IGCSE Chemistry: Mastering pH Calculations | IGCSE化学：pH计算考点精讲

📚 IGCSE Chemistry: Mastering pH Calculations | IGCSE化学：pH计算考点精讲

pH is a fundamental concept in IGCSE Chemistry that links acid-base theory with quantitative calculations. Understanding how to compute pH from hydrogen ion concentration and vice versa is a key skill tested in exams. This article provides a thorough breakdown of pH calculations, covering strong and weak acids, dilution effects, neutralisation, and common pitfalls. Each section is designed to build confidence and precision for your revision.

pH 是 IGCSE 化学里将酸碱理论与定量计算连接起来的一个基本概念。掌握从氢离子浓度计算 pH、以及从 pH 反推氢离子浓度是考试中的核心技能。本文将对 pH 计算进行全面拆解，涵盖强酸与弱酸、稀释效应、中和反应以及常见易错点。每一个小节都旨在帮助你在复习中建立信心和准确度。

1. What is pH? | 什么是 pH？

pH is a numerical scale used to specify the acidity or alkalinity of an aqueous solution. It is defined as the negative logarithm (to base 10) of the hydrogen ion concentration, [H⁺]. Mathematically, this relationship is expressed as pH = -log₁₀[H⁺]. In simpler terms, the lower the pH value, the higher the concentration of H⁺ ions in the solution.

pH 是一个用来表示水溶液酸碱度的数值标度。它被定义为氢离子浓度 [H⁺] 的负对数（以 10 为底）。数学上表示为 pH = -log₁₀[H⁺]。简单来说，pH 值越低，溶液中 H⁺ 离子的浓度就越高。

The concept was introduced to avoid dealing with very small numbers. For instance, pure water has [H⁺] = 1.0 × 10⁻⁷ mol dm⁻³ at 25 °C, which gives a far more convenient pH value of 7. IGCSE candidates must be comfortable converting between these two forms.

引入 pH 这个概念是为了避免处理极小的小数。例如，25 °C 下纯水的 [H⁺] = 1.0 × 10⁻⁷ mol dm⁻³，对应的 pH 值则是方便得多的 7。IGCSE 考生必须能熟练地在两种表示形式之间进行转换。

2. The pH Scale | pH 标度

The pH scale typically runs from 0 to 14, although values outside this range are possible for extremely concentrated acids or alkalis. A neutral solution (like pure water) has a pH of 7. Acidic solutions have a pH less than 7, and alkaline (basic) solutions have a pH greater than 7. Each unit change in pH corresponds to a ten‑fold change in [H⁺].

pH 标度通常从 0 到 14，不过在极浓的酸或碱中也可能出现超出此范围的数值。中性溶液（如纯水）的 pH = 7。酸性溶液的 pH 小于 7，而碱性溶液的 pH 大于 7。pH 每变化 1 个单位，[H⁺] 就变化 10 倍。

pH 0: [H⁺] = 1 mol dm⁻³ (strongly acidic)
pH 3: [H⁺] = 1×10⁻³ mol dm⁻³ (weakly acidic)
pH 7: [H⁺] = 1×10⁻⁷ mol dm⁻³ (neutral)
pH 11: [H⁺] = 1×10⁻¹¹ mol dm⁻³ (weakly alkaline)
pH 14: [H⁺] = 1×10⁻¹⁴ mol dm⁻³ (strongly alkaline)

pH 0：[H⁺] = 1 mol dm⁻³（强酸性）
pH 3：[H⁺] = 1×10⁻³ mol dm⁻³（弱酸性）
pH 7：[H⁺] = 1×10⁻⁷ mol dm⁻³（中性）
pH 11：[H⁺] = 1×10⁻¹¹ mol dm⁻³（弱碱性）
pH 14：[H⁺] = 1×10⁻¹⁴ mol dm⁻³（强碱性）

3. The Formula: pH = -log[H⁺] | 公式：pH = -log[H⁺]

The core equation you must memorise is:

pH = -log₁₀[H⁺]

