# Why is keq unitless?

Sep 6, 2016

Good question. Consider the equilibrium:

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

#### Explanation:

Now here, of course ${K}_{\text{eq}} = \frac{\left[A\right] \left[B\right]}{\left[C\right] \left[D\right]}$, which of course is unitless because the $m o l \cdot {L}^{-} 1$ cancels out. But of course not all equilibria are set up like that, we could conceive of, $A + B r i g h t \le f t h a r p \infty n s C$, where the units would not cancel out.

Strict application of thermodynamic principles relies on activities, $a$, not concentrations, where the activity is dimensionless by reference to a standard concentration, i.e. ${a}_{A} = \frac{\left[A\right]}{\left[{A}_{\text{standard}}\right]}$.

Thus when we use the Nernst equation $\Delta {G}^{\circ} = - R T \ln \left({K}_{\text{eq}}\right)$, we can properly take the logarithm of a dimensionless quantity.

So in summary, we should use dimensionless $\text{activities}$, however, the ${A}_{0}$ values should be near as dammit to the molar concentration.