Question

If the pKa of lactic acid is 5, then the pH of 0.005 M calcium lactate solution at \(25^\circ \text{C}\) is \(\_\_\_\_\_\_ \times 10^{-1}\) (Nearest integer).
Lactic Acid

Hint:

For salts of weak acids and strong bases, use: \[ \text{pH} = \frac{1}{2} (\text{pKa} + \log C_{\text{salt}}), \] where \(C_{\text{salt}}\) is the molar concentration of the salt.

Answer 1

Correct Answer: 85

To determine the pH of a solution of calcium lactate, we need to follow these steps:
1. Understand the dissociation: Calcium lactate dissociates into calcium ions (Ca²⁺) and lactate ions (C₃H₅O₃^-).
2. Calculate the concentration of lactate ions: The formula is:
Ca(C₃H₅O₃)₂ → Ca²⁺ + 2 C₃H₅O₃^-
From 0.005 M calcium lactate, the lactate ion concentration becomes 0.01 M.
3. Apply the Henderson-Hasselbalch equation:
\( \text{pH} = \text{pK}_a + \log{\left( \frac{[A^-]}{[HA]} \right)} \)
Assume full dissociation of lactic acid: \([HA] = 0\), \([A^-] = 0.01 \, \text{M}\).
4. Using the given pK_a: pK_a = 5. Hence, pH ≈ 1/2(14+5+log 0.01)
5. Simplify: pH ≈ 1/2(14+5+(-2)) = 1/2(17) = 8.5
6. Check the range: The computed pH value \(8.5\) falls within the expected range \(85,85 \, \text{(divided by 10 to find range)}\).
7. Conclusion: The solution pH is approximately \(85 \times 10^{-1}\).