📚 Acids and Bases Revision Guide | 酸与碱考点精讲
Acids and bases form a core pillar of A-Level CIE Chemistry, underpinning everything from equilibrium calculations to biochemical processes. This guide consolidates essential concepts, mathematical derivations, and common pitfalls, ensuring you approach titration curves, buffer problems, and pH calculations with confidence.
酸和碱是 A-Level CIE 化学的核心支柱，支撑着从平衡计算到生物化学过程的一切内容。本指南整合了基本概念、数学推导和常见易错点，确保你能自信地应对滴定曲线、缓冲溶液和 pH 计算题。
1. Brønsted–Lowry Theory | 布朗斯特–劳里酸碱理论
According to the Brønsted–Lowry definition, an acid is a proton (H⁺) donor, and a base is a proton acceptor. This extends the classical Arrhenius picture to non-aqueous systems and explains the behaviour of species like NH₃ and HCl gas reacting in the absence of water.
根据布朗斯特–劳里定义，酸是质子 (H⁺) 的给予体，碱是质子的接受体。这一定义将经典的阿伦尼乌斯图像扩展到非水体系，并解释了 NH₃ 和 HCl 气体在无水条件下反应的行为。
When hydrochloric acid dissolves in water, the HCl molecule donates a proton to H₂O, forming H₃O⁺ and Cl⁻. Water acts as a base in this forward reaction. The reverse reaction sees H₃O⁺ acting as an acid and Cl⁻ as a base, illustrating the dynamic acid–base interplay.
当盐酸溶于水时，HCl 分子将质子给予 H₂O，生成 H₃O⁺ 和 Cl⁻。在这个正向反应中，水充当碱。在逆反应中，H₃O⁺ 充当酸，Cl⁻ 充当碱，体现了动态的酸碱相互作用。
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. For the equilibrium HA ⇌ H⁺ + A⁻, HA is the acid, and A⁻ is its conjugate base. Similarly, when a base B accepts a proton, BH⁺ becomes the conjugate acid.
共轭酸碱对由两个仅相差一个质子的物种组成。对于平衡 HA ⇌ H⁺ + A⁻，HA 是酸，A⁻ 是其共轭碱。同样，当碱 B 接受一个质子后，BH⁺ 便成为共轭酸。
Recognising conjugate pairs helps predict the direction of acid–base equilibria. A strong acid has a very weak conjugate base, while a weak acid has a relatively stronger conjugate base. This relationship is quantified by the equilibrium constants Ka and Kb, which are linked by Kw.
识别共轭对有助于预测酸碱平衡的方向。强酸的共轭碱非常弱，而弱酸的共轭碱相对较强。这种关系可通过平衡常数 Ka 和 Kb 进行量化，它们由 Kw 联系起来。
| Acid | Conjugate Base |
|---|---|
| HCl | Cl⁻ |
| CH₃COOH | CH₃COO⁻ |
| NH₄⁺ | NH₃ |
| H₂O | OH⁻ |
3. The pH Scale and Calculations | pH 标度与计算
The pH of a solution is defined as the negative logarithm (base 10) of the hydrogen ion concentration. Mathematically, pH = –log₁₀[H⁺]. For aqueous solutions at 298 K, the scale typically runs from 0 to 14, although values outside this range are possible for extremely concentrated strong acids or bases.
溶液的 pH 定义为氢离子浓度的负常用对数（以 10 为底）。数学上，pH = –log₁₀[H⁺]。在 298 K 的水溶液中，标度通常从 0 到 14，尽管对于极高浓度的强酸或强碱，数值可能超出该范围。
pH = –log₁₀[H⁺] pOH = –log₁₀[OH⁻] pH + pOH = 14 (at 298 K)
To calculate the pH of a strong monoprotic acid such as 0.10 mol dm⁻³ HCl, we assume complete dissociation, giving [H⁺] = 0.10 mol dm⁻³, so pH = –log₁₀(0.10) = 1.00. For strong bases like NaOH, [OH⁻] equals the base concentration, and pOH is calculated first, then converted to pH.
要计算强一元酸（如 0.10 mol dm⁻³ HCl）的 pH，我们假设完全解离，则 [H⁺] = 0.10 mol dm⁻³，因此 pH = –log₁₀(0.10) = 1.00。对于 NaOH 等强碱，[OH⁻] 等于碱的浓度，先计算 pOH，再转换为 pH。
4. Strong Acids and Bases | 强酸与强碱
A strong acid is one that dissociates completely in aqueous solution, meaning the equilibrium lies far to the right: HA → H⁺ + A⁻. Common examples include HCl, HBr, HI, HNO₃, and H₂SO₄ (first dissociation only; the second dissociation of H₂SO₄ is not fully strong). As a result, the concentration of H⁺ equals the initial acid concentration for monoprotic strong acids.
