Acids and Bases Essentials for IB CIE Science | IB CIE 科学：酸与碱考点精讲

📚 Acids and Bases Essentials for IB CIE Science | IB CIE 科学：酸与碱考点精讲

Acids and bases are central to chemical understanding, from laboratory titrations to biochemical systems. This revision guide distils the key concepts required for IB and CIE science courses, including definitions, calculations of pH, dissociation constants, buffer action, and titration curves. By working through the paired English and Chinese explanations, you will strengthen both your conceptual grasp and your ability to apply these ideas in exam scenarios.

酸与碱是化学理解的核心，从实验室滴定到生化系统无处不在。这篇复习精讲浓缩了 IB 和 CIE 科学课程所需的关键概念，包括定义、pH 计算、解离常数、缓冲作用以及滴定曲线。通过配对的中英文讲解，你将加深对概念的掌握，并提升在考试情境中运用这些知识的能力。

1. Introduction and Learning Outcomes | 引言与学习目标

This article is designed to help you master the essential topics in acid-base chemistry for IB and CIE examinations. After studying, you should be able to define acids and bases using different theories, distinguish between strong and weak electrolytes, perform pH and pKa calculations, analyse buffer systems, and interpret titration curves with appropriate indicators.

本文旨在帮助你掌握 IB 和 CIE 考试中酸碱化学的核心主题。学习后，你应该能够用不同理论定义酸和碱，区分强电解质和弱电解质，进行 pH 和 pKa 计算，分析缓冲体系，并能结合合适的指示剂解读滴定曲线。

The content follows the typical progression found in IB Chemistry and CIE AS & A Level Chemistry syllabi, with a focus on both qualitative understanding and quantitative problem-solving. Each section builds on the previous one, so work through the material sequentially for best results.

内容遵循 IB 化学和 CIE AS 与 A Level 化学大纲的典型顺序，兼顾定性理解与定量解题。每一节都建立在前面内容的基础上，为取得最佳效果请依次学习。

2. Theories of Acids and Bases: Arrhenius, Bronsted-Lowry, Lewis | 酸碱理论：阿伦尼乌斯、布朗斯特-劳里、路易斯

The Arrhenius theory defines an acid as a substance that releases H⁺ ions in water, and a base as a substance that releases OH⁻ ions. For example, HCl → H⁺ + Cl⁻ and NaOH → Na⁺ + OH⁻. This simple model is limited to aqueous solutions and cannot explain the basicity of ammonia.

阿伦尼乌斯理论将酸定义为在水中释放 H⁺ 离子的物质，将碱定义为释放 OH⁻ 离子的物质。例如 HCl → H⁺ + Cl⁻，NaOH → Na⁺ + OH⁻。这个简单的模型仅限于水溶液，无法解释氨的碱性。

The Bronsted-Lowry theory broadens the definition: an acid is a proton (H⁺) donor, and a base is a proton acceptor. In the reaction NH₃ + H₂O ⇌ NH₄⁺ + OH⁻, water acts as an acid (donates H⁺) and ammonia acts as a base (accepts H⁺). This theory introduces conjugate acid-base pairs.

布朗斯特-劳里理论扩展了定义：酸是质子（H⁺）给体，碱是质子受体。在反应 NH₃ + H₂O ⇌ NH₄⁺ + OH⁻ 中，水作为酸（提供 H⁺），氨作为碱（接受 H⁺）。该理论引入了共轭酸碱对。

Lewis theory is even more general: an acid is an electron-pair acceptor, and a base is an electron-pair donor. This explains reactions that do not involve protons, such as BF₃ accepting an electron pair from NH₃. In IB and CIE contexts, you are expected to use Bronsted-Lowry for most aqueous proton transfers and recognise Lewis acid-base behaviour where appropriate.

路易斯理论更为普适：酸是电子对受体，碱是电子对给体。这解释了不涉及质子的反应，例如 BF₃ 接受 NH₃ 的电子对。在 IB 和 CIE 背景下，你应能使用布朗斯特-劳里理论处理大多数水质子转移，并在适当处识别路易斯酸碱行为。

3. Strong vs Weak Acids and Bases | 强酸强碱与弱酸弱碱

A strong acid completely dissociates in aqueous solution. Common examples include HCl, HBr, HI, HNO₃, H₂SO₄ (first dissociation), and HClO₄. For a monoprotic strong acid, [H⁺] equals the initial acid concentration.

强酸在水溶液中完全解离。常见例子有 HCl、HBr、HI、HNO₃、H₂SO₄（第一步解离）和 HClO₄。对于一元强酸，[H⁺] 等于酸的初始浓度。

A weak acid only partially dissociates, establishing an equilibrium between the acid molecules and the ions. A typical example is ethanoic acid: CH₃COOH ⇌ CH₃COO⁻ + H⁺. The extent of dissociation is given by the acid dissociation constant Ka.

