Measurement of ΔU and ΔH: Calorimetry

The figure shows a simple calorimeter built from a foamed-polystyrene cup, a lid, a thermometer, and a stirrer. The cup sits open to the atmosphere, so the entire experiment proceeds at constant pressure — the pressure of the room. Inside the cup is the reaction mixture, and the thermometer dips into it to record the temperature change as the reaction proceeds. The stirrer ensures the temperature is uniform throughout the mixture.

The physical idea is straightforward: if a reaction happens at constant pressure, the heat exchanged with the surroundings equals the change in enthalpy, $\Delta H$. By measuring the temperature rise (or fall) of the known mass of the reaction mixture, you can calculate the heat absorbed or released. The calorimeter itself is well insulated by the foam, so very little heat escapes to the surroundings — nearly all the heat from the reaction stays inside the cup and warms (or cools) the mixture.

The key formula that emerges from this figure is the one used to compute $\Delta H$ from the measured temperature change:

Here $q_p$ is the heat exchanged at constant pressure (which equals $\Delta H$ for the reaction), $m$ is the mass of the reaction mixture (in grams), $c$ is its specific heat capacity (in $\text{J g}^{-1} \text{K}^{-1}$), and $\Delta T$ is the change in temperature (in K or °C — the numerical value is the same for a difference). For dilute aqueous solutions, $c$ is taken as $4.18\ \text{J g}^{-1} \text{K}^{-1}$, the specific heat capacity of water.

The textbook then uses this measured $q_p$ to find the enthalpy change per mole of reactant. If $n$ moles of the limiting reactant are consumed, the molar enthalpy change is:

$\Delta H_{\text{reaction}} = \frac{q_p}{n}$ …