📚 Acids and Bases: IB CCEA Science Key Revision | IB CCEA 科学：酸与碱考点精讲
Acids and bases lie at the very heart of chemistry, linking together atomic structure, bonding, equilibrium and organic reaction mechanisms. For the IB CCEA Science course, a deep understanding of proton‑transfer, conjugate pairs, pH calculations, buffer systems and titration curves is essential not only for the exam but for making sense of the molecular world around us. This article draws together the key ideas, essential equations and common pitfalls, giving you a logically structured revision guide.
酸与碱是化学的核心，将原子结构、化学键、化学平衡以及有机反应机理串联起来。在 IB CCEA 科学课程中，透彻理解质子转移、共轭酸碱对、pH 计算、缓冲体系以及滴定曲线，不仅是应对考试的关键，更是理解身边分子世界的基础。本文梳理了核心概念、必备方程式和常见易错点，为你提供一份逻辑清晰的复习指南。
1. Defining Acids and Bases: Three Theories to Master | 定义酸和碱：必须掌握的三大理论
The Arrhenius definition describes an acid as a substance that dissociates in water to produce hydrogen ions, H⁺, and a base as a substance that dissociates to produce hydroxide ions, OH⁻. While historically important, this model is limited to aqueous solutions.
阿伦尼乌斯理论认为，酸是在水中解离产生氢离子（H⁺）的物质，碱是在水中解离产生氢氧根离子（OH⁻）的物质。尽管具有历史意义，但这一模型仅限于水溶液体系。
IB CCEA focuses strongly on the Brønsted–Lowry theory: an acid is a proton donor, a base is a proton acceptor. Crucially, every acid has a conjugate base, and every base has a conjugate acid, forming a conjugate acid–base pair that differs by a single proton, H⁺. For example, HCl and Cl⁻ are a conjugate pair; NH₃ and NH₄⁺ are another.
IB CCEA 重点考查布朗斯特–劳里理论：酸是质子给体，碱是质子受体。关键在于，每种酸都有一个共轭碱，每种碱都有一个共轭酸，它们组成一个只相差一个质子（H⁺）的共轭酸碱对。例如，HCl 和 Cl⁻ 是一对共轭酸碱，NH₃ 和 NH₄⁺ 是另一对。
Beyond Brønsted–Lowry, the Lewis theory broadens the definitions: a Lewis acid is an electron‑pair acceptor, a Lewis base is an electron‑pair donor. This includes species that do not contain proton‑transfer, such as BF₃ accepting a lone pair from NH₃.
在布朗斯特–劳里理论之外，路易斯理论进一步扩展了定义：路易斯酸是电子对受体，路易斯碱是电子对给体。这涵盖了不涉及质子转移的物种，如 BF₃ 接受来自 NH₃ 的孤对电子。
2. The pH Scale and the Ionic Product of Water, Kw | pH 标度与水的离子积 Kw
pH is defined as the negative logarithm (base 10) of the hydrogen ion concentration: pH = –log₁₀[H⁺]. For pure water at 298 K, the concentrations of H⁺ and OH⁻ each equal 1.0 × 10⁻⁷ mol dm⁻³, giving pH = 7. However, Kw = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴ mol² dm⁻⁶ at 298 K only; Kw increases with temperature, meaning neutral pH falls slightly below 7 at higher temperatures.
pH 定义为氢离子浓度的负常用对数：pH = –log₁₀[H⁺]。在 298 K 时，纯水中 [H⁺] 和 [OH⁻] 均为 1.0 × 10⁻⁷ mol dm⁻³，pH = 7。但水的离子积 Kw = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴ mol² dm⁻⁶ 仅在 298 K 成立；Kw 随温度升高而增大，因此高温时中性 pH 会略低于 7。
The pOH scale is complementary: pOH = –log₁₀[OH⁻], and pKw = pH + pOH = 14 at 298 K. Students must confidently convert between pH, [H⁺] and [OH⁻] using these relationships.
pOH 标度与之互补：pOH = –log₁₀[OH⁻]，且在 298 K 时 pKw = pH + pOH = 14。学生必须能熟练运用这些关系在 pH、[H⁺] 和 [OH⁻] 之间进行转换。
3. Strong vs Weak Acids and Bases | 强酸强碱与弱酸弱碱
A strong acid or base is fully dissociated in aqueous solution. For a strong monoprotic acid, like HCl, [H⁺] equals the initial acid concentration, so pH = –log₁₀[acid]. Similarly, a strong base such as NaOH gives [OH⁻] = [base], pOH = –log₁₀[base], and pH = 14 – pOH (at 298 K).
