# Equilibrium constants for lewis acids such as Ca2+

I need to calculate the theoretical $\mathrm{pH}$ in a $50~\mathrm{mL}$ water solution where $6.4\times10^{-4}~\mathrm{g}$ of $\ce{Ca^{2+}}$ is present. The reaction I base this on is the following

$$\ce{Ca^{2+}_{(aq)} + 2H2O_{(l)} \rightleftarrows Ca(OH)2_{(s)} + 2H^+_{(aq)}}$$

$$K = \frac{[\ce{H+}]^2}{[\ce{Ca^{2+}}]} \Rightarrow [\ce{H+}] = \sqrt{K \cdot [\ce{Ca^{2+}}]}$$

Is there a database of standard equilibrium constants for such Lewis acid reactions?

I appreciate any help!

• Please avoid latex in titles due to issues with searchability. meta.chemistry.stackexchange.com/questions/253/… – bon Apr 18 '15 at 18:23
• I have never thought of that before. Thank you for pointing it out to me! – Yoda Apr 18 '15 at 18:24

You're confusing terms here. $\ce{K_{a}}$ is the (Brønsted) acid dissociation constant. This suggests that $\ce{K_a}$ refers to the degree that a Brønsted acid dissociates into its conjugate base and hydrogen protons.

$\ce{K_{a}}$ is inapplicable to Lewis acids because Lewis acids are not proton donors.

Brønsted acids are Lewis acids in that Brønsted acids such as the hydrogen proton can accept a pair of electrons. But the converse is not true.

Lewis acids are electron acceptors. How do we measure the strength of Lewis acids? There is no universally accepted measure as there is for Brønsted acids. We could look at the enthalpy of reaction (Lewis adduct formation) between a Lewis acid and a Lewis base. This is a common method.

• Duh, that was too obvious for me to think of! Thank you. Still, terminological errors aside, is there a place where I can find the equilibrium constant for the reaction? – Yoda Apr 18 '15 at 20:34
• @AndersMB - the best I can think of is using a bunch of already calculated K values to solve the unknown K value for your reaction. Try using Ksp of calcium hydroxide with Kw and any other applicable K values. – Dissenter Apr 18 '15 at 20:39
• @AndersMB - try checking out this question to see what you might have to end up doing to solve for the unknown K value ...chemistry.stackexchange.com/questions/13624/… – Dissenter Apr 18 '15 at 20:41
• Oh, I am getting flashbacks to General Chemistry and Hess's Law! Thank you for your help. – Yoda Apr 18 '15 at 20:43

You should be able to find the constant $K_\text{a}$ for the reaction $$\ce{Ca^2+ + H2O <=> CaOH+ + H+}$$

I found a value of $\mathrm{p}K_\text{a} = 12.6$ (at 25 °C) in “Dissociation Constants of Inorganic Acids and Bases”, in CRC Handbook of Chemistry and Physics, 90th Edition (CD-ROM Version 2010), David R. Lide, ed., CRC Press/Taylor and Francis, Boca Raton, FL.

Werner Stumm, James J. Morgan Aquatic Chemistry, 3rd Edition (1996), John Wiley & Sons, New York, NY gives a value of $\log K = -12.78$.