Record temperature before, during and after mixing rather than one late reading. Extrapolating the post-reaction cooling trend back toward the mixing time estimates the rise before heat loss, if the lab method permits it. For an endothermic event the surroundings can supply heat from the room, reducing the observed cooling and biasing a positive ΔH toward zero. Incomplete reaction also reduces measured heat, but its effect on molar ΔH depends on whether the denominator uses the actually reacted amount or the planned amount. Trace both parts of q/n.