GCSE OCR Chemistry: pH Calculations – Key Points | GCSE OCR 化学：pH计算考点精讲

📚 GCSE OCR Chemistry: pH Calculations – Key Points | GCSE OCR 化学：pH计算考点精讲

pH calculations are a central part of the GCSE OCR Chemistry syllabus. Understanding how to interconvert hydrogen ion concentration and pH, and applying these ideas to strong acids, is essential for exam success. This article breaks down every key concept you need.

pH 计算是 GCSE OCR 化学课程的核心部分。理解氢离子浓度与 pH 之间的相互转换，并将这些概念应用于强酸，对于考试成功至关重要。本文将逐一解析你需要掌握的每一个关键概念。

1. The pH Scale and Its Significance | pH 标度及其意义

The pH scale measures the acidity or alkalinity of an aqueous solution. It typically runs from 0 (very acidic) to 14 (very alkaline), with 7 being neutral. Each unit change in pH represents a ten‑fold change in hydrogen ion concentration, [H⁺].

pH 标度用于衡量水溶液的酸碱性。通常范围是 0（强酸性）到 14（强碱性），7 为中性。pH 每变化 1 个单位，氢离子浓度 [H⁺] 就改变 10 倍。

A low pH means a high [H⁺]; a high pH means a low [H⁺]. Neutral solutions have [H⁺] = [OH⁻] = 1 × 10⁻⁷ mol/dm³ at 25°C.

低 pH 意味着 [H⁺] 高；高 pH 意味着 [H⁺] 低。25°C 时中性溶液中 [H⁺] = [OH⁻] = 1 × 10⁻⁷ mol/dm³。

2. The pH Equation | pH 计算公式

The relationship between pH and hydrogen ion concentration is given by:

pH 与氢离子浓度的关系由以下公式给出：

pH = –log₁₀[H⁺]

Here, [H⁺] is the concentration of hydrogen ions in mol/dm³. The negative sign means that as [H⁺] increases, pH decreases.

其中 [H⁺] 为氢离子浓度，单位为 mol/dm³。负号表示当 [H⁺] 增大时，pH 减小。

The inverse relationship is equally important:

反向关系同样重要：

[H⁺] = 10⁻ᵖᴴ

These two equations are all you need for converting between pH and [H⁺].

这两个方程是进行 pH 与 [H⁺] 互转所需的全部工具。

3. Calculating pH from Hydrogen Ion Concentration | 由氢离子浓度计算 pH

Given [H⁺], simply substitute it into pH = –log₁₀[H⁺]. For example, if [H⁺] = 0.01 mol/dm³, then pH = –log₁₀(0.01) = –log₁₀(10⁻²) = 2.

已知 [H⁺]，直接代入 pH = –log₁₀[H⁺] 即可。例如，若 [H⁺] = 0.01 mol/dm³，则 pH = –log₁₀(0.01) = –log₁₀(10⁻²) = 2。

With [H⁺] = 3.5 × 10⁻⁴ mol/dm³, pH = –log₁₀(3.5 × 10⁻⁴) ≈ 3.46 (using a calculator). The exam expects you to use a scientific calculator for such calculations.

若 [H⁺] = 3.5 × 10⁻⁴ mol/dm³，pH = –log₁₀(3.5 × 10⁻⁴) ≈ 3.46（使用科学计算器）。考试中要求你会用计算器完成此类计算。

Remember: the answer should be given to an appropriate number of decimal places, usually 2 or 3.

记住：答案通常需要保留到小数点后 2 位或 3 位。

4. Calculating [H⁺] from pH | 由 pH 计算氢离子浓度

To find [H⁺] when pH is known, use [H⁺] = 10⁻ᵖᴴ. For example, if pH = 5, then [H⁺] = 10⁻⁵ mol/dm³.

已知 pH 求 [H⁺] 时，使用 [H⁺] = 10⁻ᵖᴴ。例如，pH = 5 时，[H⁺] = 10⁻⁵ mol/dm³。

If pH = 3.7, then [H⁺] = 10⁻³·⁷ = 2.0 × 10⁻⁴ mol/dm³ (to 2 significant figures). Always express the concentration in standard form if it is very small.

若 pH = 3.7，则 [H⁺] = 10⁻³·⁷ ≈ 2.0 × 10⁻⁴ mol/dm³（保留两位有效数字）。浓度很小时务必用科学记数法表示。

This conversion is a typical exam question, often combined with strong acid stoichiometry.

这种转换是典型考题，通常与强酸的化学计量结合考查。

5. Strong Acids and Complete Dissociation | 强酸与完全电离

A strong acid is one that completely dissociates (ionises) in water. For example, hydrochloric acid: HCl → H⁺ + Cl⁻. This means the concentration of H⁺ equals the concentration of the acid, multiplied by the number of H⁺ produced per molecule.

强酸是指在水溶液中完全电离的酸。例如盐酸：HCl → H⁺ + Cl⁻。这意味着氢离子浓度等于酸的浓度乘以每分子产生的 H⁺ 个数。

Because the dissociation is complete, you do not need an equilibrium constant; the stoichiometry gives [H⁺] directly.

由于电离完全，无需使用平衡常数；根据化学计量可直接求得 [H⁺]。

Key strong acids to know: HCl, HNO₃, H₂SO₄ (first dissociation is complete, second is only partially dissociated at GCSE level, but OCR usually treats H₂SO₄ as giving 2 H⁺ for pH calculations).

需要掌握的主要强酸：HCl、HNO₃、H₂SO₄（在 GCSE 阶段，OCR 通常将硫酸视为提供 2 个 H⁺ 来进行 pH 计算，尽管第二步电离不完全，但通常忽略不计）。

6. pH of Strong Monoprotic Acids | 一元强酸的 pH 计算

Monoprotic acids release one H⁺ per molecule. For a solution of HCl of concentration c mol/dm³, [H⁺] = c, so pH = –log₁₀(c).

