📚 Acid–base Equilibria | 酸碱平衡
Acid–base equilibria form the backbone of aqueous chemistry, explaining how protons are transferred, how pH is controlled, and how buffer systems maintain stability in biological and industrial systems. A solid grasp of these concepts is essential for any A‑Level chemistry student.
酸碱平衡是水溶液化学的核心，它解释了质子如何转移、pH 如何控制，以及缓冲体系如何在生物和工业系统中保持稳定。对任何 A‑Level 化学学生来说，牢固掌握这些概念都至关重要。
1. Brønsted–Lowry Acids and Bases | 布朗斯特–劳里酸碱
According to the Brønsted–Lowry theory, an acid is a species that donates a proton (H⁺) and a base is a species that accepts a proton.
根据布朗斯特–劳里理论，酸是能够提供质子（H⁺）的物种，碱是能够接受质子的物种。
For example, when hydrogen chloride gas dissolves in water, HCl acts as an acid by donating a proton to H₂O, forming the hydronium ion H₃O⁺ and chloride ion Cl⁻: HCl + H₂O → H₃O⁺ + Cl⁻.
例如，氯化氢气体溶于水时，HCl 作为酸将质子给予 H₂O，生成水合氢离子 H₃O⁺ 和氯离子 Cl⁻：HCl + H₂O → H₃O⁺ + Cl⁻。
This theory is not limited to aqueous solutions and can describe acid–base behaviour in non‑aqueous solvents and the gas phase.
该理论并不局限于水溶液，还可以描述非水溶剂和气相中的酸碱行为。
2. Conjugate Acid–Base Pairs | 共轭酸碱对
A conjugate acid–base pair consists of two species that differ by a single proton. The acid donates a proton to become its conjugate base; the base accepts a proton to become its conjugate acid.
共轭酸碱对由相差一个质子的两个物种组成。酸失去一个质子后变成其共轭碱，碱获得一个质子后变成其共轭酸。
In the equilibrium CH₃COOH + H₂O ⇌ CH₃COO⁻ + H₃O⁺, the two pairs are CH₃COOH / CH₃COO⁻ and H₃O⁺ / H₂O. The stronger the acid, the weaker its conjugate base, and vice versa.
在平衡 CH₃COOH + H₂O ⇌ CH₃COO⁻ + H₃O⁺ 中，两对共轭酸碱对分别是 CH₃COOH/CH₃COO⁻ 和 H₃O⁺/H₂O。酸越强，其共轭碱越弱，反之亦然。
3. The Ionic Product of Water, Kw | 水的离子积 Kw
Water undergoes very slight self‑ionisation: 2H₂O ⇌ H₃O⁺ + OH⁻, which is often simplified as H₂O ⇌ H⁺ + OH⁻. The ionic product of water, Kw, is defined as Kw = [H⁺][OH⁻].
水会发生极其微弱的自离解：2H₂O ⇌ H₃O⁺ + OH⁻，常简写为 H₂O ⇌ H⁺ + OH⁻。水的离子积 Kw 定义为 Kw = [H⁺][OH⁻]。
At 298 K (25 °C), Kw has the value 1.0 × 10⁻¹⁴ mol² dm⁻⁶. This equilibrium constant is temperature‑dependent; self‑ionisation is endothermic, so Kw increases with temperature.
在 298 K（25 °C）下，Kw 的值为 1.0 × 10⁻¹⁴ mol² dm⁻⁶。该平衡常数与温度有关；自离解是吸热过程，因此温度升高时 Kw 增大。
4. pH and pOH | pH 和 pOH
The pH of a solution is defined as pH = −log₁₀[H⁺]. Similarly, pOH = −log₁₀[OH⁻]. Because Kw = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴ at 298 K, it follows that pH + pOH = 14.
溶液的 pH 定义为 pH = −log₁₀[H⁺]。类似地，pOH = −log₁₀[OH⁻]。由于在 298 K 时 Kw = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴，因此有 pH + pOH = 14。
A neutral solution at 298 K has [H⁺] = [OH⁻] = 1.0 × 10⁻⁷ mol dm⁻³, giving pH = 7. Acidic solutions have pH < 7, and alkaline solutions have pH > 7.
