Question

A weak acid with pKa 5.9 and weak base with pKb 5.8 are mixed in equal proportions. pH of the resulting solution is

• A. 7.005
• B. 7.5
• C. 7
• D. 7.05

Answer 1

The Correct Option is D

When a weak acid and a weak base are mixed in equal proportions, the resulting solution forms a buffer. The pH of a buffer solution can be calculated using the Henderson-Hasselbalch equation:

Henderson-Hasselbalch equation: 

\[ \text{pH} = \text{pKa} + \log \left( \frac{[\text{A}^-]}{[\text{HA}]} \right) \] Since the concentrations of the acid and its conjugate base are equal, the ratio \( \frac{[\text{A}^-]}{[\text{HA}]} \) is 1, so the equation simplifies to: \[ \text{pH} = \text{pKa} \]

However, we also need to take into account the relationship between pKa and pKb for the conjugate acid-base pair. The equation linking pKa and pKb is:

\[ \text{pKa} + \text{pKb} = 14 \] Substituting the given values for pKa and pKb: \[ 5.9 + 5.8 = 14 \] The pH of the buffer solution is approximately the average of the pKa and pKb values, giving: \[ \text{pH} \approx \frac{\text{pKa} + \text{pKb}}{2} = \frac{5.9 + 5.8}{2} = 7.05 \]

Conclusion:

The correct pH of the resulting solution is 7.05.

Answer: Option B: 7.05

Answer 2

When a weak acid (HA) and a weak base (B) are mixed in equal proportions, they react to form a salt (BA) of a weak acid and a weak base. $$ \text{HA} + \text{B} \rightleftharpoons \text{B}^+ + \text{A}^- $$

The pH of a solution containing the salt of a weak acid and a weak base is given by the formula for salt hydrolysis: $$ \text{pH} = 7 + \frac{1}{2} (\text{pK}_a - \text{pK}_b) $$

Given values are: 
\( \text{pK}_a = 5.9 \) 
\( \text{pK}_b = 5.8 \)

Substitute the given values into the formula: $$ \text{pH} = 7 + \frac{1}{2} (5.9 - 5.8) $$

Calculate the difference inside the parenthesis: $$ \text{pH} = 7 + \frac{1}{2} (0.1) $$

Perform the multiplication: $$ \text{pH} = 7 + 0.05 $$

Calculate the final pH: $$ \text{pH} = 7.05 $$

The final answer is \({\text{7.05}} \)