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单项选择题
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 12.80单项选择题

类似问题

At which ONE of the following pH values would lignocaine hydrochloride (weak base; pKa = 7.9; a local anaesthetic and antiarrhythmic drug) have the slowest dissolution rate?

What is the pH of a 0.47 M ammonia solution given Ka for ammonium ion is 5.56 x 10–10?

Find the percent ionization of a 0.337 M HF solution. The Ka for HF is 3.5 × 10-4.

Which of the following statements correctly explains the dissociation of ethanoic acid in water?

Which of the following statements correctly explains the dissociation of ethanoic acid in water?

In which direction does the following equilibrium lie?

The correct operational relationship between pKa and pH is that...

更多留学生实用工具

智能学习助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单