IB & WJEC Chemistry: pH Calculations – Key Points Review | IB WJEC 化学：pH计算考点精讲

📚 IB & WJEC Chemistry: pH Calculations – Key Points Review | IB WJEC 化学：pH计算考点精讲

Mastering pH calculations is essential for success in both IB and WJEC Chemistry. This topic bridges quantitative problem-solving with core concepts of acid–base equilibria, ranging from strong acids to buffer systems. In this review, we break down the most examined calculations, clarify key assumptions, and provide step-by-step guidance aligned with the IB syllabus (Topics 8 & 18) and WJEC A Level specification. Whether you are tackling titration curves, salt hydrolysis, or polyprotic acids, understanding the logic behind the numbers will boost your confidence in the exam.

在 IB 和 WJEC 化学中，掌握 pH 计算是取得高分的关键。这一主题将定量解题与酸碱平衡的核心概念紧密结合，覆盖从强酸到缓冲体系的各类题型。本篇精讲梳理最高频的考点计算，厘清关键近似条件，并提供与 IB 教学大纲（Topic 8 & 18）及 WJEC A Level 规格同步的步骤指导。不论你在处理滴定曲线、盐水解还是多元酸问题，理解数字背后的逻辑将极大提升你的应试信心。

1. Defining pH and the Ionic Product of Water (Kw) | pH定义与水的离子积

pH is defined as the negative logarithm (base 10) of the hydrogen ion concentration: pH = –log₁₀[H⁺]. Similarly, pOH = –log₁₀[OH⁻]. The two are linked by the ionic product of water, Kw = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴ at 298 K. Therefore, pH + pOH = 14 at this temperature. This relationship is the foundation for all subsequent calculations, and IB and WJEC exam questions often start by testing your ability to interconvert [H⁺], [OH⁻], pH, and pOH.

pH 定义为氢离子浓度的负对数（以10为底）：pH = –log₁₀[H⁺]。类似地，pOH = –log₁₀[OH⁻]。两者通过水的离子积 Kw = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴ （298 K 下）相互关联。因此在此温度下 pH + pOH = 14。这一关系是所有后续计算的基础，IB 和 WJEC 试题常会首先考查你在 [H⁺]、[OH⁻]、pH 和 pOH 之间相互换算的能力。

Kw = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴ (at 298 K)

2. Strong Acids and Strong Bases: Direct Calculation | 强酸强碱：直接计算

Strong acids (e.g. HCl, HNO₃, H₂SO₄ for the first proton) and strong bases (e.g. NaOH, KOH) dissociate completely in aqueous solution. For a monoprotic strong acid of concentration c, [H⁺] = c. For a strong base like NaOH, [OH⁻] = c. For Group 2 hydroxides such as Ba(OH)₂, remember that each formula unit releases two hydroxide ions: [OH⁻] = 2 × c. After finding [H⁺] or [OH⁻], calculate pH or pOH directly using the logarithmic definitions. In IB Paper 1 and WJEC multiple-choice, watch out for very dilute solutions (c < 10⁻⁷ mol dm⁻³) where the contribution from water autoionisation becomes significant.

强酸（例如 HCl、HNO₃、H₂SO₄ 的第一级电离）和强碱（例如 NaOH、KOH）在水溶液中完全解离。对于浓度为 c 的一元强酸，[H⁺] = c。对于 NaOH 这样的强碱，[OH⁻] = c。对于 Ba(OH)₂ 这样的第二族氢氧化物，请记住每个式单元释放两个氢氧根离子：[OH⁻] = 2 × c。求出 [H⁺] 或 [OH⁻] 后，直接用对数定义计算 pH 或 pOH。在 IB 试卷一和 WJEC 选择题中，要注意极稀溶液（c < 10⁻⁷ mol dm⁻³），此时水的自耦电离贡献变得显著。

3. Weak Acids and the Acid Dissociation Constant (Ka) | 弱酸与酸解离常数 Ka

Weak acids only partially dissociate, establishing an equilibrium: HA ⇌ H⁺ + A⁻. The acid dissociation constant is given by Ka = [H⁺][A⁻] / [HA]. To calculate pH, we often assume [H⁺] = [A⁻] and that the equilibrium concentration of HA is approximately the initial concentration [HA]₀. This gives the simplified expression [H⁺] ≈ √(Ka × [HA]₀) , which is valid when [HA]₀ is more than 100 times Ka. The IB expects you to use this approximation and to check its validity, while WJEC structured questions may also ask for a more exact solution using the quadratic formula when the approximation fails. pKa = –log₁₀Ka provides a convenient scale for acid strength.

