# Sieverts' law

Sieverts' law, in physical metallurgy, is a rule to predict the solubility of gases in metals. It is named after German chemist Adolf Sieverts (1874–1947).[1] The law states that the solubility of a diatomic gas in metal is proportional to the square root of the partial pressure of the gas in thermodynamic equilibrium.[2] Hydrogen, oxygen and nitrogen are examples of dissolved diatomic gases of frequent interest in metallurgy.

## Justification

Sieverts' law can be readily rationalized by considering the reaction of dissolution of the gas in the metal, which involves dissociation of the molecule of the gas. For example, for nitrogen:

N2(gas) 2 N(dissolved)

For the above reaction, the equilibrium constant, K, is:

$K^2 = {C_N^2 \over {p_{N_2}}}$

Where:

• C is the solubility
• p is the partial pressure

Therefore,

$C_N = {K \sqrt{p_{N_2}}}$