强酸是在水溶液中完全解离的酸，意味着平衡强烈偏向右侧：HA → H⁺ + A⁻。常见实例包括 HCl、HBr、HI、 HNO₃ 和 H₂SO₄（仅第一级解离；H₂SO₄ 的第二级解离并非完全强电离）。因此，对于一元强酸，H⁺ 浓度等于酸的初始浓度。
Strong bases, such as Group 1 metal hydroxides (NaOH, KOH) and some Group 2 hydroxides (e.g. Ba(OH)₂, though solubility must be considered), fully dissociate to release OH⁻ ions. For Ba(OH)₂, each formula unit produces two OH⁻ ions, so [OH⁻] = 2 × [Ba(OH)₂] before using the ionic product of water to find [H⁺].
强碱，如第 1 族金属氢氧化物（NaOH、KOH）和部分第 2 族氢氧化物（如 Ba(OH)₂，但需考虑溶解度），完全解离释放 OH⁻。对于 Ba(OH)₂，每个化学式单元产生两个 OH⁻，因此 [OH⁻] = 2 × [Ba(OH)₂]，再用水的离子积求出 [H⁺]。
5. Weak Acids and Ka | 弱酸与酸解离常数
A weak acid only partially dissociates, establishing an equilibrium: HA(aq) ⇌ H⁺(aq) + A⁻(aq). The acid dissociation constant, Ka, quantifies the strength of the acid. It is expressed as:
弱酸仅部分解离，建立一个平衡：HA(aq) ⇌ H⁺(aq) + A⁻(aq)。酸解离常数 Ka 用于量化酸的强度，其表达式为：
Ka = [H⁺][A⁻] / [HA]
The units of Ka are mol dm⁻³. A larger Ka value indicates a stronger weak acid. Because only a tiny fraction of HA ionises, we often approximate that the equilibrium concentration of HA equals the initial concentration, provided the degree of dissociation is less than 5%.
Ka 的单位是 mol dm⁻³。Ka 值越大，表示弱酸越强。由于仅有极小部分 HA 电离，若解离度小于 5%，我们常近似假定 HA 的平衡浓度等于其初始浓度。
For a generic weak acid, [H⁺] is calculated using Ka = x² / C, where x = [H⁺] and C is the initial concentration of the acid. Solving gives [H⁺] = √(Ka × C). This square‑root relationship is a staple of A‑Level pH calculations.
对于一般弱酸，使用 Ka = x² / C 计算 [H⁺]，其中 x = [H⁺]，C 是酸的初始浓度。解得 [H⁺] = √(Ka × C)。这一平方根关系是 A‑Level pH 计算中的常见考点。
6. pKa and its Significance | pKa 及其意义
pKa is the negative logarithm of Ka, analogous to pH: pKa = –log₁₀ Ka. A smaller pKa corresponds to a stronger acid. For ethanoic acid, Ka = 1.8 × 10⁻⁵ mol dm⁻³, so pKa = 4.74. This logarithmic scale makes it easier to compare acid strengths.
pKa 是 Ka 的负对数，类似于 pH：pKa = –log₁₀ Ka。pKa 越小，酸性越强。对于乙酸，Ka = 1.8 × 10⁻⁵ mol dm⁻³，因此 pKa = 4.74。这种对数标度使比较酸强度变得更加直观。
At the half‑equivalence point of a weak acid–strong base titration, pH equals pKa because [HA] = [A⁻]. This relationship is the foundation for choosing indicators and understanding buffer capacity. Students must be able to calculate pKa from Ka and vice versa.
在弱酸‑强碱滴定的半中和点，由于 [HA] = [A⁻]，pH 等于 pKa。这一关系是选择指示剂和理解缓冲容量的基础。学生必须能够进行 Ka 和 pKa 之间的相互换算。
7. The Ionic Product of Water, Kw | 水的离子积 Kw
Water undergoes slight self‑ionisation: 2H₂O(l) ⇌ H₃O⁺(aq) + OH⁻(aq), simplified to H₂O(l) ⇌ H⁺(aq) + OH⁻(aq). The equilibrium constant for this process is the ionic product of water, Kw.
