# pKa of Tris corrected for ionic strength

I have a question regarding the molar fraction calculation of Tris buffer at different temperatures.

Tris dissociates according to the following equation:

$$\ce{Tris + H2O -> Tris+ + OH-}$$

So, in order to calculate the amount of $c(\text{Tris}^+)$ and thus the amount of strong acid needed for titration, one needs to use derivation of Henderson-Hasselbalch eq.:

$$\mathrm{pH} = \mathrm{p}K_\mathrm{a}' - \log_{10}\left(\frac{[\text{Tris}^{+}]}{[\text{Tris}]}\right)$$

However, $\mathrm{p}K_\mathrm{a}'$ is $\mathrm{p}K_\mathrm{a}$ corrected for ionic strength ($I_c$) at a certain temperature.

The correction of $\mathrm{p}K_\mathrm{a}$ is done via the Debye-Hückel eqation:

$$\mathrm{p}K_\mathrm{a}' = \mathrm{p}K_\mathrm{a} -0.509\times\left| z-z^{+}\right| \sqrt{I_c}$$

Now, for Ic itself one needs to calculate the molar fraction of $[\ce{Tris+}]$:

$$I_c = 0.5\times \left([\ce{Tris+}] + [\ce{OH-}]\right)$$

which requires the use Henderson-Hasselbalch equation making this problem somewhat circular. or am I missing something?

• If you write also mass balance and charge balance can't get [tris+]?
– user43021
Commented Sep 13, 2017 at 10:33

## 1 Answer

First decide the Ic you want to work with. Second, you should correct the pka with the Debye Huckel equation and finally you use the pka corrected with the Henderson Hasselbach equation.