The pH Scale | pH 标度

📚 The pH Scale | pH 标度

The pH scale is a cornerstone of acid–base chemistry, translating the concentration of hydrogen ions in aqueous solution into a simple numerical range. Devised to quantify how acidic or basic a substance is, the scale underpins fields as diverse as biochemistry, industrial chemistry and environmental science. In the IB Chemistry programme, a thorough understanding of pH is essential for interpreting equilibrium, buffer action and the behaviour of both strong and weak acids and bases.

pH 标度是酸碱化学的基石，它将水溶液中的氢离子浓度转化为一个简单的数值范围。为了量化物质的酸性或碱性程度，这一标度支撑着生物化学、工业化学和环境科学等众多领域。在 IB 化学课程中，透彻理解 pH 对于解释平衡、缓冲作用以及强酸、弱酸和碱的行为至关重要。

1. The Concept of pH: A Logarithmic Scale | pH 的概念：对数标度

The term ‘pH’ was introduced by the Danish chemist Søren Sørensen in 1909 while he was studying proteins and enzyme activity. It stands for ‘potential of hydrogen’ and is defined as the negative logarithm to base 10 of the hydrogen ion concentration: pH = -log[H⁺], where [H⁺] is measured in mol dm⁻³. Because the scale is logarithmic, a solution with pH 3 has ten times the [H⁺] of a solution with pH 4, and one hundred times that of pH 5.

“pH” 一词由丹麦化学家 Søren Sørensen 于 1909 年研究蛋白质和酶活性时提出。它代表“氢离子活度”，定义为以 10 为底的氢离子浓度的负对数：pH = -log[H⁺]，其中 [H⁺] 的单位为 mol dm⁻³。由于标度是对数形式，pH 为 3 的溶液其 [H⁺] 是 pH 为 4 的溶液的 10 倍，是 pH 为 5 的溶液的 100 倍。

In modern chemistry the hydrogen ion is understood to exist as the hydronium ion, H₃O⁺, in water, but [H⁺] is retained for simplicity. The logarithmic compression allows chemists to handle an enormous range of concentrations – from about 10 mol dm⁻³ concentrated acid to 10⁻¹⁵ mol dm⁻³ strong alkali – with numbers typically between 0 and 14.

在现代化学中，氢离子在水中以水合氢离子 H₃O⁺ 的形式存在，但为了简便仍使用 [H⁺]。对数压缩使化学家能够用一个通常介于 0 到 14 之间的数字来处理极大的浓度范围——从约 10 mol dm⁻³ 的浓酸到 10⁻¹⁵ mol dm⁻³ 的强碱。

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2. The Ionic Product of Water, K_w | 水的离子积 K_w

Pure water undergoes autoprotolysis according to the equilibrium: 2H₂O(l) ⇌ H₃O⁺(aq) + OH⁻(aq). The equilibrium constant for this reaction is called the ionic product of water, K_w = [H⁺][OH⁻]. At 25 °C, K_w mol² dm⁻⁶. In pure water, [H⁺] = [OH⁻] = 1.0 × 10⁻⁷ mol dm⁻³, giving a neutral pH of 7.00.

纯水按照以下平衡发生自耦电离：2H₂O(l) ⇌ H₃O⁺(aq) + OH⁻(aq)。该反应的平衡常数称为水的离子积，K_w = [H⁺][OH⁻]。在 25 °C 时，K_w 的值为 1.0 × 10⁻¹⁴ mol² dm⁻⁶。在纯水中，[H⁺] = [OH⁻] = 1.0 × 10⁻⁷ mol dm⁻³，对应的中性 pH 为 7.00。

K_w is an equilibrium constant and therefore depends only on temperature. Heating increases the extent of autoionisation, so K_w becomes larger. This concept is vital when discussing the temperature dependence of pH and the meaning of a neutral solution at different temperatures.