弱酸仅部分解离，在酸分子与离子之间建立平衡。典型例子是乙酸：CH₃COOH ⇌ CH₃COO⁻ + H⁺。解离程度由酸解离常数 Ka 给出。

Strong bases fully dissociate to give OH⁻ ions, such as NaOH and KOH. Weak bases like NH₃ and amines only partially react with water to produce OH⁻. The strength of a weak base is measured by its Kb. You must be able to compare the extent of ionisation and calculate the resulting ion concentrations.

强碱完全解离产生 OH⁻ 离子，如 NaOH 和 KOH。弱碱如 NH₃ 和胺类仅部分与水反应生成 OH⁻。弱碱的强度用其 Kb 来衡量。你必须能够比较电离程度并计算所得离子浓度。

4. The pH Scale and Calculations | pH 值与计算

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

pH 定义为氢离子浓度的负对数（以 10 为底）：

pH = −log₁₀[H⁺]

For a strong monoprotic acid, [H⁺] is simply the concentration of the acid. For example, 0.010 mol dm⁻³ HCl gives pH = −log(0.010) = 2.00.

对于一元强酸，[H⁺] 就是酸的浓度。例如，0.010 mol dm⁻³ HCl 得到 pH = −log(0.010) = 2.00。

For a strong base, first calculate [OH⁻], then use the ionic product of water Kw = 1.0 × 10⁻¹⁴ at 298 K to find [H⁺]. For 0.0010 mol dm⁻³ NaOH, [OH⁻] = 0.0010 mol dm⁻³, so [H⁺] = Kw / [OH⁻] = 1.0 × 10⁻¹¹ mol dm⁻³, giving pH = 11.00.

对于强碱，先计算 [OH⁻]，然后利用水的离子积 Kw = 1.0 × 10⁻¹⁴（298 K 时）求出 [H⁺]。对 0.0010 mol dm⁻³ NaOH，[OH⁻] = 0.0010 mol dm⁻³，所以 [H⁺] = Kw / [OH⁻] = 1.0 × 10⁻¹¹ mol dm⁻³，pH = 11.00。

For weak acids, you must use the equilibrium expression. For a weak acid HA with concentration c and dissociation constant Ka, assuming [H⁺] ≪ c, the simplified formula is:

对于弱酸，必须使用平衡表达式。对于浓度为 c、解离常数为 Ka 的弱酸 HA，假设 [H⁺] ≪ c，简化公式为：

[H⁺] = √(Ka × c)

This approximation is valid when c / Ka > 100. In IB and CIE assessments, you may be required to solve quadratic equations if the approximation does not hold.

当 c / Ka > 100 时该近似有效。在 IB 和 CIE 考核中，若近似不成立，你可能需要解二次方程。

5. Autoionization of Water and Kw | 水的自解离与离子积 Kw

Water undergoes a very slight autoionization: 2H₂O ⇌ H₃O⁺ + OH⁻. The equilibrium constant for this process is Kw = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴ at 25 °C. Kw varies with temperature; at higher temperatures, Kw increases because the forward reaction is endothermic.

水有极微弱的自解离：2H₂O ⇌ H₃O⁺ + OH⁻。该过程的平衡常数 Kw = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴（25 °C）。Kw 随温度变化；温度升高时 Kw 增大，因为正反应吸热。

The relationship pKw = pH + pOH = 14.00 at 298 K allows easy conversion between pH and pOH. In neutral water, [H⁺] = [OH⁻] = 1.0 × 10⁻⁷ mol dm⁻³, so pH = 7.0.

关系式 pKw = pH + pOH = 14.00（298 K 时）便于 pH 与 pOH 之间的换算。在中性水中，[H⁺] = [OH⁻] = 1.0 × 10⁻⁷ mol dm⁻³，故 pH = 7.0。

When an acid or base is added, the product [H⁺][OH⁻] still equals Kw. This principle is used to calculate the pH of strong base solutions and to understand buffer behaviour.

当加入酸或碱时，乘积 [H⁺][OH⁻] 仍等于 Kw。这一原理用于计算强碱溶液的 pH 和理解缓冲行为。

6. Acid Dissociation Constant Ka and pKa | 酸解离常数 Ka 与 pKa

For a general weak acid HA ⇌ H⁺ + A⁻, the acid dissociation constant is:

对于一般弱酸 HA ⇌ H⁺ + A⁻，酸解离常数为：

Ka = [H⁺][A⁻] / [HA]

Ka has units of mol dm⁻³ and its magnitude indicates acid strength: the larger the Ka, the stronger the acid. Because Ka values span many orders of magnitude, pKa is often used:

Ka 的单位为 mol dm⁻³，其大小表示酸的强度：Ka 越大，酸越强。由于 Ka 值跨越多个数量级，常使用 pKa：

pKa = −log₁₀(Ka)

A smaller pKa corresponds to a stronger acid. For instance, ethanoic acid has Ka ≈ 1.8 × 10⁻⁵, so pKa ≈ 4.74. In calculations, you may be given Ka or pKa and must be able to convert between them.

pKa 越小，酸越强。例如，乙酸的 Ka ≈ 1.8 × 10⁻⁵，故 pKa ≈ 4.74。在计算中，你可能得到 Ka 或 pKa，必须能相互转换。

Comparing pKa values allows you to predict the direction of Bronsted-Lowry acid-base reactions; the equilibrium favours formation of the weaker acid (higher pKa). This concept appears frequently in multiple-choice and data-analysis questions.

