Acid–Base Equilibria | 酸碱平衡

📚 Acid–Base Equilibria | 酸碱平衡

Acid–base equilibria are central to A-Level Chemistry because they link pH calculations, weak acid/base dissociation, buffers and titration curves. This topic moves beyond the simple idea of ‘strong’ and ‘weak’ acids by quantifying how far proton-transfer reactions proceed in aqueous solution.

酸碱平衡是A-Level化学的核心内容之一，它将pH计算、弱酸弱碱的电离、缓冲溶液和滴定曲线联系在一起。这一主题超越了强酸和弱酸的简单分类，开始定量分析水溶液中质子转移反应进行的程度。

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1. Brønsted–Lowry Acids and Bases | 布朗斯特–劳里酸碱理论

A Brønsted–Lowry acid is a proton, H⁺, donor. A Brønsted–Lowry base is a proton, H⁺, acceptor.

布朗斯特–劳里酸是质子（H⁺）的给予体。布朗斯特–劳里碱是质子（H⁺）的接受体。

This definition is more general than the Arrhenius definition because it includes reactions that do not involve hydroxide ions, such as the reaction between HCl gas and NH₃ gas to form NH₄Cl.

这一定义比阿伦尼乌斯定义更为广泛，因为它包括了不涉及氢氧根离子的反应，例如HCl气体与NH₃气体反应生成NH₄Cl的反应。

When an acid donates a proton, it always needs a base to accept that proton. Acid–base reactions are therefore proton-transfer processes.

当酸给出质子时，总是需要一个碱来接受该质子。因此酸碱反应本质上是质子转移过程。

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2. Conjugate Acid–Base Pairs | 共轭酸碱对

A conjugate acid–base pair consists of two species that differ by one proton, H⁺. The acid has one more proton than its conjugate base.

共轭酸碱对是由相差一个质子（H⁺）的两个粒子组成的。酸比其共轭碱多一个质子。

• In the equilibrium HA + H₂O ⇌ H₃O⁺ + A⁻, HA and A⁻ form one conjugate acid–base pair.

  在平衡 HA + H₂O ⇌ H₃O⁺ + A⁻ 中，HA 和 A⁻ 构成一对共轭酸碱对。

• H₂O and H₃O⁺ form another conjugate pair, with H₂O acting as a base and H₃O⁺ as its conjugate acid.

  H₂O 和 H₃O⁺ 构成另一对共轭酸碱对，其中 H₂O 作为碱，H₃O⁺ 是其共轭酸。

Strong acids have very weak conjugate bases, and weak acids have relatively stronger conjugate bases. This inverse relationship helps predict the position of acid–base equilibria.

强酸具有非常弱的共轭碱，而弱酸具有相对较强的共轭碱。这种反向关系有助于预测酸碱平衡的位置。

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3. The Water Equilibrium and K_w | 水的电离平衡与 K_w

Water is amphoteric because it can act as both an acid and a base. Pure water undergoes self-ionisation:

水具有两性，因为它既可以作为酸也可以作为碱。纯水会发生自偶电离：

2H₂O(l) ⇌ H₃O⁺(aq) + OH⁻(aq)

The ionic product of water, K_w, is given by:

水的离子积 K_w 表示为：

K_w = [H₃O⁺][OH⁻] = 1.0 × 10⁻¹⁴ mol² dm⁻⁶ at 298 K

K_w is an equilibrium constant, so its value depends only on temperature. As temperature increases, K_w increases because self-ionisation is endothermic.

K_w 是一个平衡常数，因此其数值只取决于温度。温度升高时 K_w 增大，因为自偶电离是吸热过程。

In pure water at 298 K, [H₃O⁺] = [OH⁻] = 1.0 × 10⁻⁷ mol dm⁻³, so the solution is neutral.

在298 K的纯水中，[H₃O⁺] = [OH⁻] = 1.0 × 10⁻⁷ mol dm⁻³，因此溶液呈中性。

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4. The pH Scale and Calculations | pH 标度与计算

pH is defined as the negative logarithm to base 10 of the hydrogen ion concentration:

pH 定义为氢离子浓度的负常用对数：

pH = –lg[H₃O⁺]

For a solution at 298 K, pH < 7 means acidic, pH = 7 means neutral, and pH > 7 means alkaline.

