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How does the law of corresponding states compare the behavior of different substances?

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Diagram showing four physical states of matter: solid with tightly packed molecules, liquid with loosely packed molecules, gas with widely spaced molecules, and plasma with free electrons and nuclei, each labeled with descriptions and an arrow indicating increasing energy. — phase States of matter.

The law of corresponding states provides a method to compare the behavior of different substances by presuming that their properties are similar when expressed in terms of reduced variables.1

While specific values for critical temperature and pressure vary between substances, this approach normalizes these differences by defining reduced variables as the ratio of the actual variable to its associated critical constant:1

Reduced temperature ( $T_{r}$ ): $T / T_{c}$
Reduced pressure ( $p_{r}$ ): $p / p_{c}$

By plotting a phase diagram using these reduced variables, the critical point for all substances occurs at a value of unity ( $T_{r} = 1$ and $p_{r} = 1$ ). This method allows for the correlation and prediction of various properties, such as vapor pressures, densities, heat capacities, and latent heats of vaporization.1

The approach is highly effective for many compounds at temperatures between their normal boiling point and critical point, though it tends to lose accuracy near or below the triple-point temperature, where liquid behavior is more heavily influenced by solid characteristics.1