弱酸仅部分解离，建立平衡：HA ⇌ H⁺ + A⁻。酸解离常数由 Ka = [H⁺][A⁻] / [HA] 给出。计算 pH 时，我们通常假设 [H⁺] = [A⁻]，且 HA 的平衡浓度近似等于初始浓度 [HA]₀。由此得到简化式 [H⁺] ≈ √(Ka × [HA]₀) ，该式在 [HA]₀ 大于 Ka 100 倍以上时成立。IB 要求你使用这一近似并检验其有效性，而 WJEC 结构化题目在近似不成立时可能要求用二次方程求解精确值。pKa = –log₁₀Ka 给出了比较酸强度的便捷标度。

[H⁺] ≈ √(Ka × [HA]₀) and pH = –log₁₀[H⁺]

4. Weak Bases and Kb (or Ka of Conjugate Acid) | 弱碱与 Kb

Weak bases react with water: B + H₂O ⇌ BH⁺ + OH⁻. The base dissociation constant is Kb = [BH⁺][OH⁻] / [B]. Under the approximation [BH⁺] = [OH⁻] and [B] ≈ [B]₀, we obtain [OH⁻] ≈ √(Kb × [B]₀). Convert [OH⁻] to pOH and then to pH. In IB, you may also be given the Ka of the conjugate acid (BH⁺) and need to use the relationship Ka × Kb = Kw. WJEC equally expects you to link conjugate acid–base pairs through this equation, often in buffer or salt hydrolysis contexts.

弱碱与水反应：B + H₂O ⇌ BH⁺ + OH⁻。碱解离常数为 Kb = [BH⁺][OH⁻] / [B]。在近似 [BH⁺] = [OH⁻] 且 [B] ≈ [B]₀ 的条件下，我们得到 [OH⁻] ≈ √(Kb × [B]₀)。将 [OH⁻] 换算为 pOH 后求得 pH。在 IB 中，你可能会被给出共轭酸（BH⁺）的 Ka，并需要利用 Ka × Kb = Kw 这一关系。WJEC 同样要求你通过该方程关联共轭酸碱对，这在缓冲溶液或盐水解情境中十分常见。

5. pH of Salt Solutions: Hydrolysis | 盐溶液的pH：水解

Salts formed from strong acids and weak bases produce acidic solutions because the cation acts as a weak acid. Conversely, salts of weak acids and strong bases are basic due to the anion hydrolysing water to produce OH⁻. The relevant equilibrium constant is the hydrolysis constant, Kh. For a salt of a weak acid and strong base, Kh = Kw / Ka. To calculate pH, determine the concentration of the hydrolysing ion and apply the weak acid or weak base approximation. Both IB and WJEC questions often ask you to predict whether a given salt is acidic, basic, or neutral and to compute its pH.

由强酸和弱碱形成的盐水解呈酸性，因为阳离子充当弱酸。反之，弱酸强碱盐水解呈碱性，因为阴离子水解生成 OH⁻。相关平衡常数是水解常数 Kh。对于弱酸强碱盐，Kh = Kw / Ka。计算 pH 时，确定水解离子的浓度，并套用弱酸或弱碱的近似方法。IB 和 WJEC 试题常会要求你预测某种盐是酸性、碱性还是中性，并计算其 pH。

6. Buffer Solutions: Henderson–Hasselbalch and Beyond | 缓冲溶液

Buffer solutions resist pH changes and typically consist of a weak acid and its conjugate base. The Henderson–Hasselbalch equation is central: pH = pKa + log₁₀([A⁻]/[HA]). When preparing a buffer, using equal concentrations of acid and conjugate base gives pH = pKa. IB HL and WJEC require you to design buffers, calculate the pH after small additions of strong acid or base, and understand buffer capacity. For basic buffers, it is often easier to work with pOH and Kb, then convert to pH, or use the Ka of the conjugate acid.

缓冲溶液能够抵抗 pH 变化，通常由弱酸及其共轭碱组成。Henderson–Hasselbalch 方程是核心：pH = pKa + log₁₀([A⁻]/[HA])。配制缓冲溶液时，使用等浓度的酸和共轭碱可使 pH = pKa。IB HL 和 WJEC 要求你设计缓冲溶液，计算加入少量强酸或强碱后的 pH，并理解缓冲容量。对于碱性缓冲液，通常用 pOH 和 Kb 处理更为简便，然后换算为 pH，或者利用共轭酸的 Ka。

pH = pKa + log₁₀ ( [conjugate base] / [acid] )

7. pH Curves and Indicator Selection | pH曲线与指示剂选择

Titration curves plot pH against volume of titrant added. The equivalence point occurs where the analyte has been completely neutralised. For a strong acid–strong base titration, the equivalence point is at pH 7; for weak acid–strong base it lies above 7; and for weak base–strong acid it lies below 7. The choice of indicator must match the steep pH change. Common indicators include phenolphthalein (range 8.2–10.0) and methyl orange (range 3.1–4.4). IB students often answer data-analysis questions about the shape of curves and buffering regions, while WJEC demands calculation of pH at key points, such as half-equivalence (where pH = pKa).