Here, [H⁺] is the concentration of hydrogen ions in mol dm⁻³. On your calculator, the ‘log’ button gives log₁₀ directly. The negative sign ensures that higher [H⁺] (more acidic) results in a lower pH. When rearranging to find [H⁺] from pH, use the inverse equation:

[H⁺] = 10⁻ᵟᴴ

你必须记住的核心公式是：

pH = -log₁₀[H⁺]

其中 [H⁺] 是以 mol dm⁻³ 表示的氢离子浓度。在计算器上，’log’ 键直接给出 log₁₀。负号确保 [H⁺] 越高（酸性越强）时 pH 越低。当需要从 pH 值反推 [H⁺] 时，可使用逆运算：

[H⁺] = 10⁻ᵟᴴ

Make sure you are confident using the 10ˣ or antilog function on your calculator. For a pH of 2.4, press 10ˣ (-2.4) to obtain [H⁺] ≈ 4.0×10⁻³ mol dm⁻³.

请确保你能熟练使用计算器上的 10ˣ 或反对数功能。当 pH = 2.4 时，按下 10ˣ(-2.4) 即可得到 [H⁺] ≈ 4.0×10⁻³ mol dm⁻³。

4. Calculating pH from [H⁺] | 已知 [H⁺] 求 pH

Follow these steps when given a hydrogen ion concentration:

Ensure [H⁺] is in mol dm⁻³.
Take the log₁₀ of the concentration.
Apply the negative sign to obtain the pH.

当你拿到一个氢离子浓度后，按下列步骤操作：

确认 [H⁺] 的单位是 mol dm⁻³。
取该浓度的 log₁₀。
加上负号即可得到 pH。

Example 1: Calculate the pH of a solution with [H⁺] = 0.001 mol dm⁻³.
pH = -log(0.001) = -(-3) = 3.

例题 1：计算 [H⁺] = 0.001 mol dm⁻³ 的溶液的 pH。
pH = -log(0.001) = -(-3) = 3。

Example 2: What is the pH of 0.02 mol dm⁻³ nitric acid (HNO₃)?
Nitric acid is a strong monoprotic acid, so [H⁺] = 0.02 mol dm⁻³.
pH = -log(0.02) ≈ 1.70 (to 2 decimal places).

例题 2：0.02 mol dm⁻³ 硝酸 (HNO₃) 的 pH 是多少？
硝酸是强一元酸，因此 [H⁺] = 0.02 mol dm⁻³。
pH = -log(0.02) ≈ 1.70（保留两位小数）。

5. Calculating [H⁺] from pH | 已知 pH 求 [H⁺]

To find the hydrogen ion concentration from a given pH, use the relationship [H⁺] = 10⁻ᵟᴴ. The result will always be in mol dm⁻³. This calculation is especially important when comparing the acidity of two solutions or when determining the effect of dilution.

要从给定的 pH 值求氢离子浓度，使用关系式 [H⁺] = 10⁻ᵟᴴ。计算结果始终以 mol dm⁻³ 为单位。这种计算在比较两种溶液的酸性或者确定稀释效应时尤为重要。

Example 3: Determine [H⁺] for a solution with pH = 5.6.
[H⁺] = 10⁻⁵·⁶ ≈ 2.5×10⁻⁶ mol dm⁻³.

例题 3：求 pH = 5.6 的溶液的 [H⁺]。
[H⁺] = 10⁻⁵·⁶ ≈ 2.5×10⁻⁶ mol dm⁻³。

Example 4: Stomach acid has a pH around 1.5. What is its [H⁺]?
[H⁺] = 10⁻¹·⁵ ≈ 0.032 mol dm⁻³.

例题 4：胃酸的 pH 大约为 1.5。其 [H⁺] 是多少？
[H⁺] = 10⁻¹·⁵ ≈ 0.032 mol dm⁻³。

6. Strong Acids and pH | 强酸与 pH

A strong acid dissociates completely in water. For a strong monoprotic acid such as HCl or HNO₃, the concentration of H⁺ ions equals the acid concentration. Therefore, calculating pH is straightforward: [H⁺] = c(acid). For a strong diprotic acid like H₂SO₄, you must account for the two protons released per molecule, so [H⁺] = 2 × c(acid) (assuming complete dissociation of both protons, which is the usual IGCSE simplification).

