📚 Acid-Base Equilibria | 酸碱平衡
Acid-base equilibria is a core topic in Edexcel A-Level Chemistry, bringing together equilibrium principles, pH calculations and practical titration curves. Mastery of this topic enables you to predict pH changes, design buffer solutions and interpret titration data accurately.
酸碱平衡是 Edexcel A-Level 化学的核心主题之一，它综合了平衡原理、pH 计算和实际滴定曲线。掌握这一主题能让你准确预测 pH 变化、设计缓冲溶液并解读滴定数据。
1. Brønsted-Lowry Theory | 布朗斯特-劳里理论
A Brønsted-Lowry acid is a proton donor, while a Brønsted-Lowry base is a proton acceptor. For example, when hydrogen chloride dissolves in water, HCl donates a proton to H₂O, forming H₃O⁺ and Cl⁻. Here HCl is the acid and H₂O acts as a base.
布朗斯特-劳里酸是质子供体，而布朗斯特-劳里碱是质子受体。例如，氯化氢溶于水时，HCl 将质子给予 H₂O，生成 H₃O⁺ 和 Cl⁻。这里 HCl 是酸，H₂O 充当碱。
Every acid-base reaction has two conjugate acid-base pairs. In the equilibrium NH₃ + H₂O ⇌ NH₄⁺ + OH⁻, the pairs are NH₄⁺/NH₃ and H₂O/OH⁻. Identifying these pairs is essential for understanding buffer action and equilibrium position.
每个酸碱反应都有两对共轭酸碱对。在平衡 NH₃ + H₂O ⇌ NH₄⁺ + OH⁻ 中，共轭酸碱对为 NH₄⁺/NH₃ 和 H₂O/OH⁻。能识别这些酸碱对对于理解缓冲作用和平衡位置至关重要。
2. pH and Strong Acids/Bases | pH 与强酸强碱
pH is defined as the negative logarithm to base 10 of the hydrogen ion concentration. The equation is written as follows.
pH 定义为氢离子浓度的以 10 为底的负对数。其方程如下。
pH = -log₁₀[H⁺]
A strong acid such as HCl or HNO₃ fully dissociates in aqueous solution, so [H⁺] equals the acid concentration. For a 0.050 mol dm⁻³ solution of HCl, [H⁺] = 0.050 mol dm⁻³ and pH = -log₁₀(0.050) ≈ 1.30.
强酸如 HCl 或 HNO₃ 在水溶液中完全电离，因此 [H⁺] 等于酸的浓度。对于 0.050 mol dm⁻³ 的 HCl 溶液，[H⁺] = 0.050 mol dm⁻³，pH = -log₁₀(0.050) ≈ 1.30。
For strong bases such as NaOH, the base fully dissociates to give OH⁻ ions. To find pH, first use Kw to calculate [H⁺] from [OH⁻]. For example, if [NaOH] = 0.010 mol dm⁻³, then [OH⁻] = 0.010 mol dm⁻³, so [H⁺] = Kw / [OH⁻] = 1.0 × 10⁻¹⁴ / 0.010 = 1.0 × 10⁻¹² mol dm⁻³, giving pH = 12.00.
对于强碱如 NaOH，碱完全电离产生 OH⁻ 离子。求 pH 时，先用 Kw 由 [OH⁻] 计算 [H⁺]。例如，若 [NaOH] = 0.010 mol dm⁻³，则 [OH⁻] = 0.010 mol dm⁻³，所以 [H⁺] = Kw / [OH⁻] = 1.0 × 10⁻¹⁴ / 0.010 = 1.0 × 10⁻¹² mol dm⁻³，pH = 12.00。
3. Weak Acids and Ka | 弱酸与 Ka
A weak acid only partially dissociates in water. For a general weak acid HA, the equilibrium is HA ⇌ H⁺ + A⁻. The acid dissociation constant Ka is written as follows.
