# Does standard enthalpy of reaction assume a constant temperature?

I've attached a question and a solution from Reif's textbook. It seems to me that there must be the assumption of constant temperature, and I'm hoping someone can confirm. I can express the enthalpy of the system in which the reaction is occurring as $$H=H(T,P,N_1,...,N_m)$$ where the $$N_i$$ are the molecule numbers. Then the total differential of $$H$$ goes as $$dH = SdT+Vdp +\sum h_ib_i$$ where I have put the reaction equation coefficients $$b_i$$ as the change in particle number $$dN_i$$. The above only matches the solution (and the expected solution in the question) if $$dT = 0$$, though I'm not sure why this should be the case in general.

• The notations are a bit strange... Since $dH$ is a differential, the last term (the sum) should be too, $b_i$ should probably be written as $dN_i$. However there's a mistake in your equation, it's $T\,dS$, not $S\,dT$. At least if you're writing $H$ the Helmholtz free energy. It's $G$, Gibbs free energy, that is a function of $T$ and $P$ and has a $-S\,dT$ term. Commented Jun 10, 2022 at 12:55
• Standard reaction enthalpy assumes the same, standard initial and final temperatures. As the state function, it does not depend on the real or formal path, so the process need not to be isothermal. Commented Jun 21, 2022 at 9:20

According to Wikipedia article Standard enthalpy of reaction (emphasis is mine):

The standard enthalpy of a reaction is defined so as to depend simply upon the standard conditions that are specified for it, not simply on the conditions under which the reactions actually occur. There are two general conditions under which thermochemical measurements are actually made.3
(a) Constant volume and temperature: heat $$Q_{V}=\Delta U$$, where $$U$$ (sometimes written as $$E$$) is the internal energy of the system.
(b) Constant pressure and temperature: heat $$Q_P = \Delta H$$ , where $$H = U + P V$$ is the enthalpy of the system.

In other words, Yes, standard enthalpy of reaction assumes constant temperature.

A closely related concept is that of a standard state, which assumes specific temperature. The enthalpies of reactions are then calculated between substances in their standard states.

I could suggest Introduction to Physics and Chemistry of Combustion: Explosion, Flame, Detonation by Michael Liberman as a book reviewing these concepts (although they are probably covered in many chemistry texts).

• I tried to edit the equations above. I am not sure if I've got it correct. Can you check it? Commented Jun 10, 2022 at 13:58
• @BrendanDarrer thanks, I didn't pay attention that the equations were destroyed in copy-paste. Commented Jun 10, 2022 at 14:04