Editing Equilibrium constant (section)

==Effect of isotopic substitution==
[[Isotope|Isotopic]] substitution can lead to changes in the values of equilibrium constants, especially if hydrogen is replaced by [[deuterium]] (or [[tritium]]).<ref name=Laidler>[[Keith J. Laidler|Laidler K.J.]] ''Chemical Kinetics'' (3rd ed., Harper & Row 1987), p.428–433 {{ISBN|0-06-043862-2}}</ref> This ''equilibrium isotope effect'' is analogous to the [[kinetic isotope effect]] on rate constants, and is primarily due to the change in [[Quantum harmonic oscillator#Hamiltonian and energy eigenstates|zero-point vibrational energy]] of H–X bonds due to the change in mass upon isotopic substitution.<ref name=Laidler/> The zero-point energy is inversely proportional to the square root of the mass of the vibrating hydrogen atom, and will therefore be smaller for a D–X bond that for an H–X bond.

An example is a [[hydrogen atom abstraction]] reaction R' + H–R {{eqm}} R'–H + R with equilibrium constant K<sub>H</sub>, where R' and R are organic radicals such that R' forms a stronger bond to hydrogen than does R. The decrease in zero-point energy due to deuterium substitution will then be more important for R'–H than for R–H, and R'–D will be stabilized more than R–D, so that the equilibrium constant K<sub>D</sub> for R' + D–R {{eqm}} R'–D + R is greater than K<sub>H</sub>. This is summarized in the rule ''the heavier atom favors the stronger bond''.<ref name=Laidler/>

Similar effects occur in solution for [[acid dissociation constant]]s (K<sub>a</sub>) which describe the transfer of H<sup>+</sup> or D<sup>+</sup> from a weak aqueous acid to a solvent molecule: HA + H<sub>2</sub>O = H<sub>3</sub>O<sup>+</sup> + A<sup>−</sup> or DA + D<sub>2</sub>O {{eqm}} D<sub>3</sub>O<sup>+</sup> + A<sup>−</sup>. The deuterated acid is studied in [[heavy water]], since if it were dissolved in ordinary water the deuterium would rapidly exchange with hydrogen in the solvent.<ref name=Laidler/>

The product species H<sub>3</sub>O<sup>+</sup> (or D<sub>3</sub>O<sup>+</sup>) is a stronger acid than the solute acid, so that it dissociates more easily, and its H–O (or D–O) bond is weaker than the H–A (or D–A) bond of the solute acid. The decrease in zero-point energy due to isotopic substitution is therefore less important in D<sub>3</sub>O<sup>+</sup> than in DA so that K<sub>D</sub> < K<sub>H</sub>, and the deuterated acid in D<sub>2</sub>O is weaker than the non-deuterated acid in H<sub>2</sub>O. In many cases the difference of logarithmic constants pK<sub>D</sub> – pK<sub>H</sub> is about 0.6,<ref name=Laidler/> so that the pD corresponding to 50% dissociation of the deuterated acid is about 0.6 units higher than the pH for 50% dissociation of the non-deuterated acid.

For similar reasons the [[Self-ionization of water#Isotope effects|self-ionization of heavy water]] is less than that of ordinary water at the same temperature.