Which gas will have the greatest Henry's law constant?

Question

Which of these gases will have the greatest Henry's law constant in a water solution? He, Ne, Ar, Kr, or Xe. Explain

Answer 1

Henry's law constant is a proportionality factor expressing the solubility of a gas in a solute. The solubility of a given gas is directly proportional to the partial pressure of that gas in the gas phase. So, if we can determine which gas has the greatest/lowest partial pressure, or which gas is most soluble, we can tell which gas will have the largest/smallest Henry's law constant.

We are thus comparing He, Ne, Ar, Kr and Xe. Since these are all noble gases, the only real intermolecular forces holding atoms together would be London forces.

London dispersion forces are strongly influenced by size and the "polarizability" of the atom. Polarizability increases as the atomic radius increases because the electrons are further away from the nucleus and thus less tightly bound. Since atomic radius increases going down the group, Xe would the most "polarizable".

This would make Xe the most soluble in water (water being very polar), and then Kr, followed by Ar, Ne and He. Since this is the order of solubility, it would be the order of Henry's law constants as well. Thus, the order of Henry's law constant from lowest to highest would be:

He < Ne < Ar < Kr < Xe