比较 pKa 值可以预测布朗斯特-劳里酸碱反应的方向；平衡有利于生成更弱的酸（pKa 更大）。该概念常出现在选择题和数据分析题中。

7. Base Dissociation Constant Kb and pKb | 碱解离常数 Kb 与 pKb

For a weak base B in water: B + H₂O ⇌ BH⁺ + OH⁻, the base dissociation constant is:

对于水中的弱碱 B：B + H₂O ⇌ BH⁺ + OH⁻，碱解离常数为：

Kb = [BH⁺][OH⁻] / [B]

As with acids, pKb = −log₁₀(Kb). A smaller pKb indicates a stronger base. For ammonia, Kb ≈ 1.8 × 10⁻⁵ and pKb ≈ 4.74 at 298 K.

与酸类似，pKb = −log₁₀(Kb)。pKb 越小，碱越强。对氨而言，Kb ≈ 1.8 × 10⁻⁵，pKb ≈ 4.74（298 K 时）。

For a conjugate acid-base pair in aqueous solution, the relationship Ka × Kb = Kw holds, and therefore pKa + pKb = 14.00 at 25 °C. This is particularly useful when you are given Ka for a conjugate acid and need to find Kb for its base, or vice versa.

对于水溶液中的共轭酸碱对，有关系式 Ka × Kb = Kw，因此在 25 °C 时 pKa + pKb = 14.00。这在给出共轭酸的 Ka 而需要求其共轭碱的 Kb，或反之，是特别有用的。

8. Buffer Solutions | 缓冲溶液

A buffer solution resists changes in pH upon addition of small amounts of acid or base. It 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⁺). Buffer action is crucial in biological systems and industrial processes.

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（如 CH₃COOH / CH₃COO⁻）或弱碱及其共轭酸（如 NH₃ / NH₄⁺）组成。缓冲作用在生物系统和工业过程中至关重要。

When H⁺ is added, the conjugate base component reacts to form the weak acid, minimising pH change. When OH⁻ is added, the weak acid component neutralises it, protecting the pH. The pH of a buffer is determined primarily by the pKa of the weak acid and the ratio of conjugate base to acid concentrations.

当加入 H⁺ 时，共轭碱组分与其反应生成弱酸，从而使 pH 变化最小化。当加入 OH⁻ 时，弱酸组分将其中和，从而保护 pH。缓冲溶液的 pH 主要取决于弱酸的 pKa 以及共轭碱与酸浓度的比值。

Buffer capacity refers to the amount of acid or base a buffer can neutralise before pH changes significantly. It is highest when the concentrations of the acid and conjugate base are large and when their ratio is close to 1 (i.e., pH ≈ pKa).

缓冲容量是指缓冲溶液在 pH 发生显著变化前所能中和的酸或碱的量。当酸与共轭碱的浓度都较大，且二者比值接近 1（即 pH ≈ pKa）时，缓冲容量最大。

9. Henderson-Hasselbalch Equation | 亨德森-哈塞尔巴尔赫方程

The Henderson-Hasselbalch equation provides a convenient way to calculate the pH of a buffer or to design a buffer of a desired pH:

亨德森-哈塞尔巴尔赫方程提供了一种计算缓冲溶液 pH 或设计所需 pH 缓冲溶液的便捷方法：

pH = pKa + log₁₀([A⁻] / [HA])

Here [A⁻] is the concentration of the conjugate base and [HA] is the concentration of the weak acid. The equation works well when the concentrations of acid and base are not extremely dilute and the ratio is not too far from 1.

这里 [A⁻] 是共轭碱的浓度，[HA] 是弱酸的浓度。当酸和碱的浓度不是极低，且比值离 1 不太远时，该方程效果良好。

This equation explains why a buffer’s pH remains near the pKa when the two components have equal concentrations ([A⁻] = [HA] gives pH = pKa). In experimental tasks, you can use it to calculate the mass or volume of components needed to prepare a buffer solution.

