# 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 Sep 13 '17 at 10:33