K_w 是一个平衡常数，因此只依赖于温度。加热会增加水的自耦电离程度，因此 K_w 变大。在讨论 pH 的温度依赖性以及不同温度下中性溶液的含义时，这一概念至关重要。

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3. Defining pOH and Its Relationship to pH | 定义 pOH 及其与 pH 的关系

solution is defined as pOH = -log[OH⁻]. Taking the negative logarithm of the expression K_w = [H⁺][OH⁻] yields a simple additive relationship: pH + pOH = pK_w. At 25 °C, pK_w if the pH of a base is 10.3, the pOH is 3.7, giving [OH⁻] = 10⁻³·⁷ = 2.0 × 10⁻⁴ mol dm⁻³.

与 pH 类似，溶液的 pOH 定义为 pOH = -log[OH⁻]。对 K_w = [H⁺][OH⁻] 表达式取负对数可得到一个简单的加和关系：pH + pOH = pK_w。在 25 °C 时，pK_w = 14.00，因此 pH + pOH = 14.00。该等式可实现快速换算：若某碱溶液的 pH 为 10.3，则 pOH 为 3.7，由此可得 [OH⁻] = 10⁻³·⁷ = 2.0 × 10⁻⁴ mol dm⁻³。

Linking pH and pOH simplifies calculations for basic solutions. Instead of working through K_w algebraically, one can calculate pOH directly from [OH⁻] and then subtract from 14.00 to find pH. This method is particularly useful in titration curves and buffer problems.

将 pH 与 pOH 关联起来可简化碱性溶液的计算。无需通过 K_w 进行代数运算，便可直接由 [OH⁻] 计算出 pOH，然后用 14.00 相减得出 pH。这种方法在滴定曲线和缓冲问题中特别有用。

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4. The pH Scale Range at 25 °C | 25 °C 时 pH 标度的范围

Although the theoretical pH range is not limited to 0– pH > 7.00. Concentrated strong acids can have a negative pH (e.g. 12 mol dm⁻³ HCl has pH ≈ –1), while concentrated strong alkalis can exceed pH 14.

尽管理论上 pH 范围并不局限于 0–14，但实验室中遇到的大多数水溶液都落在这个区间内。在 25 °C 时，若 pH < 7.00 则为酸性，pH = 7.00 为中性，pH > 7.00 则为碱性。浓强酸的 pH 值可以为负（例如 12 mol dm⁻³ HCl 的 pH 约为 –1），而浓强碱的 pH 可超过 14。

The familiar classification is qualitative: a solution with pH 5 is weakly acidic, while one with pH 12 is strongly basic. Biological systems tend to operate near pH 7.4 (blood), whereas gastric juice is highly acidic at pH 1–2. Recognising the typical pH values of common substances helps students connect abstract numbers to real-world examples.

人们熟悉的分类是定性的：pH 为 5 的溶液是弱酸性，而 pH 为 12 的则是强碱性。生物系统通常在 pH 7.4 左右运行（血液），而胃液则呈强酸性，pH 为 1–2。识别常见物质的典型 pH 值有助于学生将抽象数字与现实例子联系起来。

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5. pH of Strong Acids and Strong Bases | 强酸与强碱的 pH

te solution. For a monoprotic strong acid of concentration c, [H⁺] = c, and therefore pH = – tions often treat the first H⁺ contribution as dominant unless high precision is required.

强酸（如 HCl、H₂SO₄（第一步电离）和 HNO₃）在稀溶液中可视为完全电离。对于浓度为 c 的一元强酸，[H⁺] = c，因此 pH = –log c。例如 0.0100 mol dm⁻³ 的 HCl 溶液 pH = 2.00。对于 H₂SO₄，第二步电离较弱，但除非需要高精度，IB 计算通常将第一步 H⁺ 的贡献视为主要来源。

KOH, dissociate fully to release OH⁻ ions. For a concentration c of NaOH, [OH⁻] = c, pOH = –log c, and pH = 14.00 – pOH. A 0.0050 mol dm⁻³ NaOH solution has pOH = –log(0.0050) = 2.30, giving pH = 11.70.