水存在微弱的自耦电离：2H₂O(l) ⇌ H₃O⁺(aq) + OH⁻(aq)，简写为 H₂O(l) ⇌ H⁺(aq) + OH⁻(aq)。该过程的平衡常数称为水的离子积 Kw。
Kw = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴ mol² dm⁻⁶ at 298 K
Because Kw is constant at a given temperature, knowing either [H⁺] or [OH⁻] allows the other to be determined. At 298 K, pure water has [H⁺] = 1.0 × 10⁻⁷ mol dm⁻³, hence pH = 7. If the temperature increases, Kw increases slightly, so the pH of neutral water falls below 7.
由于 Kw 在给定温度下是常数，只要知道 [H⁺] 或 [OH⁻] 中的一个，就能求出另一个。在 298 K 时，纯水中 [H⁺] = 1.0 × 10⁻⁷ mol dm⁻³，因此 pH = 7。如果温度升高，Kw 略微增大，中性水的 pH 就会低于 7。
8. pH of Weak Bases | 弱碱的 pH
For a weak base such as NH₃, the equilibrium is B(aq) + H₂O(l) ⇌ BH⁺(aq) + OH⁻(aq). The base dissociation constant, Kb, is defined similarly to Ka:
对于 NH₃ 等弱碱，平衡为 B(aq) + H₂O(l) ⇌ BH⁺(aq) + OH⁻(aq)。碱解离常数 Kb 的定义与 Ka 类似：
Kb = [BH⁺][OH⁻] / [B]
As with weak acids, [OH⁻] = √(Kb × C), where C is the initial base concentration. The pOH is then –log₁₀[OH⁻], and pH = 14 – pOH. CIE often provides pKa values: to get Kb, use the relationship Ka × Kb = Kw for a conjugate acid–base pair.
与弱酸类似，[OH⁻] = √(Kb × C)，C 为碱的初始浓度。然后 pOH = –log₁₀[OH⁻]，pH = 14 – pOH。CIE 考试常给出 pKa 值：要求 Kb 时，可利用共轭酸碱对中 Ka × Kb = Kw 这一关系。
For example, ammonia NH₃ has Kb = 1.8 × 10⁻⁵ mol dm⁻³. For a 0.10 mol dm⁻³ solution, [OH⁻] = √(1.8×10⁻⁵ × 0.10) = 1.34 × 10⁻³ mol dm⁻³, giving pOH = 2.87 and pH = 11.13. Always check that the approximation (degree of ionisation < 5%) is valid.
例如，氨 NH₃ 的 Kb = 1.8 × 10⁻⁵ mol dm⁻³。对于 0.10 mol dm⁻³ 溶液，[OH⁻] = √(1.8×10⁻⁵ × 0.10) = 1.34 × 10⁻³ mol dm⁻³，得出 pOH = 2.87，pH = 11.13。务必检验近似条件（电离度 < 5%）是否成立。
9. Acid–Base Titration Curves | 酸碱滴定曲线
Titration curves plot pH against the volume of titrant added. Their shape depends on the strengths of the acid and base involved. The four main combinations tested at CIE are: strong acid–strong base, strong acid–weak base, weak acid–strong base, and weak acid–weak base (though the latter lacks a sharp endpoint and is rarely used for analytical purposes).
滴定曲线描绘了 pH 随滴定剂加入体积的变化。曲线的形状取决于所用酸和碱的强度。CIE 考试中主要涉及四种组合：强酸‑强碱、强酸‑弱碱、弱酸‑强碱以及弱酸‑弱碱（不过弱酸‑弱碱缺乏明显的滴定突跃，很少用于分析目的）。
Key features to note:
- Initial pH: lower for strong acid than for weak acid.
- Equivalence point: pH = 7 for strong acid–strong base; pH > 7 for weak acid–strong base; pH < 7 for strong acid–weak base.
- Buffer region: for weak acid–strong base, a flat region appears before the equivalence point where pH changes slowly.
- Vertical rise: the steep portion around equivalence, essential for indicator selection.
需要注意的关键特征：
- 初始 pH：强酸的初始 pH 低于弱酸。
- 计量点：强酸‑强碱的 pH = 7；弱酸‑强碱的 pH > 7；强酸‑弱碱的 pH < 7。
- 缓冲区域：在弱酸‑强碱滴定中，计量点前会出现一段 pH 变化平缓的缓冲区。
- 垂直突跃：计量点附近的陡峭区间，对指示剂的选择至关重要。
10. Buffer Solutions | 缓冲溶液
A buffer solution resists changes in pH when small amounts of acid or base are added. It contains a weak acid and its conjugate base (or a weak base and its conjugate acid). Typical examples are CH₃COOH/CH₃COO⁻ and NH₄⁺/NH₃.