在298 K时，pH < 7 为酸性，pH = 7 为中性，pH > 7 为碱性。

To find [H₃O⁺] from pH, use the inverse relationship:

若要从 pH 求 [H₃O⁺]，使用其逆运算：

[H₃O⁺] = 10⁻ᵖᴴ mol dm⁻³

pOH is defined similarly as pOH = –lg[OH⁻]. At 298 K, pH + pOH = 14.

pOH 的定义类似，pOH = –lg[OH⁻]。在298 K时，pH + pOH = 14。

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5. Strong Acids and Bases | 强酸和强碱

Strong acids such as HCl, HNO₃ and H₂SO₄ dissociate completely in aqueous solution. Therefore, for a monoprotic strong acid, [H₃O⁺] equals the acid concentration.

HCl、HNO₃ 和 H₂SO₄ 等强酸在水溶液中完全电离。因此，对于一元强酸，[H₃O⁺] 等于酸的浓度。

For a 0.10 mol dm⁻³ solution of HCl, [H₃O⁺] = 0.10 mol dm⁻³ and pH = –lg(0.10) = 1.00.

对于 0.10 mol dm⁻³ 的 HCl 溶液，[H₃O⁺] = 0.10 mol dm⁻³，pH = –lg(0.10) = 1.00。

Strong bases such as NaOH and KOH dissociate completely to give OH⁻. To calculate pH, find [OH⁻], then use K_w to find [H₃O⁺].

NaOH 和 KOH 等强碱完全电离产生 OH⁻。要计算 pH，先求 [OH⁻]，再利用 K_w 求出 [H₃O⁺]。

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6. Weak Acids and K_a | 弱酸与 K_a

Weak acids such as ethanoic acid, CH₃COOH, only partially dissociate in water. The acid dissociation constant, K_a, measures the extent of dissociation:

乙酸（CH₃COOH）等弱酸在水中仅部分电离。酸解离常数 K_a 衡量电离的程度：

K_a = [H₃O⁺][A⁻] / [HA]

The units of K_a are mol dm⁻³, although K_a is often quoted as a numerical value with implied units.

K_a 的单位是 mol dm⁻³，不过在引用 K_a 时常会省略单位。

For a weak acid, the approximation [H₃O⁺] = √(K_a × [HA]) is valid when the degree of dissociation is less than about 5%.

对于弱酸，当电离度小于约5%时，可使用近似式 [H₃O⁺] = √(K_a × [HA])。

The smaller the K_a value, the weaker the acid and the less it dissociates.

K_a 越小，酸性越弱，电离程度越低。

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7. Weak Bases and K_b | 弱碱与 K_b

Weak bases such as ammonia, NH₃, accept protons only partially. The base dissociation constant, Kb, is defined by:

氨（NH₃）等弱碱只能部分接受质子。碱解离常数 Kb 定义为：

Kb = [NH₄⁺][OH⁻] / [NH₃]

As with K_a, a smaller Kb value indicates a weaker base. For a weak base, [OH⁻] can be approximated as √(Kb × [base]).

与 K_a 类似，Kb 越小，碱性越弱。对于弱碱，[OH⁻] 可用近似式 √(Kb × [碱浓度]) 计算。

To calculate the pH of a weak base solution, first calculate [OH⁻], then convert to [H₃O⁺] using K_w.

计算弱碱溶液的 pH 时，先求 [OH⁻]，再用 K_w 换算为 [H₃O⁺]。

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8. pK_a and pK_b Relationships | pK_a 与 pK_b 的关系

pK_a and pK_b are logarithmic forms of K_a and Kb:

pK_a 和 pK_b 是 K_a 与 Kb 的对数形式：

pK_a = –lg K_a and pK_b = –lg Kb

For a conjugate acid–base pair in aqueous solution at 298 K, the following relationship holds:

对于水溶液中的共轭酸碱对，在298 K时存在以下关系：

K_a × Kb = K_w = 1.0 × 10⁻¹⁴

Taking negative logarithms gives pK_a + pK_b = 14 at 298 K. This is very useful when converting between acid and base constants.

取负对数可得 pK_a + pK_b = 14（298 K）。这一关系在酸碱常数之间换算时非常有用。

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9. Buffer Solutions | 缓冲溶液

A buffer solution resists changes in pH when small amounts of acid or base are added. It consists of a weak acid and its conjugate base, or a weak base and its conjugate acid.

缓冲溶液能在加入少量酸或碱时抵抗 pH 的变化。它由弱酸及其共轭碱，或弱碱及其共轭酸组成。

For an acidic buffer, the equilibrium is HA ⇌ H⁺ + A⁻. The buffer works because the weak acid neutralises added base, while the conjugate base neutralises added acid.

