# Limitations of Henry's law

Consider the diagram Henry's law is a gas law that states that the amount of dissolved gas in a liquid is proportional to its partial pressure above the liquid. The proportionality factor is called Henry's law constant.

Suppose the weights on the piston are so increased such that the pressure of the gas becomes numerically equal to Henry's law constant.

Then Henry's law gives that the mole fraction of the gas in solution is equal to 1.

Mole fraction of solute in solvent being equal to 1 implied that there is absolutely no solvent.

But in the situation described by the diagram, the solvent molecules are always present.

How is this so? Perhaps there is a limitation to Henry's law which has not been mentioned?

• That's right, Henry's law ceases to work before you get to pressures that high. – Ivan Neretin Jul 10 '20 at 5:58

## 2 Answers (Source: chem.libretexts.org)

In the image, we see that for a "real gas" (indicated by non-ideal solution), Henry's law is applicable for $$\ce{\chi} << 1$$.

As, $$\ce{p = K_H \cdot \chi}$$ hence the pressure should be low.

## Limitations of Henry's law:

• The pressure should be low and the temperature should be high i.e the gas should behave like an ideal gas.

• The gas should not undergo compound formation with the solvent or association or dissociation in the solvent.

If you think of Raoult's law as a special case of Henry's law (since in both cases the vapor pressure of a substance is proportional to its mole fraction in solution) then there isn't really a problem.

The case you describe where the solute concentration in solution spans the range $$\chi=0-1$$ and observes the equation

$$\chi=\frac{p}{K}$$

where $$K$$ is equal to $$p*$$, the vapor pressure of the solute in the pure liquid state, is the case of a substance exhibiting ideal Raoult's law behavior over its entire concentration range.

However, if $$K_H$$ is not equal to $$p*$$ then Raoult's law is not observed over that concentration range, and this is then a more general case of Henry's law with an upper concentration limit on the ideal behavior of the solution. Where that limit is somewhat arbitrary, it occurs when the solute deviates sufficiently from the extrapolated behavior under dilute conditions. In fact, the best way to understand Henry's law is as a limiting law applicable strictly for infinitely dilute solutions:

$$K_H = \lim_{\chi\rightarrow0}\frac{p}{\chi}$$

that is, the constant $$K_H$$ is defined as the slope of the curve of p versus $$\chi$$ as the concentration goes to zero.

Where the deviation from linear behavior is observed and the law is violated is in general an empirical question: we apply Henry's law when it works well enough, and not beyond that. The ideal behavior in both Raoult's and Henry's laws means, as explained in another answer, that where the rules apply the behavior of the solute in solution does not depend on its concentration. Note however that even an associating or dissociating compound is expected to display Henry's law behavior at sufficiently low concentrations.