# 19.12: The Temperature Dependence of \(\Delta H\)

The definition of the standard state does not fix the temperature. Usually the temperature of tabulation is given in the table (usually 25^{o}C) and if we need to use the values at different temperatures we need to convert. The way to do that is to use:

\[H(T) = H(T_1) + C_p(T-T_1) + ….\]

After all

\[\left(\dfrac{\partial H}{\partial T}\right)_P = C_p\]

If the temperature change is small C_{p} can often be taken as a constant. If not we need it as function of the temperature in the range of interest and we must integrate. Because the reaction enthalpy involves the enthalpies of all reactants and products, we must take into account all their changes, i.e. all the heat capacities.

If we can neglect temperature dependence of \(C_p\) we get

\[Δ_rH(T) = Δ_rH(T_o) + Δ_rC_p.(T-T_o)\]

Of course to calculate Δ_{r}C_{p} we need to use the appropriate stoiciometric coefficients e.g.:

\[H_2O_{(l)} + Na \rightarrow NaOH + 0.5 H_2 (water)\]

\[Δ_rC_p= 0.5C-p(H_2) + C_p(NaOH) - C-pNa + C_pH_2OH_(l)\]

## Changing pressure

The standard pressure in one bar. Yes, Δ_{r}H also depends on pressure, but typically not very strongly so.