强碱通常为第 1 族氢氧化物，如 NaOH 或 KOH，它们完全解离释放 OH⁻ 离子。对于浓度为 c 的 NaOH，[OH⁻] = c，pOH = –log c，pH = 14.00 – pOH。0.0050 mol dm⁻³ 的 NaOH 溶液 pOH = –log(0.0050) = 2.30，因此 pH = 11.70。

In both cases the calculation is straightforward and relies only on the stoichiometric concentration of the acid or base. Students should be careful to distinguish between monobasic, dibasic and tribasic acids when determining [H⁺] from the concentration.

在这两种情况下，计算都很简单，仅取决于酸或碱的化学计量浓度。学生在由浓度确定 [H⁺] 时，应注意区分一元、二元和三元酸。

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6. pH of Weak Acids and the Acid Dissociation Constant, K_a | 弱酸的 pH 与酸解离常数 K_a

A weak acid, HA, does not dissociate fully in water, establishing an equilibrium: HA(aq) ⇌ H⁺(aq) + A⁻(aq). The acid dissociation constant is defined as K_a solution of initial concentration c, assuming the dissociation x is small relative to c, an approximation gives: [H⁺] ≈ √K_a × c, and hence pH = –log √K_a × c. This approximation is valid if c / K_a > 100.

弱酸 HA 在水中不完全解离，建立起平衡：HA(aq) ⇌ H⁺(aq) + A⁻(aq)。酸解离常数定义为 K_a = [H⁺][A⁻] / [HA]。对于初始浓度为 c 的纯弱酸溶液，假设解离度 x 远小于 c，可使用近似式：[H⁺] ≈ √K_a × c，由此得到 pH = –log √K_a × c。当 c / K_a > 100 时，该近似有效。

The pK_a value, defined as pK_a = –log K_a, provides a quick measure of acid strength: the smaller the pK_a, the stronger the weak acid. For ethanoic acid, K_a = 1.8 × 10⁻⁵, giving pK_a = 4.74. A 0.10 mol dm⁻³ solution then has [H⁺] ≈ √1.8×10⁻⁵ × 0.10 = 1.34 × 10⁻³ mol dm⁻³, pH ≈ 2.87.

pK_a 值定义为 pK_a = –log K_a，可快速衡量酸的强度：pK_a 越小，弱酸越强。对于乙酸，K_a = 1.8 × 10⁻⁵，即 pK_a = 4.74。0.10 mol dm⁻³ 的溶液 [H⁺] ≈ √1.8×10⁻⁵ × 0.10 = 1.34 × 10⁻³ mol dm⁻³，pH ≈ 2.87。

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7. pH of Weak Bases and K_b | 弱碱的 pH 与 K_b

Weak bases such as NH₃ accept protons from water: NH₃(aq) + H₂O(l) ⇌ NH₄⁺(aq) + OH⁻(aq). The base dissociation constant is K_b = [NH₄⁺][OH⁻] / [NH₃]. For an initial concentration c, if dissociation is small, [OH⁻] ≈ √K_b × c. Then pOH = –log[OH⁻] and pH = 14.00 – pOH. As with weak acids, the approximation holds when c / K_b > 100.

弱碱（如 NH₃）从水中接受质子：NH₃(aq) + H₂O(l) ⇌ NH₄⁺(aq) + OH⁻(aq)。碱解离常数为 K_b = [NH₄⁺][OH⁻] / [NH₃]。对于初始浓度 c，若解离很小，[OH⁻] ≈ √K_b × c。然后 pOH = –log[OH⁻]，pH = 14.00 – pOH。与弱酸类似，当 c / K_b > 100 时该近似成立。

The conjugate relationship means K_a × K_b = K_w for a conjugate acid–base pair. This allows pK_a + pK_b = 14.00 at 25 °C. For ammonia, K_b = 1.8 × 10⁻⁵; thus the conjugate acid NH₄⁺ has K_a = 5.6 × 10⁻¹⁰. IB students are expected to move comfortably between K_a and K_b using the K_w link.

共轭关系意味着对于共轭酸碱对 K_a × K_b =

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