PAC determination of reaction enthalpies and volume changes

As presented in The Photoacoustic Effect chapter, PAC allows the measurement of reaction enthalpies according to a simple energy balance.

eq1 (1)

Although this equation is correct, one should have in mind that PAC does not afford the heat produced (ΔnrH) directly. The quantity that is determined (through the microphone) is a volume change resulting from two contributions: one from the heat produced, which is related to the reaction enthalpy through the above energy balance, and another from the chemical volume change (ΔcV), which is not. The experimentally obtained value, adequately called the observed heat (ΔobsH), is a sum of those two terms [1,2]:

eq2 (2)

The chemical volume change ΔcV is due to the different volumes occupied by reactants and products and, together with the expansion generated by the heat produced, contributes to the measured signal by the microphone. The adiabatic expansion coefficient of the solution (Χ) ensures that eq 2 is dimensionally consistent.

Therefore, to obtain the correct reaction enthalpy (ΔrH) one needs first to introduce eq 2 in eq 1 and solve for ΔuH.

eq3 (3)

Now recall from The Photoacoustic Effect chapter that ΔrH is obtained by dividing the enthalpy of the photochemical reaction (ΔuH) by the efficiency of this process (Φr), i.e. the reaction quantum yield; the same applies if we want to relate the reaction volume change (ΔrV) to the chemical volume change in the photochemical process, eqs 4 and 5.

eq4 (4)
eq5 (5)

With these equations in mind, dividing both terms of eq 3 by Φr we obtain eq 6, which is used to calculate the reaction enthalpy from the PAC value of ΔobsH.

eq6 (6)

Eq 6 sumarizes two important aspects of PAC determination of reaction enthalpies. First, that we need accurate values of the reaction quantum yield, which can be obtained by other techniques, usually actinometry. Second, that we must always correct for the reaction volume change. Luckily, the correction term can be neglected in some cases. In other cases it can be estimated or determined by other techniques [3].

It is important to stress that in some studies the quantity of interest is the reaction volume, and not the enthalpy. An interesting example is provided by PAC studies of protein folding.