📚 IB Chemistry: The pH Scale and Acidity | IB化学：pH标度与酸碱度
The pH scale is one of the most practical tools in chemistry. It allows us to describe the acidity or alkalinity of a solution using a single number, rather than expressing concentrations that may vary over many orders of magnitude. In IB Chemistry, understanding pH is essential for acid-base equilibria, titrations, buffer systems, and many everyday applications.
pH标度是化学中最实用的工具之一。它用单一数值来描述溶液的酸碱性，而不用去处理可相差许多数量级的浓度数值。在IB化学中，理解pH对酸碱平衡、滴定、缓冲体系以及许多日常应用都至关重要。
1. Acid-Base Strength vs. Concentration | 酸碱强度与浓度的区别
Acid strength describes how completely an acid dissociates in water. A strong acid, such as HCl, dissociates almost fully: HCl → H⁺ + Cl⁻. A weak acid, such as ethanoic acid (CH₃COOH), only partially dissociates: CH₃COOH ⇌ CH₃COO⁻ + H⁺. Strength is an intrinsic property of the acid.
酸碱强度描述的是酸在水中解离的完全程度。强酸如HCl几乎完全解离：HCl → H⁺ + Cl⁻。弱酸如乙酸CH₃COOH仅部分解离：CH₃COOH ⇌ CH₃COO⁻ + H⁺。强度是酸本身的内在性质。
Concentration, on the other hand, refers to the amount of acid dissolved in a given volume of solution. A concentrated weak acid can have a lower pH than a dilute strong acid, or vice versa, depending on conditions. IB Chemistry requires you to separate these ideas clearly when predicting pH values.
而浓度是指在一定体积溶液中所溶解酸量的多少。浓的弱酸的pH可能比稀的强酸更低，也可能更高，具体取决于条件。IB化学要求你清晰区分这两个概念，以便正确预测pH值。
2. The Definition of pH | pH的定义
The pH scale was introduced by Sørensen in 1909. It is defined as the negative logarithm to base 10 of the hydrogen ion concentration:
pH标度由Sørensen于1909年提出。其定义为氢离子浓度的负十进制对数：
pH = −log₁₀[H⁺]
Here [H⁺] is measured in mol/dm³. A ten-fold increase in hydrogen ion concentration decreases pH by one unit. For a solution with [H⁺] = 1.0 × 10⁻⁴ mol/dm³, pH = 4.00.
其中[H⁺]的单位是mol/dm³。氢离子浓度每增大10倍，pH就减少1个单位。若[H⁺] = 1.0 × 10⁻⁴ mol/dm³，则pH = 4.00。
Because logarithms compress a wide range, pH allows chemists to compare very dilute hydrogen ion concentrations conveniently. On calculators, the pH is normally rounded to two decimal places.
由于对数将宽范围数值压缩，pH使化学家可以方便地比较极稀的氢离子浓度。计算时pH通常保留两位小数。
3. The pH Scale and Its Range | pH标度及其范围
At 25 °C, pure water has [H⁺] = [OH⁻] = 1.0 × 10⁻⁷ mol/dm³, giving pH = 7.00. Solutions with pH below 7 are acidic; pH above 7 are basic. pH = 7 is neutral at this temperature.
在25 °C时，纯水中[H⁺] = [OH⁻] = 1.0 × 10⁻⁷ mol/dm³，即pH = 7.00。pH低于7的溶液为酸性；pH高于7的溶液为碱性；在此温度下pH = 7为中性。
Although the common scale is 0 to 14, pH values can fall outside this range. A concentrated strong acid can have pH below 0, and a concentrated strong base can have pH above 14. The scale is simply a convention, not a physical limit.
虽然常见pH范围是0到14，但pH值也可能超出此范围。浓强酸的pH可能低于0，浓强碱的pH可能高于14。这个标度只是惯例，并不是物理限制。
Temperature affects pH because the ionisation of water is endothermic. At higher temperatures, Kw increases and the neutral pH becomes lower than 7. IB exam questions usually state 25 °C unless otherwise specified.
温度会影响pH，因为水的电离是吸热过程。温度升高时，Kw增大，中性的pH会低于7。IB考试题目通常会注明25 °C，除非另有说明。
4. Calculating pH, pOH, and Kw | 计算pH、pOH与Kw
Water autoionises according to the equilibrium: H₂O ⇌ H⁺ + OH⁻. The ion product constant is:
水存在自偶电离平衡：H₂O ⇌ H⁺ + OH⁻。其离子积常数为：
Kw = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴ mol² dm⁻⁶ at 25 °C
Taking negative logarithms of both sides gives a useful relation:
对等式两边同时取负对数，可得一个常用关系式：
pOH = −log₁₀[OH⁻] and pH + pOH = 14.00
For a solution with [OH⁻] = 1.0 × 10⁻³ mol/dm³, pOH = 3.00, so pH = 11.00. You can also find [H⁺] by [H⁺] = Kw / [OH⁻], then calculate pH directly.
