Humidity-temperature response of OH production

At fixed relative humidity and fixed excited-oxygen concentration, a water-reaction hydroxyl radical source scales as $e_s(T)/T$ when concentrations are number densities. Thus $d\ln P_{\mathrm{OH}}/dT=\Delta H_{\mathrm{vap}}/(R{T}^2)-1/T$ under constant latent heat and rate coefficient. Using only $e_s$ instead gives a vapor pressure or fixed-pressure mole-fraction approximation. Neither derivative follows without a humidity condition.