# What is the difference between ΔfH and H-H° in NIST–JANAF tables?

Can someone explain the difference between $$Δ_\mathrm{f}H$$ and $$H-H^\circ$$ in NIST–JANAF tables?

As a side note, "JANAF" stands for Joint Army–Navy–Air Force; these tables were designed to provide quick access to the thermodynamic data for rocket scientists.

Here, $$Δ_\mathrm{f}H^\circ$$ is the standard enthalpy of formation. The difference $$H-H^\circ(T_\mathrm{r})$$ is required to calculate the standard enthalphy of reaction $$Δ_\mathrm{r}H^\circ$$ if in the given temperature range a reaction takes place.

There is a thorough explanation in Silbey's Physical Chemistry [1, p. 62]:

The JANAF tables give standard enthalpies of formation at a series of temperatures, and so these values may be used directly to calculate enthalpies of reaction. [...] Some thermodynamic tables give values of $$\bar{H}^\circ_T - \bar{H}^\circ_{298}$$ to assist in the calculation of $$Δ_\mathrm{r}H^\circ$$ for a chemical reaction or phase transition:

$$\bar{H}^\circ_T - \bar{H}^\circ_{298} = \int_\pu{298 K}^T \bar{C}^\circ_P \mathrm{d}T$$

Depending on the table, $$Δ_\mathrm{r}H^\circ$$ for phase transitions in the intervening temperature range may be added to the right-hand side of the equation.

NIST-JANAF tables are given for a reference temperature $$T_\mathrm{r}$$ and a standard state pressure $$p^\circ$$. Unless stated otherwise, $$T_\mathrm{r} = \pu{298.15 K}$$ and $$p^\circ = \pu{0.1 MPa}$$ [2].

### References

1. Silbey, R. J.; Alberty, R. A.; Bawendi, M. G. Physical Chemistry, 4th ed.; Wiley: Hoboken, NJ, 2005. ISBN 978-0-471-21504-2.
2. NIST-JANAF Thermochemical Tables, 4th ed.; Chase, M. W. J., Ed.; American Institute of Physics: Washington, DC : New York, 1998. ISBN 978-1-56396-831-0.
• Does $T_\mathrm{r}$ stand for room temperature? Jan 29 '19 at 18:15
• @KarstenTheis - no $T_{r}$ is a reference temperature (which may be 25C but doesn't have to be). Just above the bit shown in the question there is a line stating what $T_{r}$ is for the table. Jan 29 '19 at 18:33
• @KarstenTheis Jon Custer already commented (wow that was fast:) ), but essentially yes, the reference temperature is close to the RT. NIST usually uses $T_\mathrm{r} = \pu{298.15 K}$ (I updated the answer, too). Jan 29 '19 at 18:38