强酸在水中完全电离。对于像 HCl 或 HNO₃ 这样的强一元酸，H⁺ 离子的浓度等于酸的浓度。因此，pH 的计算非常直接：[H⁺] = c(acid)。而对于像 H₂SO₄ 这样的强二元酸，你必须考虑每个分子释放两个质子，所以 [H⁺] = 2 × c(acid)（假设两个质子都完全电离，这是 IGCSE 通常的简化处理）。

Let’s look at a common example:

Calculate the pH of 0.005 mol dm⁻³ H₂SO₄.

[H⁺] = 2 × 0.005 = 0.010 mol dm⁻³.
pH = -log(0.010) = 2.0.

看一个常见例题：

计算 0.005 mol dm⁻³ H₂SO₄ 的 pH。

[H⁺] = 2 × 0.005 = 0.010 mol dm⁻³。
pH = -log(0.010) = 2.0。

7. Weak Acids and pH | 弱酸与 pH

Weak acids, such as ethanoic acid (CH₃COOH), only partially dissociate in water. This means that [H⁺] is much lower than the stated acid concentration. For the same molar concentration, a weak acid will always have a higher pH than a strong acid. At IGCSE level, you are not required to calculate the pH of weak acids using the acid dissociation constant (Kₐ); however, you must be able to compare their behaviour qualitatively. For instance, 0.1 mol dm⁻³ HCl has pH ≈ 1, while 0.1 mol dm⁻³ CH₃COOH might have pH ≈ 3.

弱酸（如乙酸 CH₃COOH）在水中只会部分电离。这意味着 [H⁺] 远低于酸的标示浓度。在相同摩尔浓度下，弱酸的 pH 总是高于强酸。在 IGCSE 阶段，你不需要利用酸解离常数 (Kₐ) 计算弱酸的 pH；但你必须能够定性地比较它们的行为。例如，0.1 mol dm⁻³ HCl 的 pH ≈ 1，而 0.1 mol dm⁻³ CH₃COOH 的 pH 大约为 3。

You may also be asked to predict the pH change on dilution (see next section) or to explain why a weak acid has a higher pH. The answer lies in the equilibrium position: the forward reaction (HA ⇌ H⁺ + A⁻) lies far to the left, limiting the number of H⁺ ions in solution.

你也可能被问到稀释对弱酸 pH 变化的影响（见下一节），或者解释为什么弱酸的 pH 更高。答案在于平衡的位置：正向反应 (HA ⇌ H⁺ + A⁻) 的平衡位置更偏向左方，从而限制了溶液中 H⁺ 离子的数量。

8. Dilution and pH Changes | 稀释与 pH 变化

When an acidic solution is diluted with water, the concentration of H⁺ decreases, leading to an increase in pH. The magnitude of this change depends on whether the acid is strong or weak. For a strong acid, diluting by a factor of 10 (i.e., making the volume 10 times larger) reduces [H⁺] to one-tenth, so the pH rises by exactly 1 unit. For example, 0.1M HCl has pH=1; after 10-fold dilution, pH becomes 2.

当酸性溶液用水稀释时，H⁺ 浓度下降，导致 pH 升高。这种变化的幅度取决于酸是强酸还是弱酸。对于强酸，稀释 10 倍（即将体积变为原来的 10 倍）会使 [H⁺] 变为原来的十分之一，因此 pH 恰好上升 1 个单位。例如，0.1M HCl 的 pH=1；10 倍稀释后，pH 变为 2。

Weak acids behave differently because the equilibrium shifts to release more H⁺ as the solution is diluted. Consequently, [H⁺] does not decrease by a full factor of 10, and the pH rises by less than 1 unit. This concept is frequently tested in multiple-choice questions. Remember: the pH of a weak acid solution is less sensitive to dilution.