弱酸在水中仅部分电离。对于一般的弱酸 HA，平衡为 HA ⇌ H⁺ + A⁻。酸离解常数 Ka 表示如下。
Ka = [H⁺][A⁻] / [HA]
Since the dissociation of a weak acid produces equal amounts of H⁺ and A⁻, we can assume [H⁺] = [A⁻]. If the initial concentration of the acid is c and the degree of dissociation is small, then at equilibrium [HA] ≈ c. Substituting gives [H⁺] = √(Ka × c).
由于弱酸电离产生等量的 H⁺ 和 A⁻，我们可以假设 [H⁺] = [A⁻]。若酸的初始浓度为 c 且电离度很小，则平衡时 [HA] ≈ c。代入可得 [H⁺] = √(Ka × c)。
For ethanoic acid at 25 °C, Ka = 1.8 × 10⁻⁵ mol dm⁻³. The pH of a 0.100 mol dm⁻³ solution is calculated as [H⁺] = √(1.8 × 10⁻⁵ × 0.100) = 1.34 × 10⁻³ mol dm⁻³, so pH = -log₁₀(1.34 × 10⁻³) ≈ 2.87.
对于 25 °C 下的乙酸，Ka = 1.8 × 10⁻⁵ mol dm⁻³。0.100 mol dm⁻³ 溶液的 pH 计算为 [H⁺] = √(1.8 × 10⁻⁵ × 0.100) = 1.34 × 10⁻³ mol dm⁻³，因此 pH = -log₁₀(1.34 × 10⁻³) ≈ 2.87。
4. pKa and Acid Strength | pKa 与酸性强度
pKa is defined as the negative logarithm of Ka, providing a more convenient scale for comparing acid strength.
pKa 定义为 Ka 的负对数，为比较酸的强度提供了更方便的尺度。
pKa = -log₁₀ Ka
The smaller the pKa value, the larger the Ka and the stronger the acid. For example, ethanoic acid has pKa = 4.74, while chloroethanoic acid has pKa = 2.86, confirming that chloroethanoic acid is the stronger acid.
pKa 值越小，Ka 越大，酸性越强。例如，乙酸的 pKa = 4.74，而氯乙酸的 pKa = 2.86，这证实氯乙酸是更强的酸。
During a titration, the pKa of a weak acid equals the pH at the half-equivalence point. This relationship is used to determine Ka experimentally from a pH titration curve.
在滴定过程中，弱酸的 pKa 等于半等当量点处的 pH。这一关系常用于通过 pH 滴定曲线实验测定 Ka。
5. Weak Bases and Kb | 弱碱与 Kb
A weak base such as aqueous ammonia only partially reacts with water. The equilibrium is NH₃ + H₂O ⇌ NH₄⁺ + OH⁻, and the base dissociation constant Kb is expressed as follows.
弱碱如氨水仅与水部分反应。平衡为 NH₃ + H₂O ⇌ NH₄⁺ + OH⁻，碱离解常数 Kb 表示如下。
Kb = [NH₄⁺][OH⁻] / [NH₃]
Using the same approximation as for weak acids, [OH⁻] = √(Kb × c) where c is the initial concentration of the weak base. For a 0.100 mol dm⁻³ ammonia solution with Kb = 1.8 × 10⁻⁵ mol dm⁻³, [OH⁻] = √(1.8 × 10⁻⁵ × 0.100) = 1.34 × 10⁻³ mol dm⁻³.
使用与弱酸相同的近似方法，[OH⁻] = √(Kb × c)，其中 c 是弱碱的初始浓度。对于 Kb = 1.8 × 10⁻⁵ mol dm⁻³ 的 0.100 mol dm⁻³ 氨溶液，[OH⁻] = √(1.8 × 10⁻⁵ × 0.100) = 1.34 × 10⁻³ mol dm⁻³。
To obtain pH, first calculate [H⁺] from [OH⁻] using Kw. Here [H⁺] = 1.0 × 10⁻¹⁴ / 1.34 × 10⁻³ = 7.46 × 10⁻¹² mol dm⁻³, so pH = -log₁₀(7.46 × 10⁻¹²) ≈ 11.13.
