Question

A buffer solution is prepared by mixing 0.2 M sodium acetate and 0.1 M acetic acid. If $pK_{a}$ for acetic acid is 4.7, find the pH.

• A. 3.0
• B. 4.0
• C. 5.0
• D. 2.0

Hint:

Logic Tip: If the concentration of the salt is strictly greater than the concentration of the weak acid ($[\text{Salt}]>[\text{Acid}]$), the logarithm term will be positive. This guarantees that the final $pH$ will be strictly greater than the $pK_a$. Knowing this immediately limits the answer to values $> 4.7$, leaving only Option C.

Answer 1

The Correct Option is C

Concept:
For an acidic buffer solution composed of a weak acid and its conjugate base (salt), the pH can be calculated using the Henderson-Hasselbalch equation: $$pH = pK_a + \log_{10}\left(\frac{[\text{Salt}]}{[\text{Acid}]}\right)$$
Step 1: Identify the given components and values.
Weak Acid: Acetic acid ($CH_3COOH$), Concentration $[\text{Acid}] = 0.1\text{ M}$ Salt (Conjugate Base): Sodium acetate ($CH_3COONa$), Concentration $[\text{Salt}] = 0.2\text{ M}$ Acid dissociation constant, $pK_a = 4.7$
Step 2: Apply the Henderson-Hasselbalch equation.
Substitute the known values into the equation: $$pH = 4.7 + \log_{10}\left(\frac{0.2}{0.1}\right)$$ $$pH = 4.7 + \log_{10}(2)$$
Step 3: Calculate the final pH value.
Using the standard logarithmic value $\log_{10}(2) \approx 0.3010$: $$pH = 4.7 + 0.3010$$ $$pH = 5.001$$ Rounding to one decimal place, the pH is $5.0$.