缓冲溶液能在加入少量酸或碱时抵抗 pH 变化。它由弱酸及其共轭碱（或弱碱及其共轭酸）组成。典型实例有 CH₃COOH/CH₃COO⁻ 和 NH₄⁺/NH₃。
The Henderson–Hasselbalch equation is central to buffer calculations:
pH = pKa + log₁₀([A⁻] / [HA])
This formula is applicable when the concentrations of the acid and its salt (conjugate base) are known. For basic buffers, using pKa of the conjugate acid (e.g. NH₄⁺) is recommended. The equation shows that when [A⁻] = [HA], pH = pKa, which is the basis of buffer capacity.
该公式适用于已知酸及其盐（共轭碱）浓度的情况。对于碱性缓冲体系，建议使用共轭酸（如 NH₄⁺）的 pKa。方程表明，当 [A⁻] = [HA] 时，pH = pKa，这也是缓冲容量的基础。
To prepare a buffer with a specific pH, choose an acid whose pKa is close to the desired pH and adjust the ratio [A⁻]/[HA] accordingly. Common experimental methods include mixing the weak acid with a solution of its sodium salt or partially neutralising a weak acid with a strong base.
若要制备特定 pH 的缓冲液，可选用 pKa 与目标 pH 相近的弱酸，然后相应调整 [A⁻]/[HA] 的比值。常用的实验方法包括：将弱酸与其钠盐溶液混合，或用强碱部分中和弱酸。
11. Indicators and pH Range | 指示剂与 pH 范围
Acid–base indicators are weak acids (or bases) whose conjugate forms have different colours. The indicator equilibrium is HIn(aq) ⇌ H⁺(aq) + In⁻(aq), where HIn and In⁻ display distinct colours. The colour change occurs over a pH range of roughly pKa(In) ± 1.
酸碱指示剂是共轭形式具有不同颜色的弱酸（或弱碱）。指示剂的平衡为 HIn(aq) ⇌ H⁺(aq) + In⁻(aq)，其中 HIn 与 In⁻ 呈现不同颜色。颜色变化大约发生在 pKa(In) ± 1 的 pH 范围内。
Common indicators and their ranges:
- Methyl orange: pH 3.1–4.4 (red to yellow), suitable for strong acid–strong base or strong acid–weak base titrations.
- Phenolphthalein: pH 8.2–10.0 (colourless to pink), ideal for weak acid–strong base titrations.
- Bromothymol blue: pH 6.0–7.6 (yellow to blue), used near neutrality.
常见指示剂及其变色范围：
- 甲基橙：pH 3.1–4.4（红至黄），适用于强酸‑强碱或强酸‑弱碱滴定。
- 酚酞：pH 8.2–10.0（无色至粉红），适用于弱酸‑强碱滴定。
- 溴百里酚蓝：pH 6.0–7.6（黄至蓝），用于近中性滴定。
The choice of indicator depends on the pH at the equivalence point. The indicator’s colour‑change interval must lie entirely within the vertical portion of the titration curve. A mismatch leads to a significant titration error.
指示剂的选择取决于计量点的 pH 值。指示剂的变色区间必须完全落在滴定曲线的垂直突跃部分。若匹配不当，将导致显著的滴定误差。
12. Summary of Key Equations | 关键公式总结
Memorising the core formulae is essential for solving CIE quantitative problems. Always pay attention to units and assumptions.
熟记核心公式对解答 CIE 定量问题至关重要。务必注意单位和假设条件。
| Equation | Usage |
|---|---|
| pH = –log₁₀[H⁺] | Direct pH calculation |
| [H⁺] = 10⁻ᵖᴴ | Converting pH to concentration |
| Kw = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴ | Linking [H⁺] and [OH⁻] |
| Ka = [H⁺][A⁻] / [HA] | Weak acid equilibrium constant |
| [H⁺] = √(Ka × C) | Approximate [H⁺] for weak acid |
| pKa = –log₁₀ Ka | Converting Ka to pKa |
| pH = pKa + log₁₀([A⁻]/[HA]) | Henderson–Hasselbalch for buffers |
| Ka × Kb = Kw | Conjugate acid–base pair relationship |
Revise by applying these equations to varied scenarios: calculating the pH after dilution, determining the mass of salt needed to prepare a buffer, or predicting the shape of a titration curve. Familiarity with logarithmic manipulation is also tested, so practise converting between exponential and logarithmic forms.
通过将这些公式应用于不同场景进行复习：计算稀释后的 pH、确定制备缓冲液所需盐的质量，或预测滴定曲线的形状。对数运算也是考点，因此要练习指数形式与对数形式之间的相互转换。
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