298 K 下的中性溶液中 [H⁺] = [OH⁻] = 1.0 × 10⁻⁷ mol dm⁻³，pH = 7。酸性溶液的 pH < 7，碱性溶液的 pH > 7。
5. Strong Acids and Strong Bases | 强酸和强碱
A strong acid is fully dissociated in aqueous solution. Common examples include HCl, HNO₃ and H₂SO₄ (first dissociation complete). For a monoprotic strong acid, [H⁺] equals the acid concentration, so pH = −log₁₀[acid].
强酸在水溶液中完全解离。常见例子包括 HCl、HNO₃ 和 H₂SO₄（第一步完全解离）。对于一元强酸，[H⁺] 等于酸浓度，因此 pH = −log₁₀[酸]。
A strong base, such as NaOH or KOH, is also fully dissociated, giving [OH⁻] equal to the base concentration. The pH can then be found using pOH = −log₁₀[base] and pH = 14 − pOH (at 25 °C).
强碱如 NaOH 或 KOH 同样完全解离，[OH⁻] 等于碱浓度。然后可利用 pOH = −log₁₀[碱] 及 pH = 14 − pOH（25 °C 下）求得 pH。
6. Weak Acids and Ka | 弱酸与酸解离常数 Ka
A weak acid, such as ethanoic acid CH₃COOH, dissociates only partially in water. The equilibrium constant for this reaction is the acid dissociation constant, Ka: Ka = [H⁺][A⁻] / [HA].
弱酸，例如乙酸 CH₃COOH，在水中仅部分解离。该反应的平衡常数称为酸解离常数 Ka：Ka = [H⁺][A⁻] / [HA]。
For a weak acid, we often assume that the amount dissociated is negligible compared to the initial concentration. This leads to the approximation [H⁺] ≈ √(Ka × [HA]₀), allowing simple pH calculation.
对于弱酸，通常假设其解离量与初始浓度相比可忽略不计。于是可用近似公式 [H⁺] ≈ √(Ka × [HA]₀) 来简化 pH 的计算。
It is essential to check that the approximation is valid; usually it is acceptable when [HA]₀ / Ka > 100.
使用该近似时必须验证其有效性；通常当 [HA]₀ / Ka > 100 时是可行的。
7. Weak Bases and Kb | 弱碱与碱解离常数 Kb
A weak base, such as ammonia NH₃, reacts partially with water to produce OH⁻ ions: NH₃ + H₂O ⇌ NH₄⁺ + OH⁻. The base dissociation constant Kb is Kb = [NH₄⁺][OH⁻] / [NH₃].
弱碱（如氨 NH₃）与水部分反应生成 OH⁻ 离子：NH₃ + H₂O ⇌ NH₄⁺ + OH⁻。碱解离常数 Kb 为 Kb = [NH₄⁺][OH⁻] / [NH₃]。
Using the same small‑dissociation approximation, [OH⁻] ≈ √(Kb × [base]₀). The pH is then obtained from [OH⁻] and Kw.
采用相同的小解离量近似，可得 [OH⁻] ≈ √(Kb × [碱]₀)。然后由 [OH⁻] 和 Kw 求得 pH。
8. pKa and pKb | pKa 与 pKb
For convenience, acid and base strengths are often expressed as pKa = −log₁₀Ka and pKb = −log₁₀Kb. The smaller the pKa, the stronger the acid.
为方便起见，酸碱强度常用 pKa = −log₁₀Ka 和 pKb = −log₁₀Kb 表示。pKa 越小，酸性越强。
For a conjugate acid–base pair at 298 K, the relationship pKa + pKb = 14 holds because Ka × Kb = Kw.
