Question

I need to make a 0.50M Tris buffer with a pH of 8.75. I have access to Tris (a weak acid) and the sodium salt of Tris (think A-). The Ka of Tris is 8.5x10-9 and the pKa of Tris is 8.07. What are the [HA] and [A-] concentrations of this 0.50M buffer at pH 8.75? Part B: [A-] = _____

Answer 1

TRIS is actually a weak base, not an acid, so what you probably have is tris (this is the base of the buffer and we will call it A) and tris hydrochloride, which is the conjugate acid of tris, and we'll cal AH⁺.

To calculate their concentration ratio, we can use the Henderson Hasselbach equation:

$pH=pKa+log\left ( \frac{[A]}{[AH^{+}]} \right )$

We can rearrange to calculate the ratio:

$\frac{[A]}{[AH^{+}]}=10^{pH-pKa}=10^{8.75-8.07}=4.79$ (equation 1)

We also know that the total concentration of the species has to be 0.50 M, so we also have:

$[A]+[AH^{+}]=0.50M$

We can introduce equation 1 here to get:

$4.79[AH^{+}]+[AH^{+}]=5.79[AH^{+}]=0.50M$

And we can calculate:

$[AH^{+}]=\frac{0.50M}{5.79}=0.086\: M$

And:

$[A]=0.50M-[AH^{+}]=0.414\: M$