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# Tris(hydroxymethyl)aminomethane, commonly called TRIS or Trizma, is often used as a buffer in biochemical studies. Its buffering range is from pH 7 to $9 ,$ and $K _ { b }$ is $1.19 \times 10 ^ { - 6 }$ for the reaction$\left( \mathrm { HOCH } _ { 2 } \right) _ { 3 } \mathrm { CNH } _ { 2 } ( a q ) + \mathrm { H } _ { 2 } \mathrm { O } ( l ) \rightleftharpoons \left( \mathrm { HOCH } _ { 2 } \right) _ { 3 } \mathrm { CNH } _ { 3 } + ( a q ) + \mathrm { OH } ^ { - } ( a q )\\ {\begin{array} {l}{\text{TRIS} \quad \quad \quad \quad \quad \quad \quad \quad \text{TRISH}^+} \end{array}}$What is the optimum pH for TRIS buffers?

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We have a buffer solution that consist of TRIS and TRISH$^+$.

$\mathrm{ TRIS(aq) + H_2O(l) \rightleftharpoons TRISH^+(aq) + OH^-(aq) }$

$\bullet$ $\mathrm{K_b}$ value of TRIS is $1.19 \cdot 10^{-6}$

Therefore, $\mathrm{K_a}$ value is

$\mathrm{ K_a = \frac { K_w } { K_b } = \frac { 1.00 \cdot 10^{-14} } { 1.19 \cdot 10^{-6} } = 8.40 \cdot 10^{-9} }$

#### (a)

The optimum pH for TRIS buffers is the one where [TRIS] = [TRISH$^+$].

Let us calculate the pH using Henderson-Hasselbalch equation

\begin{align*} \mathrm{ pH } &= \mathrm{ pK_a + log\left( \frac { [TRIS] } { [TRISH^+] } \right) }\\ &= \mathrm{ -log(K_a) + log(1) }\\ &= \mathrm{ -log(8.40 \cdot 10^{-9}) }\\ &= 8.08\\ &\approx {\color{#4257b2}8.1} \end{align*}

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