强酸或强碱在水溶液中完全解离。对于一元强酸，如 HCl，[H⁺] 等于酸的初始浓度，所以 pH = –log₁₀[acid]。同样，强碱如 NaOH 给出 [OH⁻] = [base]，pOH = –log₁₀[base]，pH = 14 – pOH（298 K 时）。
Weak acids and bases only partially dissociate, establishing an equilibrium. The acid dissociation constant, Ka, and the base dissociation constant, Kb, quantify the strength. For a weak acid HA: Ka = [H⁺][A⁻]/[HA]. The smaller the Ka (or the larger the pKa), the weaker the acid. For weak bases, Kb = [BH⁺][OH⁻]/[B]. IB CCEA often asks you to estimate pH using the approximation [H⁺] ≈ √(Ka × [HA]0), provided the acid is weak and not extremely dilute.
弱酸和弱碱仅部分解离，建立平衡。酸解离常数 Ka 和碱解离常数 Kb 用于衡量酸碱强度。对于弱酸 HA：Ka = [H⁺][A⁻]/[HA]。Ka 越小（或 pKa 越大），酸越弱。对于弱碱，Kb = [BH⁺][OH⁻]/[B]。IB CCEA 经常要求用近似公式 [H⁺] ≈ √(Ka × [HA]0) 估算 pH，前提是酸足够弱且浓度不太稀。
4. pKa and pKb Relationships | pKa 与 pKb 的关系
For any conjugate acid–base pair in aqueous solution at 298 K, pKa + pKb = 14 (since Kw = Ka × Kb). This means that if you know the Ka of an acid, you can instantly find the Kb of its conjugate base. For example, the Ka of ethanoic acid is 1.8 × 10⁻⁵, so the Kb of the ethanoate ion is 5.6 × 10⁻¹⁰.
对于水溶液中的任何共轭酸碱对，在 298 K 时 pKa + pKb = 14（因为 Kw = Ka × Kb）。这意味着如果知道酸的 Ka，就能立即求出其共轭碱的 Kb。例如，乙酸的 Ka 为 1.8 × 10⁻⁵，则乙酸根离子的 Kb 为 5.6 × 10⁻¹⁰。
This relationship also explains why the conjugate base of a weak acid is a weak base, and vice‑versa. A strong acid has a negligible Ka value for its conjugate base — essentially no basic character in water.
这一关系也解释了为什么弱酸的共轭碱是弱碱，反之亦然。强酸的共轭碱在水中几乎不显碱性，其 Kb 值可忽略。
5. Buffer Solutions: Principle and Calculations | 缓冲溶液：原理与计算
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 (acidic buffer), or a weak base and its conjugate acid (basic buffer). The equilibrium between the two components absorbs added H⁺ or OH⁻.
缓冲溶液能抵抗外加少量酸或碱引起的 pH 变化。它由弱酸及其共轭碱（酸性缓冲液）或弱碱及其共轭酸（碱性缓冲液）组成。两组分间的平衡可吸收外加的 H⁺ 或 OH⁻。
The Henderson–Hasselbalch equation for an acidic buffer is: pH = pKa + log₁₀([A⁻]/[HA]). This shows that pH remains close to pKa when the concentrations of acid and conjugate base are similar. Buffer capacity is greatest when the ratio [A⁻]:[HA] is between 1:10 and 10:1.
酸性缓冲液的亨德森–哈塞尔巴尔赫方程为：pH = pKa + log₁₀([A⁻]/[HA])。这表明当酸和共轭碱的浓度相近时，pH 接近 pKa。当 [A⁻]:[HA] 比例在 1:10 到 10:1 之间时，缓冲容量最大。
IB CCEA questions will often ask you to calculate the pH of a buffer prepared by mixing a weak acid with its salt, or by partially neutralising a weak acid. Always set up the equilibrium expression, and remember that the volume is common so you can use moles directly in the ratio.