为求得 pH，先用 Kw 由 [OH⁻] 计算 [H⁺]。此处 [H⁺] = 1.0 × 10⁻¹⁴ / 1.34 × 10⁻³ = 7.46 × 10⁻¹² mol dm⁻³，所以 pH = -log₁₀(7.46 × 10⁻¹²) ≈ 11.13。
6. Ionic Product of Water Kw | 水的离子积 Kw
Water undergoes very slight self-ionisation according to the equilibrium 2H₂O ⇌ H₃O⁺ + OH⁻. The ionic product of water, Kw, is defined as follows.
水按照平衡 2H₂O ⇌ H₃O⁺ + OH⁻ 发生极轻微的自偶电离。水的离子积 Kw 定义如下。
Kw = [H⁺][OH⁻]
At 25 °C, Kw has the value 1.0 × 10⁻¹⁴ mol² dm⁻⁶. This means that in pure water [H⁺] = [OH⁻] = 1.0 × 10⁻⁷ mol dm⁻³, giving pH = 7.00.
在 25 °C 时，Kw 的值为 1.0 × 10⁻¹⁴ mol² dm⁻⁶。这意味着纯水中 [H⁺] = [OH⁻] = 1.0 × 10⁻⁷ mol dm⁻³，因此 pH = 7.00。
The self-ionisation of water is endothermic, so increasing temperature shifts the equilibrium to the right and increases Kw. As a result, the pH of pure water becomes less than 7 at temperatures above 25 °C, even though the solution is still neutral because [H⁺] still equals [OH⁻].
水的自偶电离是吸热过程，因此升高温度会使平衡向右移动并增大 Kw。结果，在高于 25 °C 的温度下纯水的 pH 小于 7，但溶液仍然是中性的，因为 [H⁺] 仍等于 [OH⁻]。
7. Buffer Solutions | 缓冲溶液
A buffer solution resists changes in pH when small amounts of acid or base are added. A common acidic buffer consists of a weak acid and its conjugate base, such as ethanoic acid and sodium ethanoate.
缓冲溶液能在加入少量酸或碱时抵抗 pH 的变化。常见的酸性缓冲液由弱酸及其共轭碱组成，例如乙酸和乙酸钠。
When a small amount of acid is added, the added H⁺ ions react with the conjugate base CH₃COO⁻ to form CH₃COOH. When a small amount of base is added, the OH⁻ ions react with the weak acid CH₃COOH to form CH₃COO⁻ and water. In both cases the pH changes only slightly.
当加入少量酸时，加入的 H⁺ 离子与共轭碱 CH₃COO⁻ 反应生成 CH₃COOH。当加入少量碱时，OH⁻ 离子与弱酸 CH₃COOH 反应生成 CH₃COO⁻ 和水。两种情况下 pH 仅发生微小变化。
A basic buffer can be made from a weak base and its conjugate acid, such as ammonia and ammonium chloride. It works by the same principle but controls pH in the basic range.
碱性缓冲液可由弱碱及其共轭酸制成，例如氨和氯化铵。其作用原理相同，但在碱性范围内控制 pH。
8. Buffer Calculations | 缓冲溶液的计算
The pH of an acidic buffer can be calculated using the equilibrium expression for the weak acid. Rearranging Ka = [H⁺][A⁻] / [HA] gives the following useful form.
酸性缓冲液的 pH 可用弱酸的平衡表达式计算。将 Ka = [H⁺][A⁻] / [HA] 重排可得到以下有用形式。
pH = pKa + log₁₀([A⁻] / [HA])
In a buffer made from 0.10 mol dm⁻³ ethanoic acid and 0.20 mol dm⁻³ sodium ethanoate, [HA] = 0.10 mol dm⁻³ and [A⁻] = 0.20 mol dm⁻³. With pKa = 4.74, pH = 4.74 + log₁₀(0.20 / 0.10) = 4.74 + 0.30 = 5.04.
