Confusion in solubility expressions in Henry's Law

While reading about Henry's law and solubility I frequently come across two relations:

1. $$C = k_{h}P$$ (c = concentration of a dissolved gas)
2. $$P = k_{h}x$$ (x = solubility/mole_fraction)

What is the difference in these two expressions, do they seem to contradict each other? I am not able to decide whether a gas with higher $$k_{h}$$ would be more soluble or less soluble. Please help me out with the same I am new to this topic

• Please define all variables. Note that asterisk is not a proper multiplication sign and should never be used as such outside code listings. A meaningful title also wouldn't hurt. Apr 10, 2021 at 14:02
• kh in 1. is not the kh from the Henry law, but rather a solubility constant at given partial pressure. There should be used a different symbol for that. Note that the Henry constant uses the capital K. Apr 10, 2021 at 14:06
• @Poutnik google search of henry's law constant gives me that expression. Also I think I've read it elsewhere too. But as mentioned earlier I am not sure about this topic so it would be good if you could correct me wherever you think I am going wrong Apr 10, 2021 at 14:11
• It cannot be proportional to p ( in lower letter ) for the same molar fractions and at the same time reciprocal to p for the same concentrations. As concentrations are not reciprocal to molar fractions. See en.wikipedia.org/wiki/Henry%27s_law for different used symbols. Apr 10, 2021 at 14:22

Sander (Ref. 1) has compiled a useful review of Henry's law constants in water that includes an introduction showing notation and conversions.

There are two types of Henry's law constants:

1. Solubility constants convert from pressure to concentration in solution (solubility):

$$c=Hp$$

1. Volatility constants convert from concentration in solution (solubility) to pressure:

$$p=Kc$$

Usually it is possible to determine which constant is reported by inspecting the units.

References

1. R. Sander. Compilation of Henry’s law constants (version 4.0) for water as solvent. Atmos. Chem. Phys., 15, 4399–4981, 2015. www.atmos-chem-phys.net/15/4399/2015/doi:10.5194/acp-15-4399-2015