弱酸的表现则不同，因为在稀释时平衡会移动从而释放出更多的 H⁺。因此，[H⁺] 不会完全下降到原来的十分之一，pH 的上升幅度会小于 1 个单位。这一概念在选择题中经常出现。请记住：弱酸溶液的 pH 对稀释不那么敏感。

9. pH in Neutralisation Reactions | 中和反应中的 pH

During a neutralisation reaction between an acid and an alkali, the pH changes gradually until it reaches the equivalence point. Monitoring pH with a meter or indicator allows us to determine the end point of a titration. In a strong acid – strong base titration (e.g., HCl + NaOH), the equivalence point occurs at pH = 7 because the salt formed is neutral. If a weak acid is titrated with a strong base, the equivalence point is alkaline (pH > 7) due to the hydrolysis of the conjugate base. Conversely, a weak base – strong acid titration yields an acidic equivalence point (pH < 7).

在酸与碱的中和反应中，pH 会逐渐变化，直至达到等当点。用 pH 计或指示剂监测 pH 可以帮助我们确定滴定的终点。在强酸-强碱滴定（如 HCl + NaOH）中，由于生成的盐是中性的，等当点出现在 pH = 7。如果用强碱滴定弱酸，由于共轭碱的水解，等当点为碱性（pH > 7）。相反，弱碱-强酸滴定的等当点则是酸性的（pH < 7）。

While detailed titration curve calculations are beyond the scope of basic IGCSE, you should be able to interpret simple graphs and pick appropriate indicators. Phenolphthalein changes colour in the pH range 8.3–10.0, so it is suitable for strong base titrations, while methyl orange (3.1–4.4) works for strong acid titrations.

虽然详细的滴定曲线计算超出了基础 IGCSE 的要求，但你应该能够解读简单的线图并选择合适的指示剂。酚酞在 pH 8.3–10.0 范围内变色，因此适用于强碱滴定；而甲基橙 (3.1–4.4) 适合用于强酸滴定。

10. Common Mistakes and Exam Tips | 常见错误与应试技巧

Mistake 1: Forgetting the negative sign. Many students write pH = log[H⁺] and obtain a negative answer for an acidic solution. Always check: a solution with [H⁺] > 1×10⁻⁷ mol dm⁻³ must have a pH less than 7.

错误 1：忘了负号。很多学生写出 pH = log[H⁺]，结果对酸性溶液得到负数。一定要检查：[H⁺] > 1×10⁻⁷ mol dm⁻³ 的溶液，其 pH 必定小于 7。

Mistake 2: Confusing [H⁺] with acid concentration for diprotic acids. If you are given 0.1 mol dm⁻³ H₂SO₄, do not use 0.1 directly in the pH formula unless you have first multiplied by the number of protons released.

错误 2：对于二元酸，混淆 [H⁺] 与酸的浓度。如果题目给出 0.1 mol dm⁻³ H₂SO₄，不要直接把 0.1 代入 pH 公式，除非你已先乘上其释放的质子数。

Mistake 3: Giving pH to an inappropriate number of significant figures. Usually, the pH should be reported to 2 decimal places, as it is derived from a concentration that typically has 2 or 3 significant figures.

错误 3：pH 的有效数字位数不当。通常 pH 应保留 2 位小数，因为它来自通常有 2 到 3 位有效数字的浓度值。

Tip: Practise using the calculator’s 10ˣ and log functions without looking at the manual. Work through plenty of examples, and always check if your answer makes sense: very acidic (pH 0-2), weakly acidic (pH 4-6), neutral (pH 7), weakly alkaline (pH 8-11), strongly alkaline (pH 12-14).

技巧：不查说明书也要能熟练使用计算器的 10ˣ 和 log 功能。多做练习，并始终检查你的答案是否合理：强酸性 (pH 0-2)，弱酸性 (pH 4-6)，中性 (pH 7)，弱碱性 (pH 8-11)，强碱性 (pH 12-14)。

11. Worked Practice Calculations | 练习计算实例

Question 1: A student prepares a solution of hydrochloric acid by dissolving 0.365 g of HCl gas in water to make 1.00 dm³ of solution. (Mᵣ of HCl = 36.5) Calculate the pH of the solution.