在 298 K 下，对于共轭酸碱对，因 Ka × Kb = Kw 而有 pKa + pKb = 14。
9. Buffer Solutions | 缓冲溶液
A buffer solution resists changes in pH when small amounts of acid or base are added. It typically consists of a weak acid and its conjugate base (e.g. CH₃COOH / CH₃COO⁻) or a weak base and its conjugate acid (e.g. NH₃ / NH₄⁺).
缓冲溶液能在加入少量酸或碱时抵抗 pH 的变化。它通常由弱酸及其共轭碱（如 CH₃COOH / CH₃COO⁻）或弱碱及其共轭酸（如 NH₃ / NH₄⁺）组成。
The buffer works by the equilibrium HA ⇌ H⁺ + A⁻. Added H⁺ reacts with A⁻ to form HA, while added OH⁻ reacts with HA to form A⁻ and water, keeping the [H⁺] nearly constant.
缓冲作用的原理是平衡 HA ⇌ H⁺ + A⁻。加入的 H⁺ 会与 A⁻ 反应生成 HA，加入的 OH⁻ 则与 HA 反应生成 A⁻ 和水，从而使 [H⁺] 几乎保持不变。
10. Henderson–Hasselbalch Equation | 亨德森–哈塞尔巴尔赫方程
The pH of a buffer can be calculated using the Henderson–Hasselbalch equation:
pH = pKa + log₁₀([A⁻] / [HA])
缓冲溶液的 pH 可用亨德森–哈塞尔巴尔赫方程计算：
pH = pKa + log₁₀([A⁻] / [HA])
This equation assumes that the concentrations of the conjugate base and weak acid are appreciable and that the approximations inherent in the derivation are valid.
该方程假设共轭碱和弱酸的浓度足够大，且推导过程中的近似是成立的。
11. Acid–Base Titrations | 酸碱滴定
In an acid–base titration, the pH is monitored as a standard solution of one reactant is added to the other. The shape of the pH curve depends on the strength of the acid and base involved.
在酸碱滴定中，随着将一种反应物的标准溶液加入另一种反应物，持续监测 pH 的变化。pH 曲线的形状取决于所涉及的酸和碱的强度。
- Strong acid – strong base: The equivalence point occurs at pH 7, and the curve shows a very steep vertical rise.
- 强酸 – 强碱：等当点出现在 pH 7，曲线呈现非常陡峭的垂直上升。
- Weak acid – strong base: The equivalence point lies above pH 7; the initial buffer region is prominent and the half‑equivalence point gives pH = pKa.
- 弱酸 – 强碱：等当点位于 pH > 7 的区域；初期的缓冲区域十分明显，半等当点处 pH = pKa。
- Weak base – strong acid: The equivalence point lies below pH 7, and the half‑equivalence point corresponds to pKa of the conjugate acid.
- 弱碱 – 强酸：等当点位于 pH < 7，半等当点对应共轭酸的 pKa。
12. Indicator Selection | 指示剂的选择
An acid–base indicator is itself a weak acid or base whose conjugate forms have different colours. The indicator changes colour over a pH range roughly given by pKᵢₙ ± 1, where pKᵢₙ is the indicator’s pKa.
酸碱指示剂本身是一种弱酸或弱碱，其共轭形式具有不同的颜色。指示剂变色的 pH 范围约为 pKᵢₙ ± 1，其中 pKᵢₙ 是指示剂的 pKa。
To choose an appropriate indicator, its colour‑change range should fall within the steep vertical section of the titration curve, ensuring that the end point coincides closely with the equivalence point.
要选择合适的指示剂，其变色范围应落在滴定曲线陡峭的垂直段内，以确保终点与等当点尽可能重合。
| Indicator | pH range | Suitable titration |
|---|---|---|
| Methyl orange | 3.1 – 4.4 | Strong acid – strong base / weak base |
| Phenolphthalein | 8.2 – 10.0 | Strong acid – strong base / weak acid |
| 指示剂 | pH 范围 | 适用滴定 |
|---|---|---|
| 甲基橙 | 3.1 – 4.4 | 强酸–强碱 / 弱碱 |
| 酚酞 | 8.2 – 10.0 | 强酸–强碱 / 弱酸 |
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