Question at position 21 What is the pH of a 3.0 M solution of piperidine, C5H10NH? Kb for C5H10NH is 1.3 × 10–3. 5.32 1.20 8.68 12.80Single choice
A
5.32
B
1.20
C
8.68
D
12.80

Question

Question at position 21 What is the pH of a 3.0 M solution of piperidine, C5H10NH? Kb for C5H10NH is 1.3 × 10–3. 5.32 1.20 8.68 12.80

BlackTom AI · Accepted Answer

Piperidine is a weak base; use its Kb to find [OH-], then convert to pH.

1) Relevant concepts
- For a weak base B: B + H2O ⇌ BH+ + OH–, Kb = [BH+][OH–]/[B].
- At initial concentration C and small x formed, [OH–] ≈ x ≈ sqrt(Kb·C) if x << C. pOH = −log[OH–]; pH = 14 − pOH.

2) Step-by-step reasoning and calculation
Write the equilibrium expression:
Kb = x^2 / (C − x), where x = [OH–] at equilibrium and C = 3.0 M.

Use the usual approximation first:
x ≈ sqrt(Kb · C) = sqrt(1.3×10^−3 × 3.0).

Compute inside the root:
1.3×10^−3 × 3.0 = 3.9×10^−3 = 0.0039.

Take the square root:
x ≈ sqrt(0.0039) ≈ 0.06245 M (this is [OH–]).

Check approximation: x/C = 0.06245/3.0 ≈ 0.0208 (≈2.1%), so the approximation is valid.

Compute pOH and pH:
pOH = −log10(0.06245) ≈ 1.204
pH = 14.000 − 1.204 = 12.796 ≈ 12.80

(If solved exactly via the quadratic: x = [−Kb + sqrt(Kb^2 + 4KbC)]/2 = [−0.0013 + sqrt(0.00000169 + 0.0156)]/2 ≈ 0.0618 M, giving pH ≈ 12.79 — same result within rounding.)

3) Why this answer is correct
A 3.0 M solution of a weak base with Kb = 1.3×10^−3 produces a substantial [OH–] (~6×10^−2 M), giving a strongly basic pH near 12.8. The algebra and the small-x check confirm the numeric result.

4) Why the other options are incorrect
- 1.20: corresponds to a strongly acidic solution (pH ~1.2), impossible for a base.
- 5.32: slightly acidic to neutral range; inconsistent with expected basicity from a 3.0 M base.
- 8.68: only mildly basic (pOH = 5.32); this implies [OH–] ≈ 4.8×10^−6 M, far too small given the large base concentration.

5) Conclusion
Calculated pH ≈ 12.80, which matches the provided correct answer: 12.80.

Question at position 21 What is the pH of a 3.0 M solution of piperidine, C5H10NH? Kb for C5H10NH is 1.3 × 10–3. 5.32 1.20 8.68 12.80Single choice

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