对于酸性缓冲溶液，平衡为 HA ⇌ H⁺ + A⁻。缓冲作用的原因是弱酸能中和加入的碱，而共轭碱能中和加入的酸。

The pH of an acidic buffer can be calculated using the Henderson–Hasselbalch equation:

酸性缓冲溶液的 pH 可用亨德森–哈塞尔巴尔赫方程计算：

pH = pK_a + lg([A⁻] / [HA])

Buffer capacity is greatest when the concentrations of the weak acid and conjugate base are equal, giving pH = pK_a.

当弱酸和共轭碱浓度相等时，缓冲容量最大，此时 pH = pK_a。

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10. Acid–Base Titration Curves | 酸碱滴定曲线

Titration curves show how pH changes as a base is added to an acid, or an acid is added to a base. The shape depends on the strengths of the acid and base.

滴定曲线表示向酸中加碱或向碱中加酸时 pH 的变化。曲线形状取决于酸和碱的强弱。

For a strong acid–strong base titration, the pH changes very sharply around the equivalence point, from about pH 3 to pH 11. The equivalence point is at pH 7.

强酸–强碱滴定时，在化学计量点附近 pH 变化非常剧烈，从约 pH 3 到 pH 11。化学计量点的 pH 为 7。

For a weak acid–strong base titration, the equivalence point is above pH 7 because the conjugate base of the weak acid hydrolyses to produce OH⁻.

弱酸–强碱滴定的化学计量点 pH 大于 7，因为弱酸的共轭碱水解产生 OH⁻。

For a strong acid–weak base titration, the equivalence point is below pH 7. Weak acid–weak base titrations do not show a sharp vertical section, so they are usually avoided in volumetric analysis.

强酸–弱碱滴定的化学计量点 pH 小于 7。弱酸–弱碱滴定没有明显的垂直段，因此在容量分析中通常避免使用。

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11. Choosing Indicators | 指示剂的选择

An acid–base indicator is a weak acid or base whose acid and conjugate base forms have different colours. The colour changes over a range of about pH = pK_ind ± 1.

酸碱指示剂是一种弱酸或弱碱，其酸式和共轭碱式具有不同颜色。颜色变化范围约为 pH = pK_ind ± 1。

Indicator	pH range	Colour change
Methyl orange	3.1–4.4	Red to yellow
Phenolphthalein	8.3–10.0	Colourless to pink

An indicator is suitable for a titration if its pH range falls within the sharp vertical portion of the titration curve.

如果指示剂的 pH 变色范围落在滴定曲线的垂直陡变段内，则该指示剂适合该滴定。

For a strong acid–strong base titration, both methyl orange and phenolphthalein are suitable because the vertical section is very large. For a weak acid–strong base titration, phenolphthalein is suitable but methyl orange is not.

强酸–强碱滴定中，甲基橙和酚酞都适用，因为垂直段范围很大。弱酸–强碱滴定适用酚酞，而甲基橙不适用。

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12. Summary of Key Equations | 核心公式汇总

The most important equations for acid–base equilibria are collected below. Being able to select and apply the correct equation is a key examination skill.

以下汇总了酸碱平衡中最重要的公式。能够选择并正确应用公式是一项关键的考试技能。

• pH = –lg[H₃O⁺] and [H₃O⁺] = 10⁻ᵖᴴ

  pH = –lg[H₃O⁺]；[H₃O⁺] = 10⁻ᵖᴴ

• K_w = [H₃O⁺][OH⁻] = 1.0 × 10⁻¹⁴ mol² dm⁻⁶ at 298 K

  K_w = [H₃O⁺][OH⁻] = 1.0 × 10⁻¹⁴ mol² dm⁻⁶（298 K）

• K_a = [H₃O⁺][A⁻] / [HA] and pK_a = –lg K_a

  K_a = [H₃O⁺][A⁻] / [HA]；pK_a = –lg K_a

• Kb = [OH⁻][conjugate acid] / [base] and pK_b = –lg Kb

  Kb = [OH⁻][共轭酸] / [碱]；pK_b = –lg Kb

• K_a × Kb = K_w and pK_a + pK_b = 14 at 298 K

  K_a × Kb = K_w；pK_a + pK_b = 14（298 K）

• Buffer pH = pK_a + lg([conjugate base] / [weak acid])

  缓冲溶液 pH = pK_a + lg([共轭碱] / [弱酸])

Always check the temperature when using K_w and pH values, because both K_w and neutral pH depend on temperature.

使用 K_w 和 pH 数值时，务必核对温度，因为 K_w 和中性 pH 都随温度变化。

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