Coffee-Cup Calorimetry: Why Is the Enthalpy Too Small?
Students dissolve 5.00 g of ammonium nitrate, NH4NO3, in 50.0 mL of water in a coffee-cup calorimeter. They record an initial temperature of 22.4 °C and, after stirring, a final temperature of 16.8 °C. The class assumes the solution has the density of water (1.00 g/mL) and a specific heat of 4.18 J/(g·°C), and neglects the calorimeter’s own heat capacity. A student calculates the enthalpy of solution and gets a value that is lower than the accepted +25.7 kJ/mol. Another student says the sign should be negative because the temperature went down. The teacher wants students to use the data to evaluate both the sign and the magnitude of the result, and to propose improvements rather than simply calling the difference “human error.”
1. Calculate the heat transferred and the enthalpy of solution per mole of NH4NO3. State and justify the sign.
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Mass of solution ≈ 50.0 mL × 1.00 g/mL + 5.00 g = 55.0 g. ΔT = 16.8 °C − 22.4 °C = −5.6 °C. q_solution = m c ΔT = (55.0 g)(4.18 J/(g·°C))(−5.6 °C) = −1.29 × 10^3 J = −1.29 kJ. The solution lost heat, so the reaction absorbed it: q_reaction = +1.29 kJ. Moles NH4NO3 = 5.00 g / 80.04 g/mol = 0.0625 mol. ΔH_solution = q_reaction / n = +1.29 kJ / 0.0625 mol = +20.6 kJ/mol. The sign is positive because dissolving ammonium nitrate is endothermic; the temperature drop is evidence that the system absorbed heat from the solution, not that the enthalpy is negative.
2. The class value is lower than the accepted +25.7 kJ/mol. Identify two plausible sources of error and state whether each would make the measured ΔH too low or too high.
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One source is heat leaking in from the room: the solution is colder than the surroundings, so it absorbs heat during the experiment, making the observed temperature drop smaller. That makes q_reaction and ΔH too low (less positive). A second source is neglecting the calorimeter’s heat capacity: the cup and thermometer also cool and release heat to the reaction, again reducing the measured temperature drop and making ΔH too low. A third source is incomplete dissolution: undissolved NH4NO3 means less endothermic process per mole, also making ΔH too low. By contrast, overestimating the solution mass would make q and ΔH too high, so not every error points the same way. The direction of the error matters.
3. Propose two specific improvements to the calorimetry design and explain how each would reduce the discrepancy.
Read the worked answer
First, use a calorimeter with a known heat capacity and include it in the calculation: q_reaction = −(q_solution + q_calorimeter), where q_calorimeter = C_cal ΔT. This corrects for heat exchanged with the cup and thermometer and should raise the measured ΔH toward the accepted value. Second, insulate the calorimeter better (lid, nested cups, or a commercial calorimeter) and use a temperature sensor to record a cooling curve, then extrapolate back to the time of mixing. This reduces heat exchange with the room and corrects for the fact that the reaction and temperature measurement are not instantaneous. Using a more precise mass for the solution and confirming complete dissolution would also help. These changes target specific error directions rather than just adding more trials.