IB CCEA 考题常要求学生计算由弱酸与其盐混合，或通过部分中和弱酸制备的缓冲液 pH。始终建立平衡表达式，并注意体积相同，因此可以直接用物质的量之比代入。
6. Acid–Base Titrations and pH Curves | 酸碱滴定与 pH 曲线
Titration curves plot pH against volume of added titrant. The shape reveals information about acid strength, concentration and the equivalence point. Four classic curves must be recognised:
pH 滴定曲线描绘了 pH 随滴定剂加入体积的变化。曲线形状揭示了酸碱强度、浓度以及等当点的信息。必须识别四种经典曲线：
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Strong acid – strong base: very steep vertical section, equivalence point pH = 7.
强酸 – 强碱：垂直线段非常陡峭，等当点 pH = 7。
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Strong acid – weak base: equivalence point pH < 7 (acidic, due to hydrolysis of the conjugate acid).
强酸 – 弱碱：等当点 pH < 7（酸性，因共轭酸水解）。
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Weak acid – strong base: equivalence point pH > 7 (basic, due to conjugate base hydrolysis); a buffer region exists at half‑neutralisation where pH = pKa.
弱酸 – 强碱：等当点 pH > 7（碱性，因共轭碱水解）；半中和点存在缓冲区域，此时 pH = pKa。
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Weak acid – weak base: very gradual change, no sharp vertical jump; such titrations are generally avoided for analysis.
弱酸 – 弱碱：变化非常平缓，没有明显的垂直突跃；这类滴定通常不用于分析。
Indicators are chosen so that their pKa lies within the steep part of the curve, ensuring a sharp colour change at the endpoint.
选择指示剂时，应使其 pKa 位于滴定曲线陡峭区间内，以确保终点时颜色变化明显。
7. Indicators and Their Colour Changes | 指示剂与颜色变化
An acid–base indicator is itself a weak acid or base, with a distinct colour for its protonated form (HIn) and its deprotonated form (In⁻). The colour change interval is approximately pKa ± 1. For example, phenolphthalein (pKa ≈ 9.3) changes from colourless to pink in the pH range 8.3–10.0, making it ideal for weak acid–strong base titrations.
酸碱指示剂本身是一种弱酸或弱碱，其质子化形式（HIn）和去质子化形式（In⁻）呈现不同颜色。变色范围大致为 pKa ± 1。例如，酚酞（pKa ≈ 9.3）在 pH 8.3–10.0 范围内从无色变为粉红色，非常适合弱酸–强碱滴定。
Methyl orange (pKa ≈ 3.5) shifts from red to yellow in the range 3.1–4.4, suitable for strong acid–strong base or strong acid–weak base titrations. You must be able to justify the selection of an indicator by comparing its pKa with the pH jump on the curve.
甲基橙（pKa ≈ 3.5）在 pH 3.1–4.4 范围内由红变黄，适用于强酸–强碱或强酸–弱碱滴定。必须能够通过比较指示剂的 pKa 与曲线上 pH 突跃范围，来论证指示剂的选择。
8. Salt Hydrolysis and the pH of Salt Solutions | 盐的水解与盐溶液 pH
The ions of a dissolved salt can act as Brønsted–Lowry acids or bases through hydrolysis. The resulting pH depends on the parent acid and base:
溶解盐的离子可以通过水解充当布朗斯特–劳里酸或碱。最终 pH 取决于形成该盐的母体酸和碱：
| Parent Acid / Base | 盐的来源 | Resulting pH |
| Strong acid + Strong base | 强酸 + 强碱 | ≈ 7 (neutral) |
| Strong acid + Weak base | 强酸 + 弱碱 | < 7 (acidic) |
| Weak acid + Strong base | 弱酸 + 强碱 | > 7 (basic) |
For example, ammonium chloride (NH₄Cl) contains the ammonium ion, which is the conjugate acid of the weak base NH₃; it donates a proton to water, producing H₃O⁺ and lowering the pH.
例如，氯化铵（NH₄Cl）含有铵根离子，它是弱碱 NH₃ 的共轭酸；铵根离子向水分子提供质子，生成 H₃O⁺，使溶液 pH 降低。
9. Amphiprotic Species and Autoprotolysis | 两性质子物种与自质子解
An amphiprotic substance can both donate and accept a proton. Water is the classic example: 2H₂O ⇌ H₃O⁺ + OH⁻ (autoprotolysis). Other important amphiprotic ions include HCO₃⁻, HSO₄⁻, H₂PO₄⁻ and the amino acid zwitterion. Questions often ask you to write equations showing a species acting as both an acid and a base, or to predict which reaction dominates based on Ka values.
