C5H5N is a weak base and has a pKb value of 8.75. What is the pH of an aqueous buffer solution that is 0.300 M C5H5N(aq) and 0.500 M C5H5NHCl(aq)?

Question

C5H5N is a weak base and has a pKb value of 8.75.  What is the pH of an aqueous buffer solution that is 0.300 M C5H5N(aq) and 0.500 M C5H5NHCl(aq)?

BlackTom AI · Accepted Answer

To solve this buffer problem, we identify the base B as C5H5N and its conjugate acid BH+ as C5H5NH+. The Henderson–Hasselbalch equation for a weak base buffer is pOH = pKb + log([BH+]/[B]), and then pH = 14 − pOH.

Option-by-option analysis:

Option 1: 5.25
This would correspond to a pOH of 14 − 5.25 = 8.75. Substituting into pOH = pKb + log([BH+]/[B]) with pKb = 8.75 would require log([BH+]/[B]) = 0, i.e., [BH+] = [B]. However the given concentrations are 0.500 M BH+ and 0.300 M B, not equal, so this value does not match the buffer composition.

Option 2: 5.47
A pH of 5.47 implies pOH ≈ 8.53. Using pOH = 8.75 + log([BH+]/[B]), we would need log([BH+]/[B]) ≈ −0.22, so [BH+]/[B] ≈ 0.60, which contradicts the actual ratio 0.500/0.300 ≈ 1.667. Thus this pH is inconsistent with the given concentrations.

Option 3: 5.03
This is the calculated pH from the proper Henderson–Hasselbalch setup. Compute pOH = pKb + log([BH+]/[B]) = 8.75 + log(0.500/0.300) = 8.75 + log(1.6667) ≈ 8.75 + 0.222 ≈ 8.972. Then pH = 14 − pOH ≈ 14 − 8.972 ≈ 5.028, which rounds to 5.03. This aligns with the given buffer composition and constants.

Option 4: 8.97
A pH of 8.97 would indicate a highly basic solution, corresponding to a much higher pOH (~5.03). This would require a ratio [BH+]/[B] that is far less than 1, which contradicts the given concentrations where the conjugate acid is more abundant than the base.

Option 5: 8.53
This pH would correspond to pOH ≈ 5.47. Using the equation pOH = 8.75 + log([BH+]/[B]), this would require log([BH+]/[B]) ≈ −3.28, i.e., an extremely small [BH+]/[B] ratio far from the provided 0.500/0.300 = 1.667. Therefore it cannot be correct for this buffer.

In summary, only Option 3 (5.03) is consistent with the Henderson–Hasselbalch calculation for a 0.300 M base and 0.500 M conjugate acid with pKb = 8.75, yielding pH ≈ 5.03.

C5H5N is a weak base and has a pKb value of 8.75. What is the pH of an aqueous buffer solution that is 0.300 M C5H5N(aq) and 0.500 M C5H5NHCl(aq)?

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