题目 1：某学生将 0.365 g 氯化氢气体溶于水，配制成 1.00 dm³ 溶液。(HCl 的相对分子质量 Mᵣ = 36.5) 计算该溶液的 pH。

Solution / 解答：
Moles of HCl = mass / Mᵣ = 0.365 / 36.5 = 0.0100 mol.
Concentration = moles / volume = 0.0100 / 1.00 = 0.0100 mol dm⁻³.
HCl is a strong monoprotic acid, so [H⁺] = 0.0100 mol dm⁻³.
pH = -log(0.0100) = 2.00.

HCl 的物质的量 = 质量 / Mᵣ = 0.365 / 36.5 = 0.0100 mol。
浓度 = 物质的量 / 体积 = 0.0100 / 1.00 = 0.0100 mol dm⁻³。
HCl 是强一元酸，因此 [H⁺] = 0.0100 mol dm⁻³。
pH = -log(0.0100) = 2.00。

Question 2: Lemon juice has a pH of 2.3. Determine the hydrogen ion concentration, [H⁺], in the juice.

题目 2：柠檬汁的 pH 为 2.3。求柠檬汁中氢离子浓度 [H⁺]。

Solution / 解答：
[H⁺] = 10⁻²·³ ≈ 5.0×10⁻³ mol dm⁻³ (to 2 significant figures).

[H⁺] = 10⁻²·³ ≈ 5.0×10⁻³ mol dm⁻³（保留两位有效数字）。

Question 3: A 0.100 mol dm⁻³ solution of ethanoic acid has a pH of 2.9. Explain why this pH is higher than that of 0.100 mol dm⁻³ HCl, and calculate the approximate [H⁺] in the ethanoic acid solution.

题目 3：0.100 mol dm⁻³ 的乙酸溶液 pH 为 2.9。解释为什么该 pH 高于 0.100 mol dm⁻³ HCl 的 pH，并计算乙酸溶液中近似的 [H⁺]。

Solution / 解答：
HCl is a strong acid and dissociates completely, giving [H⁺] = 0.100 mol dm⁻³ and pH = 1.0. Ethanoic acid is a weak acid, so only a small fraction of molecules release H⁺; hence [H⁺] is much lower, leading to a higher pH.
For ethanoic acid: [H⁺] = 10⁻²·⁹ ≈ 1.3×10⁻³ mol dm⁻³.

HCl 是强酸，能完全电离，因此 [H⁺] = 0.100 mol dm⁻³，pH = 1.0。乙酸是一种弱酸，只有一小部分分子会释放 H⁺；因此 [H⁺] 低得多，导致 pH 更高。
对于乙酸：[H⁺] = 10⁻²·⁹ ≈ 1.3×10⁻³ mol dm⁻³。

12. Summary and Key Takeaways | 总结与关键要点

Mastering pH calculations is about understanding the logarithmic relationship and applying it confidently to strong acids, weak acids, and dilutions. Remember the core formulas: pH = -log[H⁺] and [H⁺] = 10⁻ᵟᴴ. Practise with both monoprotic and diprotic strong acids, and be able to compare the behaviour of weak acids qualitatively. Avoid common errors such as forgetting the negative sign or misusing the acid concentration for diprotic acids. With consistent practice, pH problems can become some of the most reliable marks on your IGCSE Chemistry paper.

掌握 pH 计算的关键在于理解对数关系，并能自信地将其应用于强酸、弱酸和稀释过程。记住核心公式：pH = -log[H⁺] 和 [H⁺] = 10⁻ᵟᴴ。既要有练习一元强酸和二元强酸的计算，又要能够定性地比较弱酸的行为。避免常见错误，如忘记负号或对二元酸误用酸的浓度。通过持续练习，pH 题目可以成为你 IGCSE 化学试卷中十拿九稳的得分点。

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IGCSE Chemistry: Mastering pH Calculations | IGCSE化学：pH计算考点精讲