两性质子物种既能给出质子也能接受质子。水是最经典的例子：2H₂O ⇌ H₃O⁺ + OH⁻（自质子解）。其他重要的两性离子包括 HCO₃⁻、HSO₄⁻、H₂PO₄⁻ 以及氨基酸的两性离子。考题常要求写出显示某物种既作为酸又作为碱的方程式，或根据 Ka 值判断哪一反应占主导。
10. Experimental Determination of Ka / pKa | 实验测定 Ka / pKa
IB CCEA expects familiarity with at least two methods: pH measurement of a weak acid solution of known concentration, and the half‑neutralisation method using a pH curve. In the half‑neutralisation of a weak acid with a strong base, the point where exactly half the acid has been neutralised gives [HA] = [A⁻], so pH = pKa. From the titration curve you can read off the pH at this volume and thus determine pKa.
IB CCEA 要求熟悉至少两种方法：测量已知浓度弱酸溶液的 pH，以及利用滴定曲线的半中和法。在用强碱滴定弱酸时，当酸恰好被中和一半时，[HA] = [A⁻]，此时 pH = pKa。从滴定曲线上读取该体积所对应的 pH，即可确定 pKa。
The direct pH method uses the approximation [H⁺] ≈ √(Ka × c), where c is the initial acid concentration, and then Ka = [H⁺]²/c. Be prepared to discuss assumptions and sources of error.
直接 pH 法使用近似公式 [H⁺] ≈ √(Ka × c)（c 为酸的初始浓度），然后 Ka = [H⁺]²/c。准备讨论假设条件和误差来源。
11. Common Pitfalls and How to Avoid Them | 常见误区与应对策略
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Confusing strong and concentrated: a strong acid is 100 % dissociated regardless of concentration; a concentrated weak acid can have a lower pH than a dilute strong acid, but it remains only partially dissociated.
混淆“强”与“浓”：强酸无论浓度多少都完全解离；浓的弱酸虽然 pH 可能比稀强酸低，但仍然只是部分解离。
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Neglecting the effect of temperature on Kw: a neutral solution at 313 K may have pH < 7 but [H⁺] = [OH⁻]. Never assert that pH = 7 is always neutral.
忽视温度对 Kw 的影响：313 K 时中性溶液的 pH 可能低于 7，但 [H⁺] = [OH⁻]。切勿断言 pH = 7 就是中性。
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Forgetting to convert between pH and [H⁺] correctly: practice the antilog functionality — [H⁺] = 10⁻pH. Quoting pH to two decimal places is standard.
忘记正确进行 pH 与 [H⁺] 的转换：练习反对数运算 —— [H⁺] = 10⁻pH。pH 通常保留两位小数。
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Using the Henderson–Hasselbalch equation with concentrations directly from the mixture: ensure you use equilibrium concentrations, but for buffers the ratio of moles works because volume cancels.
直接使用混合物浓度代入 Henderson–Hasselbalch 方程：应使用平衡浓度，但对于缓冲液，使用物质的量之比是可行的，因体积会约掉。
12. Linking Theory to the IB CCEA Exam | 将理论与 IB CCEA 考试联系起来
Exam questions frequently weave together several concepts: you might be asked to explain why a certain salt produces an alkaline solution, calculate the pH of a buffer after adding a small amount of OH⁻, or interpret a titration curve to identify the pKa of an unknown acid. Data‑based questions may require you to deduce Ka from a table of pH measurements. Always show clear working, state any assumptions (e.g., [HA]₀ ≈ [HA] at equilibrium), and check that your final answer is physically sensible — for instance, pH of a weak base buffer should be above 7.
考试题目经常综合多个概念：可能要求解释某种盐为何呈碱性，计算加入少量 OH⁻ 后缓冲液的 pH，或通过分析滴定曲线确定未知酸的 pKa。基于数据的题目可能要求从 pH 测量表格推导 Ka。务必展示清晰的步骤，说明假设（例如平衡时 [HA]₀ ≈ [HA]），并检查最终答案是否合理 —— 例如弱碱缓冲液的 pH 应大于 7。
Mastering these core ideas and practising multi‑step calculations will give you the confidence to tackle any acid–base problem the IB CCEA Science paper presents.
掌握这些核心概念并练习多步骤计算，将使你有信心应对 IB CCEA 科学试卷中任何有关酸碱的问题。
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