# Kb of hydride anion

I can't find any data about the Kb value of the hydride anion except that it's huge. Does anyone know what it is, or how I can characterize it?

I know I can use electrochemical means but the only reaction I find with hydride ion is this one:

http://en.wikipedia.org/wiki/Hydride#Hydride_ion

I think I got it figured out using electrochemical means, thanks to Aditya’s suggestion to consult $K_\text{a}$ values rather than $K_\text{b}$ values.

Consider these two half reactions:

$\ce{2e- +H2->2H-}\tag{$E^\circ=-2.25~\mathrm{V}$}$

$\ce{H2 + 2H2O -> 2H3O+ + 2e-}\tag{$E^\circ=0.00~\mathrm{V}$}$

Coupling these two half reactions results in:

$\ce{2H2 +2H2O ->2H3O+ +2H- }\tag{$E^\circ=-2.25~\mathrm{V}$}$

Application of the Nernst equation can help us find an equilibrium constant for this reaction.

$\Delta G^\circ = -nFE^\circ = -(2)(96\,500~\mathrm{C/mol})(-2.25~\mathrm{V}) = +434\,250~\mathrm{J/mol}$

Value makes sense; we’d expect the reaction of hydrogen gas as an acid with water to be highly disfavorable.

$\Delta G^\circ = -RT\ln K=-\left(8.31~\mathrm{J/(mol\cdot K)}\right)(298~\mathrm{K})\ln K=+434\,250~\mathrm{J/mol}$

$K = 6.97464\times10^{-77}$

Now, this $K$ correspond to this equilibrium:

$\ce{2H2 +2H2O ->2H3O+ +2H- }$

So we must take the square root of the found equilibrium constant to generate a value for $K_\text{a}(\ce{H2})= 8.35\times10^{-39}$.

And finally this lines up well with Aditya’s finding that the $\mathrm{p}K_\text{a}$ of $\ce{H2}$ is 35; the −log of the above $K_\text{a}$ value I found is 38. Nice.

Recall that $\mathrm{p}K_\text{b}$ of hydride is actually $14-\mathrm{p}K_\text{a}$ of hydrogen gas. The value I found is $\mathrm{p}K_\text{a}=35$, so $\mathrm{p}K_\text{b}=14-35=-21$.

• You mean Kw/Ka of hydrogen gas? – Dissenter Aug 13 '14 at 17:21
• That 35 value also sounds like a pKa value rather than a Ka value. Can't imagine hydrogen gas being that acidic. – Dissenter Aug 13 '14 at 17:21