在由 0.10 mol dm⁻³ 乙酸和 0.20 mol dm⁻³ 乙酸钠组成的缓冲液中，[HA] = 0.10 mol dm⁻³，[A⁻] = 0.20 mol dm⁻³。已知 pKa = 4.74，pH = 4.74 + log₁₀(0.20 / 0.10) = 4.74 + 0.30 = 5.04。
When calculating the pH after adding a small amount of strong acid or base, first work out the new moles of HA and A⁻, then convert to concentrations before substituting into the buffer equation.
在计算加入少量强酸或强碱后的 pH 时，先计算出新的 HA 和 A⁻ 的物质的量，再换算为浓度，然后代入缓冲方程。
9. Titration Curves | 滴定曲线
A pH titration curve shows how pH changes as a base is added to an acid, or vice versa. The shape of the curve depends on whether the acid and base are strong or weak.
pH 滴定曲线显示将碱加入酸中（或反之）时 pH 如何变化。曲线的形状取决于酸和碱是强还是弱。
For a strong acid-strong base titration, the curve starts at a low pH and rises gradually, then shows a very steep vertical section around the equivalence point. The equivalence point pH is exactly 7.00 at 25 °C.
对于强酸-强碱滴定，曲线从低 pH 开始逐渐上升，然后在等当量点附近出现非常陡直的垂直段。等当量点处的 pH 在 25 °C 时恰好为 7.00。
For a weak acid-strong base titration, the initial pH is higher, and there is a buffer region before the equivalence point. The equivalence point pH is greater than 7 because the conjugate base of the weak acid hydrolyses to produce OH⁻ ions.
对于弱酸-强碱滴定，初始 pH 较高，且在等当量点之前有一个缓冲区域。等当量点处的 pH 大于 7，因为弱酸的共轭碱水解产生 OH⁻ 离子。
10. Indicators and Choice | 指示剂及其选择
An acid-base indicator is a weak acid whose conjugate base has a different colour. The indicator changes colour over a pH range centred approximately on its pKa value.
酸碱指示剂是一种弱酸，其共轭碱具有不同的颜色。指示剂在其 pKa 值附近的一个 pH 范围内发生颜色变化。
Common indicators include methyl orange, which changes from red to yellow over pH 3.1-4.4, and phenolphthalein, which changes from colourless to pink over pH 8.2-10.0.
常见指示剂包括甲基橙，其在 pH 3.1-4.4 范围内由红变黄，以及酚酞，其在 pH 8.2-10.0 范围内由无色变为粉红色。
The chosen indicator must change colour within the steep vertical section of the titration curve. For a strong acid-strong base titration, both methyl orange and phenolphthalein are suitable because the vertical section covers pH 3-11.
所选指示剂必须在滴定曲线的陡直垂直段内变色。对于强酸-强碱滴定，甲基橙和酚酞都适用，因为垂直段覆盖 pH 3-11。
11. pH Curves for Different Combinations | 不同组合的 pH 曲线
Each titration type has a characteristic equivalence point pH. Strong acid-strong base has pH 7, strong acid-weak base has pH below 7, weak acid-strong base has pH above 7, and weak acid-weak base has a poorly defined vertical section.
每种滴定类型都有特征性的等当量点 pH。强酸-强碱为 pH 7，强酸-弱碱低于 7，弱酸-强碱高于 7，而弱酸-弱碱的垂直段不明显。
The table below summarises suitable indicators for common titrations.
下表总结了常见滴定适用的指示剂。
| Titration type | Equivalence point pH | Suitable indicator |
|---|---|---|
| Strong acid + strong base | 7 | Methyl orange or phenolphthalein |
| Strong acid + weak base | < 7 | 更多咨询请联系16621398022（同微信）
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