Solve the equilibrium problem to calculate the pH of a solution that is 0.075 M nitrous acid (HNO2) and 0.15 M in sodium nitrite (NaNO2), Ka= 4.5 × 10-4.

Question

BlackTom AI · Accepted Answer

Henderson-Hasselbalch equation applies because this is a buffer composed of a weak acid (HNO2) and its conjugate base (NO2− from NaNO2).

1) Relevant knowledge points and concepts
- For a buffer, pH ≈ pKa + log([A−]/[HA]) (Henderson-Hasselbalch).
- pKa = −log(Ka).
- Alternatively, from Ka = [H+][A−]/[HA] one can solve for [H+] directly: [H+] = Ka·[HA]/[A−].

2) Step-by-step reasoning
- Compute pKa from Ka.
- Compute the ratio [A−]/[HA].
- Use Henderson-Hasselbalch to find pH (or compute [H+] using the Ka expression and convert to pH).

3) Calculations with intermediate steps
- Ka = 4.5 × 10−4.
- pKa = −log(4.5 × 10−4) = −(log 4.5 + log 10−4) = −(0.65321 − 4) = 3.34679 ≈ 3.347.
- Ratio [A−]/[HA] = 0.150 / 0.075 = 2.000.
- log([A−]/[HA]) = log(2) = 0.30103.
- pH = pKa + log([A−]/[HA]) = 3.34679 + 0.30103 = 3.64782 ≈ 3.65.

Alternative check (Ka expression):
- [H+] = Ka·[HA]/[A−] = (4.5 × 10−4)·(0.075/0.15) = (4.5 × 10−4)·0.5 = 2.25 × 10−4.
- pH = −log(2.25 × 10−4) = 3.6478 ≈ 3.65 (same result).

4) Why the correct answer is correct
Because the solution is a classic weak-acid/conjugate-base buffer, the Henderson-Hasselbalch relation directly yields pH = pKa + log([A−]/[HA]) and the numerical substitution produces 3.65. The direct Ka calculation gives the same [H+] and pH, confirming consistency.

5) Why other options are incorrect
- 3.47 is close to pKa (3.347) but ignores the effect of the base being twice the acid; it omits the +log(2) term.
- 2.87, 0.82, 1.12 are far from the buffer result; they would result from incorrect algebra, wrong ratio, or misidentifying concentrations or Ka units.

6) Conclusion
Calculated pH = 3.65, which matches the provided correct answer (3.65).

Solve the equilibrium problem to calculate the pH of a solution that is 0.075 M nitrous acid (HNO2) and 0.15 M in sodium nitrite (NaNO2), Ka= 4.5 × 10-4.单项选择题

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