# What are the units of base dissociation constant Kb ?

## Are they $m o l . {\mathrm{dm}}^{- 3}$?

Jan 21, 2017

Equilibrium constants, and acid/base dissociation constants fall under this umbrella, are usually regarded as dimensionless....

#### Explanation:

Of course for the reaction:

$A + B r i g h t \le f t h a r p \infty n s C + D$,

we would write the equilibrium constant as, ${K}_{\text{eq}} = \frac{\left[C\right] \left[D\right]}{\left[A\right] \left[B\right]}$.

Here, CLEARLY, the units of concentration cancel to give ${K}_{\text{eq}}$ as a DIMENSIONLESS number. This is useful when we use the Nernst equation, where $- \ln {K}_{\text{eq}} = \Delta {G}^{\circ}$.

However, sometimes, we encounter an equilibrium rxn where the units do not cancel out, and in these circumstances we would strictly use DIMENSIONLESS standard state activities, where the concentration is expressed as an activity relative to a standard.

So thus, for the association of say, ${F}^{-}$, we would write:

${F}^{-} + {H}_{2} O \left(l\right) r i g h t \le f t h a r p \infty n s H F + H {O}^{-}$

${K}_{b} = \frac{\left[H F\right] \left[H {O}^{-}\right]}{\left[{F}^{-}\right]} \cong \frac{{a}_{H F} \times {a}_{H {O}^{-}}}{{a}_{{F}^{-}}}$

Where ${a}_{H F}$ etc. are standard state activities with reference to standard conditions, and are thus dimensionless. Usually we can substitute the activity for the concentration and vice versa without loss of precision and accuracy.