A solution contains 2×10-3 mol/L of a weak acid (pK=3.5) and 2×10-3 mol/L of its conjugate base. Its pH is best approximated by which one of the following?
**Core Concept**
The Henderson-Hasselbalch equation is used to calculate the pH of a solution containing a weak acid and its conjugate base in equilibrium. This equation accounts for the dissociation of the acid and the presence of its conjugate base.
**Why the Correct Answer is Right**
Using the Henderson-Hasselbalch equation, pH = pKa + log10([A-]/[HA]), where [A-] is the concentration of the conjugate base and [HA] is the concentration of the weak acid. Given that the concentrations of the weak acid and its conjugate base are equal (2x10^-3 mol/L), the ratio [A-]/[HA] is 1. Therefore, log10(1) = 0, and pH = pKa + 0 = 3.5. This is consistent with the pKa of the weak acid, which is 3.5.
**Why Each Wrong Option is Incorrect**
**Option A:** 4.1 is incorrect because it is higher than the pKa of the weak acid, which would occur if the ratio [A-]/[HA] was greater than 1.
**Option B:** 3.9 is incorrect because it is lower than the pKa of the weak acid, which would occur if the ratio [A-]/[HA] was less than 1.
**Option D:** 3.1 is incorrect because it is significantly lower than the pKa of the weak acid, which would occur if the acid was fully dissociated.
**Clinical Pearl / High-Yield Fact**
When a weak acid and its conjugate base are present in equal concentrations, the pH of the solution is equal to the pKa of the acid. This is a useful approximation to remember when calculating pH in biochemistry problems.
✓ Correct Answer: C. 3.5