Starting with 0.05 M of the base form of histidine, calculate the concentration of the acid form needed to prepare the buffer at pH 7.
The correct answer and explanation is:
To prepare a buffer at pH 7 using histidine, we need to consider its acid-base equilibrium. Histidine has a pKa around 6.0 for its imidazole group, which is relevant for the buffering action at physiological pH. The relevant equation for the acid-base equilibrium of histidine is: Histidine (base form)+H+⇌Histidine (acid form)\text{Histidine (base form)} + \text{H}^+ \rightleftharpoons \text{Histidine (acid form)}
1. Henderson-Hasselbalch Equation
The Henderson-Hasselbalch equation allows us to calculate the ratio of acid and base forms in the buffer solution: pH=pKa+log([Base][Acid])\text{pH} = \text{pKa} + \log \left( \frac{[\text{Base}]}{[\text{Acid}]} \right)
Substitute the values:
- pH = 7
- pKa = 6.0 (for histidine’s imidazole group)
2. Solve for the Ratio of Base to Acid
Rearrange the equation to solve for the ratio of the base form to the acid form: 7=6.0+log([Base][Acid])7 = 6.0 + \log \left( \frac{[\text{Base}]}{[\text{Acid}]} \right) 1=log([Base][Acid])1 = \log \left( \frac{[\text{Base}]}{[\text{Acid}]} \right) 101=[Base][Acid]10^1 = \frac{[\text{Base}]}{[\text{Acid}]} [Base][Acid]=10\frac{[\text{Base}]}{[\text{Acid}]} = 10
This means that the concentration of the base form is 10 times the concentration of the acid form.
3. Define the Total Concentration
The total concentration of histidine (both acid and base forms) is given as 0.05 M. Let the concentration of the acid form be xx, and the base form will be 10 times that, i.e., 10x10x.
Therefore, the total concentration is: x+10x=0.05x + 10x = 0.05 11x=0.0511x = 0.05 x=0.0511=0.00455 Mx = \frac{0.05}{11} = 0.00455 \, \text{M}
4. Conclusion
The concentration of the acid form needed to prepare the buffer at pH 7 is approximately 0.00455 M.
In summary, using the Henderson-Hasselbalch equation, the base form of histidine is 10 times more concentrated than the acid form at pH 7. The total concentration of histidine is 0.05 M, and the concentration of the acid form required to achieve the desired pH is 0.00455 M.