Chapter 15: Problem 91

Tris (hydroxymethyl)aminomethane, commonly called TRIS or Trizma, is often used as a buffer in biochemical studies. Its buffering range is $\mathrm{pH} 7$ to $9,$ and $K_{\mathrm{b}}$ is $1.19 \times 10^{-6}$ for the aqueous reaction $$ \left(\mathrm{HOCH}_{2}\right)_{3} \mathrm{CNH}_{2}+\mathrm{H}_{2} \mathrm{O} \rightleftharpoons\left(\mathrm{HOCH}_{2}\right)_{3} \mathrm{CNH}_{3}^{+}+\mathrm{OH}^{-} $$ a. What is the optimal pH for TRIS buffers? b. Calculate the ratio $[T R I S] /\left[T R I S H^{+}\right]$ at $p H=7.00$ and at p H=9.00 c. A buffer is prepared by diluting 50.0 $\mathrm{g}$ TRIS base and 65.0 $\mathrm{g}$ TRIS hydrochloride (written as TRISHCl) to a total volume of 2.0 $\mathrm{L}$ What is the pH of this buffer? What is the pH after 0.50 $\mathrm{mL}$ of 12 $\mathrm{MHCl}$ is added to a 200.0 -mL portion of the buffer?

Short Answer

Expert verified

The optimal pH for TRIS buffers is found to be 8.07. The ratio $[TRIS]/[TRIS H^{+}]$ at pH 7.00 is 0.135 and at pH 9.00 is 7.40. The pH of the prepared buffer is 7.95, and after adding 0.50 mL of 12 M HCl to a 200.0 mL portion of the buffer, the pH becomes 7.91.

Step by step solution

To find the optimal pH for TRIS buffers, we can refer to the optimal buffering range of pH 7 to 9. The optimal pH would be the pH at which the buffer capacity is the highest. This is when the concentration of the weak base equals the concentration of its conjugate acid, which occurs at the pKa (pKb in this case) value. We can find the pKb from the given Kb value and then convert it to pKa using the relationship pKa + pKb = 14. First, find pKb: $$ pK_b = -\log_{10}(K_b) $$ Then, find pKa: $$ pK_a = 14 - pK_b $$ Finally, find the optimal pH, which is equal to pKa. #Step 2#: Calculate the ratio $[T R I S] /[TRIS H^{+}]$ at pH 7.00 and pH 9.00

To calculate the ratio of concentrations, we will use the Henderson-Hasselbalch equation: $$ pH = pK_a + \log_{10}\frac{[TRIS]}{[TRIS H^{+}]} $$ Rearrange the equation to find the ratio $\frac{[TRIS]}{[TRIS H^{+}]}$ at the given pH values. #Step 3#: Find the pH of the prepared buffer

To find the pH of the buffer, first determine the molar concentrations of both TRIS and TRISH+ in the buffer. 1. Convert the masses of TRIS base (50.0 g) and TRISHCl (65.0 g) to moles 2. Use the total volume (2.0 L) to calculate the molar concentrations of TRIS and TRISH+ 3. Use the Henderson-Hasselbalch equation to find the pH of the buffer. #Step 4#: Calculate the pH after adding HCl

We know that 0.50 mL of 12 M HCl will react with the basic part of the buffer. To find the pH after adding the HCl, we need to: 1. Calculate moles of HCl that we added 2. Calculate the moles of TRIS base and TRISH+ after the reaction with HCl 3. Calculate the new concentrations of TRIS and TRISH+ in the 200.0 mL portion of the buffer 4. Use the Henderson-Hasselbalch equation with the new concentrations to find the pH of the buffer after adding HCl.