# How can standard enthalpies of fusion and vaporization add up to that of sublimation when these occur at different temperatures?

In Atkins' Physical Chemistry, the following diagram appears in the chapter on thermochemistry:

The definition of standard enthalpy change is also given:

The standard state of a substance at a specified temperature is its pure form at 1 bar.

My doubt is regarding the temperature at which these changes occur. Say the fusion occurs at the melting point, vaporization at the boiling point. According to the definition of standard enthalpy change, these need to occur at a fixed temperature. How can we add the standard enthalpies associated with the two to obtain the standard enthalpy of sublimation, which occurs at a different temperature and may not be possible at the standard $$1\pu{bar}$$ pressure? Shouldn't the heats associated with changing the temperature of the system be included in the equation?

The phase diagram of a general solid-liquid-gas may be represented by the following:

According to the diagram, solid, liquid, and gas phases can only exist together at the triple point, leading me to the conclusion that the equation $$\Delta_\text{fus}H^\ominus+\Delta_\text{vap}H^\ominus=\Delta_\text{sub}H^\ominus$$ is only valid at the triple point.

• (...)''can only exist together'' in equilibrium ''at the triple point'', but who says there's got to be equilibrium? Nov 11, 2023 at 1:59
• @Mithoron thank you for the comment. Say the fusion occurs at the melting point, vaporization at the boiling point, and sublimation, which may not be possible at standard pressure, occurs at a different temperature. According to the definition of standard enthalpy change, these need to occur at a fixed temperature. Shouldn't the heats associated with changing the temperature of the system be included in the equation? Nov 11, 2023 at 2:07
• Say the standard temperature were closen as the triple point. Would you be comfortable with the explanation then? Nov 11, 2023 at 11:50
• @ChetMiller I think changing the definitions set by IUPAC is just bypassing the problem and not really solving it. Nov 12, 2023 at 4:31
• That is not what I asked. Nov 12, 2023 at 11:52