Measurement of ΔU and ΔH using Calorimetry

Measuring $\Delta U$: the bomb calorimeter. For chemical reactions, heat evolved at constant volume is measured using a bomb calorimeter. The inner vessel -- the "bomb" itself -- and its cover are made of strong steel, with the cover fitted tightly using a metal lid and screws, so the sealed volume genuinely cannot change during the reaction.

A weighed amount of the sample sits in a small platinum cup, connected to electrical ignition wires that can strike an arc to instantly kindle combustion. The bomb is closed tightly and pressurised with excess oxygen, then immersed in water inside the calorimeter's inner volume; a stirrer sits in the gap between the calorimeter wall and the bomb, keeping the surrounding water uniformly mixed. Striking the sample electrically starts the reaction.

A known amount of combustible substance burns in the oxygen inside the sealed bomb. The heat evolved is absorbed both by the calorimeter itself and by the water surrounding it, and the resulting temperature rise is read on a sensitive Beckman thermometer. Because the bomb is sealed, its volume cannot change -- so whatever heat is measured this way IS, by definition, the heat of combustion at CONSTANT VOLUME, $\Delta U_C^0$.

The total heat produced, $\Delta U_C^0$, is the sum of the heat absorbed by the calorimeter and by the water:

• Heat absorbed by the calorimeter: $q_1=k\Delta T$, where $k=m_cC_c$ is the calorimeter constant ($m_c$ = mass of the calorimeter, $C_c$ = its heat capacity).
• Heat absorbed by the water: $q_2=m_wC_w\Delta T$, where $m_w$ is the mass of water and $C_w$ is its molar heat capacity ($75.29\ \text{J K}^{-1}\text{mol}^{-1}$).

The calorimeter constant $k$ itself is found by burning a KNOWN mass of a standard reference sample -- benzoic acid, whose heat of combustion is accurately known ($-3227\ \text{kJ mol}^{-1}$) -- and back-calculating $k$ from the resulting $\Delta T$. …

Measuring $\Delta H$: the coffee-cup calorimeter. Heat change at constant (atmospheric) pressure can instead be measured using a much simpler apparatus -- a coffee-cup calorimeter. Instead of the bomb calorimeter's sealed steel vessel, a styrofoam cup is used. Styrofoam makes a good adiabatic wall: it doesn't allow the heat produced by the reaction to transfer out to the surroundings, so essentially all of that heat energy is absorbed by the water sitting inside the cup itself. This method is suitable specifically for reactions where there is no appreciable change in volume (so no meaningful expansion work needs to be accounted for separately).

The temperature change of the water is measured and converted to a heat quantity using

where $m_w$ is the mass of water present and $C_w$ is its molar heat capacity ($75.29\ \text{J K}^{-1}\text{mol}^{-1}$, the same value used for the bomb calorimeter). …

Application 1: calculating a heat of formation from combustion data. Because the heat of combustion of many organic compounds can be measured with relative ease (Sections ~7.7.1/~7.7.2), it is frequently used to back out a heat of FORMATION that would be much harder to measure directly. Worked example: finding $\Delta H_f^0$ of methane from the known combustion enthalpies of H$_2$ ($-285.8$), C(graphite) ($-393.5$), and CH$_4$ itself ($-890.4$ kJ mol$^{-1}$), remembering that the standard formation enthalpy of every pure element is defined as zero. Write out the target formation equation and the three combustion equations as a thermochemical set:

Since methane sits on the PRODUCT side of the target equation (i), reaction (iv) must be reversed:

Combining by Hess's law, (i) $=$ [(ii)$\times2$] $+$ (iii) $+$ (v):

So the heat of formation of methane works out to $-74.7\ \text{kJ mol}^{-1}$.

Application 2: calorific value of food and fuels. The calorific value is defined as the amount of heat produced (in calories or joules) when one gram of a substance is completely burnt. Its SI unit is $\text{J kg}^{-1}$, though in practice it is usually quoted in $\text{cal g}^{-1}$.

The rest of the enthalpy catalogue. Rounding off the list of named enthalpy quantities begun back in Section 7.5.2:

Heat of solution -- the change in enthalpy when one mole of a substance dissolves in a specified quantity of solvent at a given temperature.

Heat of neutralisation -- "the change in enthalpy when one gram equivalent of an acid is completely neutralised by one gram equivalent of a base (or vice versa) in dilute solution." Remarkably, this comes out to almost exactly the SAME value, $-57.32$ kJ, for ANY strong acid neutralised by any strong base:

The reason is Arrhenius's theory of acids and bases: strong acids and strong bases both ionise COMPLETELY in aqueous solution, so in every one of the reactions above, what is really happening -- underneath the spectator ions -- is the identical net-ionic reaction

which is why the measured heat of neutralisation stays constant regardless of which particular strong acid or strong base was used.

Molar heat of fusion -- "the change in enthalpy when one mole of a solid substance is converted into the liquid state at its melting point." Example, ice: $H_2O(s)\xrightarrow{273\text{K}}H_2O(l)$, $\Delta H_{fusion}=+5.98$ kJ.

Molar heat of vapourisation -- "the change in enthalpy when one mole of liquid is converted into vapour state at its boiling point." Example, water: $H_2O(l)\xrightarrow{373\text{K}}H_2O(v)$, $\Delta H_{vap}=+40.626$ kJ. …