滴定曲线绘制 pH 随滴定剂加入体积的变化。等当点是分析物被完全中和的体积点。强酸强碱滴定的等当点为 pH 7；弱酸强碱的等当点大于 7；弱碱强酸的等当点小于 7。指示剂的选择必须与陡峭的 pH 跃迁匹配。常用指示剂有酚酞（范围 8.2–10.0）和甲基橙（范围 3.1–4.4）。IB 学生常回答关于曲线形状和缓冲区域的数据分析题，而 WJEC 要求计算关键点的 pH，例如半等当点（此时 pH = pKa）。

8. Polyprotic Acids and Amphoteric Species | 多元酸与两性物质

Polyprotic acids ionise in steps, each with its own Ka value (Ka1, Ka2 …). For most diprotic acids, Ka1 >> Ka2, so the first ionisation determines the pH, and the contribution of the second step can be ignored unless concentrations are extremely low. Sulphuric acid is a special case: the first proton is strong, but the second is weak. Amphoteric species such as HCO₃⁻ can act as both acids and bases. For a solution of an amphoteric ion, pH is approximately the average of the two pKa values: pH ≈ (pKa1 + pKa2) / 2. IB HL and WJEC both test this approximation and related calculations.

多元酸逐级电离，每一步都有其自身的 Ka 值（Ka1、Ka2 …）。对于多数二元酸，Ka1 >> Ka2，因此第一级电离决定 pH，第二级电离的贡献可以忽略，除非浓度极低。硫酸是一个特例：第一级质子为强酸，第二级则为弱酸。HCO₃⁻ 等两性物质既可作酸又可作碱。对于两性离子的溶液，pH 近似等于两个 pKa 值的平均值：pH ≈ (pKa1 + pKa2) / 2。IB HL 和 WJEC 都会考查这一近似及相关计算。

9. Temperature Dependence of Kw and Neutral pH | Kw 的温度依赖与中性pH

Kw increases with temperature because the autoionisation of water is endothermic. At higher temperatures, the concentrations of H⁺ and OH⁻ rise, so the pH of pure water drops below 7, yet the solution remains neutral because [H⁺] = [OH⁻]. Exam questions may ask you to calculate the pH of neutral water at an elevated temperature given Kw. Always remember that ‘neutral’ means [H⁺] = [OH⁻], not pH = 7. This concept is a classic IB distinction and appears in WJEC thermochemistry-linked problems.

Kw 随温度升高而增大，因为水的自耦电离是吸热过程。温度升高时，H⁺ 和 OH⁻ 的浓度都增加，因此纯水的 pH 降至 7 以下，但溶液仍为中性，因为 [H⁺] = [OH⁻]。考试题目可能会给出高温下的 Kw，要求你计算此时中性水的 pH。始终牢记，“中性”意味着 [H⁺] = [OH⁻]，而非 pH = 7。这是 IB 中的一个经典辨析点，也会出现在 WJEC 与热化学关联的问题中。

10. Exam Tips and Common Pitfalls | 考试技巧与常见错误

Many marks are lost through simple oversights. Always check whether the acid is strong or weak before choosing a method. When using approximations, verify that the degree of dissociation is less than 5% or that c/Ka > 100. Keep track of significant figures based on the least precise data given. Use ICE (Initial, Change, Equilibrium) tables to organise equilibrium concentrations, especially for weak acids and buffers. For buffer calculations, remember that adding small amounts of strong acid converts some conjugate base to acid, shifting the ratio. Practise interconverting pH, [H⁺], pOH, and [OH⁻] until it becomes second nature.

许多丢分源于简单的疏忽。在选择方法前，务必确认酸是强是弱。使用近似时，要验证解离度是否小于 5% 或 c/Ka > 100。根据题目中最不精确的数据确定有效数字位数。利用 ICE（起始、变化、平衡）表格梳理平衡浓度，这对弱酸和缓冲溶液尤为重要。在缓冲溶液计算中，记住加入少量强酸会将部分共轭碱转化为酸，改变 [A⁻]/[HA] 比。反复练习 pH、[H⁺]、pOH 和 [OH⁻] 之间的相互换算，直到像本能一样熟练。

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IB & WJEC Chemistry: pH Calculations – Key Points Review | IB WJEC 化学：pH计算 考点精讲