该方程解释了为什么当两组分浓度相等时（[A⁻] = [HA] 得 pH = pKa），缓冲溶液的 pH 保持在 pKa 附近。在实验任务中，你可以用它来计算配制缓冲溶液所需组分的质量或体积。

10. Acid-Base Titrations and Curves | 酸碱滴定与滴定曲线

An acid-base titration involves the gradual addition of a solution of known concentration (the titrant) to a solution of unknown concentration (the analyte) until the reaction is complete. The equivalence point occurs when the moles of acid equal the moles of base according to the stoichiometry.

酸碱滴定是将已知浓度溶液（滴定剂）逐滴加入到未知浓度溶液（待测物）中，直到反应完全。当酸的物质的量与碱的物质的量按化学计量比相等时，即为等当点。

Titration curves plot pH against volume of titrant added. The shape depends on the strengths of the acid and base:

Strong acid – strong base: Equivalence point at pH 7, sharp vertical jump.
Weak acid – strong base: Equivalence point above 7 due to conjugate base hydrolysis; buffer region before equivalence.
Strong acid – weak base: Equivalence point below 7; buffer region in the acidic range.
Weak acid – weak base: Gradual pH change, no sharp jump, difficult to titrate.

滴定曲线是以 pH 对加入滴定剂体积作图。形状取决于酸碱的强度：

强酸 – 强碱：等当点在 pH 7，有陡直的垂直段。
弱酸 – 强碱：等当点高于 7，因共轭碱水解；等当点前有缓冲区域。
强酸 – 弱碱：等当点低于 7；酸性范围存在缓冲区域。
弱酸 – 弱碱：pH 渐变，无陡直段，难以滴定。

For polyprotic acids, multiple equivalence points can be observed. You must be able to sketch and interpret these curves, identifying the half-equivalence point where pH = pKa, which is essential for Ka determination.

多元酸可观察到多个等当点。你必须能绘制和解读这些曲线，识别半等当点（此时 pH = pKa），这对 Ka 的测定至关重要。

11. Indicators and Their Selection | 指示剂及其选择

Acid-base indicators are weak acids or bases that change colour over a specific pH range. The colour change occurs because the protonated and deprotonated forms have different colours. The endpoint of a titration is signalled when the indicator changes colour.

酸碱指示剂是可在特定 pH 范围内改变颜色的弱酸或弱碱。颜色变化是由于质子化和去质子化形式具有不同的颜色。当指示剂变色时，标志着滴定到达终点。

An indicator is suitable if its colour change interval lies entirely within the sharp pH jump of the titration curve. Common indicators and their pH ranges are shown below:

如果指示剂的变色区间完全落在滴定曲线 pH 突跃范围内，则该指示剂是合适的。常见指示剂及其 pH 范围如下表所示：

Indicator	pH Range	Colour Change (acid to base)
Methyl orange	3.1 – 4.4	Red to yellow
Bromothymol blue	6.0 – 7.6	Yellow to blue
Phenolphthalein	8.3 – 10.0	Colourless to pink

For a strong acid-strong base titration, either methyl orange or phenolphthalein can be used because the sharp pH jump spans from around 3 to 11. For a weak acid-strong base titration, phenolphthalein is suitable because the equivalence point is alkaline.

对于强酸-强碱滴定，甲基橙或酚酞均可使用，因为 pH 突跃范围大约从 3 到 11。对于弱酸-强碱滴定，酚酞较为合适，因其等当点呈碱性。

12. Summary and Key Takeaways | 总结与要点

Mastery of acid-base chemistry requires a firm grip on definitions (Arrhenius, Bronsted-Lowry, Lewis), the pH scale, and the interconnected constants Ka, Kb, Kw. Being able to switch between concentration and logarithmic scales (pH, pKa, pKb) is vital for problem solving.

掌握酸碱化学要求牢固把握定义（阿伦尼乌斯、布朗斯特-劳里、路易斯）、pH 标度以及相互关联的常数 Ka、Kb、Kw。能在浓度与对数标度（pH、pKa、pKb）之间转换对于解题至关重要。

Buffers and titration curves link theory with practical applications. Remember that a buffer works most effectively at pH close to the pKa of its weak acid component, and that the Henderson-Hasselbalch equation is your best tool for quantitative buffer design.

缓冲溶液和滴定曲线将理论与实践应用联系起来。请记住，缓冲溶液在 pH 接近其弱酸组分的 pKa 时最为有效，而亨德森-哈塞尔巴尔赫方程是你进行缓冲溶液定量设计的最佳工具。

Regular practice with exam-style questions, particularly those that ask you to interpret unfamiliar data or sketch titration curves, will solidify your confidence. Keep this guide as a quick reference while you revise.

经常练习考试风格的题目，尤其是那些要求你解读陌生数据或绘制滴定曲线的题目，将巩固你的信心。复习时请将这份指南作为快速参考。

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Acids and Bases Essentials for IB CIE Science | IB CIE 科学：酸与碱 考点精讲