一元酸每分子释放一个 H⁺。对于浓度为 c mol/dm³ 的盐酸溶液，[H⁺] = c，因此 pH = –log₁₀(c)。

Example: 0.050 mol/dm³ HNO₃ gives [H⁺] = 0.050, pH = –log₁₀(0.050) = 1.30. Similarly, 0.005 mol/dm³ HCl gives pH = –log₁₀(0.005) = 2.30.

示例：0.050 mol/dm³ 的 HNO₃，[H⁺] = 0.050，pH = –log₁₀(0.050) = 1.30。同理，0.005 mol/dm³ HCl 的 pH = –log₁₀(0.005) = 2.30。

Always check that your pH lies between 0 and 7 for acidic solutions.

务必检查酸性溶液的 pH 是否在 0 到 7 之间。

7. pH of Strong Diprotic Acids | 二元强酸的 pH 计算

Sulfuric acid, H₂SO₄, is diprotic. For OCR GCSE calculations, it is assumed to provide 2 H⁺ per molecule: H₂SO₄ → 2H⁺ + SO₄²⁻.

硫酸 H₂SO₄ 是二元酸。在 OCR GCSE 的计算中，假定每分子提供 2 个 H⁺：H₂SO₄ → 2H⁺ + SO₄²⁻。

Thus, if the acid concentration is c mol/dm³, then [H⁺] = 2c. pH = –log₁₀(2c).

因此，若酸浓度为 c mol/dm³，则 [H⁺] = 2c，pH = –log₁₀(2c)。

Example: 0.010 mol/dm³ H₂SO₄ gives [H⁺] = 0.020 mol/dm³, pH = –log₁₀(0.020) = 1.70.

示例：0.010 mol/dm³ H₂SO₄，[H⁺] = 0.020 mol/dm³，pH = –log₁₀(0.020) = 1.70。

Be careful: if the question states that only the first proton is completely dissociated, you would use [H⁺] = c, but this is rarely specified at GCSE.

注意：若题目指明只有第一个质子完全电离，则应使用 [H⁺] = c，但 GCSE 阶段极少这样要求。

8. Effect of Dilution on pH | 稀释对 pH 的影响

Diluting an acid with water decreases [H⁺] and thus increases pH. If you dilute a strong acid by a factor of 10, [H⁺] decreases by a factor of 10, and pH increases by 1 unit.

用水稀释酸会降低 [H⁺]，从而使 pH 升高。将强酸稀释 10 倍，[H⁺] 减小为原来的 1/10，pH 增加 1 个单位。

Example: 10 cm³ of 0.1 mol/dm³ HCl (pH 1) is diluted to 100 cm³ with water. New [H⁺] = 0.01 mol/dm³, pH = 2.

示例：取 10 cm³ 0.1 mol/dm³ HCl（pH = 1），加水稀释至 100 cm³。新的 [H⁺] = 0.01 mol/dm³，pH = 2。

Diluting 100 times increases pH by 2, and so on. However, note that extremely dilute acids (below ~2×10⁻⁷ mol/dm³) approach neutrality due to the auto-ionisation of water, but such cases are beyond GCSE.

稀释 100 倍则 pH 增加 2，以此类推。但需注意，极稀的酸（低于约 2×10⁻⁷ mol/dm³）会因水的自耦电离而趋近中性，这超出了 GCSE 范围。

9. Measuring pH | pH 的测定

pH can be measured using a pH meter (a probe connected to a digital meter) or an indicator. Universal indicator solution or paper shows a range of colours from red (acidic) through green (neutral) to purple (alkaline).

pH 可用 pH 计（连接数字仪表的探头）或指示剂进行测定。通用指示剂溶液或试纸会显示从红（酸性）经绿（中性）到紫（碱性）的颜色变化。

A pH meter gives a numerical reading to one or two decimal places and is more accurate than an indicator.

pH 计可以给出到小数点后一位或两位的数字读数，比指示剂更准确。

In exam questions, you may need to compare the pH values of different solutions after dilution or neutralisation.

在考试题中，你可能需要比较不同溶液经过稀释或中和后的 pH 值。

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

Mistake 1: Forgetting that pH is a logarithmic scale. A solution of pH 3 has ten times the [H⁺] of pH 4, not twice.

错误 1：忘记了 pH 是对数标度。pH = 3 的溶液其 [H⁺] 是 pH = 4 的 10 倍，而不是 2 倍。

Mistake 2: Using the wrong formula. Always use pH = –log₁₀[H⁺] and [H⁺] = 10⁻ᵖᴴ.

错误 2：用错公式。始终使用 pH = –log₁₀[H⁺] 和 [H⁺] = 10⁻ᵖᴴ。

Mistake 3: Forgetting that strong diprotic acids yield 2 H⁺ per molecule. Double the concentration when calculating [H⁺] from acid concentration.

错误 3：忘记二元强酸每分子产生 2 个 H⁺。在根据酸浓度计算 [H⁺] 时要乘以 2。

Tip: Write down the dissociation equation first, then determine the mole ratio, then calculate [H⁺], and finally calculate pH.

技巧：先写出电离方程式，确定摩尔比，再计算 [H⁺]，最后求 pH。

Practise using your calculator’s log and 10ˣ buttons efficiently, showing all workings in structured steps.

练习熟练使用计算器上的 log 和 10ˣ 键，并以清晰步骤展示所有运算过程。

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GCSE OCR Chemistry: pH Calculations – Key Points | GCSE OCR 化学：pH计算 考点精讲