对于[OH⁻] = 1.0 × 10⁻³ mol/dm³的溶液，pOH = 3.00，因此pH = 11.00。你也可以先用[H⁺] = Kw / [OH⁻]求出[H⁺]，再直接计算pH。
5. Strong vs. Weak Acids and Bases | 强酸弱酸、强碱弱碱
Strong acids and bases dissociate fully in aqueous solution. Common strong acids include HCl, HBr, HI, HNO₃, H₂SO₄ and HClO₄. Common strong bases include NaOH, KOH and Ba(OH)₂. Their equilibrium positions lie far to the right.
强酸和强碱在水中完全解离。常见强酸包括HCl、HBr、HI、HNO₃、H₂SO₄和HClO₄。常见强碱包括NaOH、KOH和Ba(OH)₂。它们的平衡位置远远偏向右边。
Weak acids and bases only partially dissociate. Ethanoic acid, carbonic acid, ammonia and amines fall into this category. Their strength is described by equilibrium constants:
弱酸和弱碱仅部分解离。乙酸、碳酸、氨和胺类都属于此类。它们的强度用平衡常数来描述：
Ka = [H⁺][A⁻] / [HA] and Kb = [BH⁺][OH⁻] / [B]
Larger Ka values mean stronger acids, and larger Kb values mean stronger bases. It is common to use pKa = −log₁₀Ka; a smaller pKa corresponds to a stronger acid.
Ka值越大，酸越强；Kb值越大，碱越强。通常也使用pKa = −log₁₀Ka；pKa越小，酸越强。
6. pH of Strong Acids and Strong Bases | 强酸和强碱的pH
For a strong monoprotic acid that fully dissociates, the hydrogen ion concentration equals the initial acid concentration. Thus pH = −log₁₀[acid]. For example, 0.020 mol/dm³ HCl has [H⁺] = 0.020 mol/dm³, so pH = 1.70.
对于完全解离的强一元酸，氢离子浓度等于初始酸浓度。因此pH = −log₁₀[酸]。例如，0.020 mol/dm³ HCl的[H⁺] = 0.020 mol/dm³，所以pH = 1.70。
Strong bases require an extra step. First find [OH⁻], then pOH, then pH = 14.00 − pOH. For 0.010 mol/dm³ NaOH, [OH⁻] = 0.010 mol/dm³, pOH = 2.00, and pH = 12.00.
强碱则需要多一步：先求[OH⁻]，再求pOH，最后用pH = 14.00 − pOH。对于0.010 mol/dm³ NaOH，[OH⁻] = 0.010 mol/dm³，pOH = 2.00，因此pH = 12.00。
For dibasic bases like Ba(OH)₂, be careful: each mole of Ba(OH)₂ produces two moles of OH⁻. A 0.0050 mol/dm³ Ba(OH)₂ solution has [OH⁻] = 0.010 mol/dm³ and pH = 12.00.
对于Ba(OH)₂这类二元碱要小心：每摩尔Ba(OH)₂产生两摩尔OH⁻。0.0050 mol/dm³ Ba(OH)₂溶液中的[OH⁻] = 0.010 mol/dm³，pH = 12.00。
7. pH of Weak Acids: Using Ka | 弱酸的pH：使用Ka
Weak acids do not dissociate fully, so pH cannot be found directly from concentration. Instead, we use an ICE table and Ka. For a generic weak acid HA:
弱酸不会完全解离，因此不能直接从浓度求pH。我们需要使用ICE表（初始-变化-平衡）和Ka。对一般弱酸HA：
HA ⇌ H⁺ + A⁻, Ka = [H⁺][A⁻] / [HA]
If the initial concentration is c and the extent of dissociation is x, then at equilibrium [H⁺] = x, [A⁻] = x, and [HA] ≈ c. Because x is very small for a weak acid, the approximation Ka ≈ x² / c is often valid.
若初始浓度为c，解离度为x，则平衡时[H⁺] = x，[A⁻] = x，[HA] ≈ c。由于弱酸的x很小，近似式Ka ≈ x² / c通常成立。
Solving for x gives [H⁺] = √(Ka × c). For 0.100 mol/dm³ ethanoic acid with Ka = 1.8 × 10⁻⁵ mol/dm³:
解出x得[H⁺] = √(Ka × c)。对于0.100 mol/dm³乙酸，Ka = 1.8 × 10⁻⁵ mol/dm³：
[H⁺] = √(1.8 × 10⁻⁵ × 0.100) = 1.34 × 10⁻³ mol/dm³, pH = 2.87
Notice this pH is higher than that of a strong acid of the same concentration. The approximation fails when the acid is very dilute or Ka is large; then the quadratic equation must be used.
注意：相同浓度下，这个pH高于强酸的pH。当酸极稀或Ka较大时，该近似不再成立，此时必须使用二次方程精确求解。
8. pH of Salt Solutions: Hydrolysis | 盐溶液的pH：水解
Salts are produced in neutralisation reactions, but their solutions are not always neutral. This is due to hydrolysis: the ions react with water to generate H⁺ or OH⁻.
盐产生于中和反应，但其溶液并不总是中性。这是因为水解：离子与水反应生成H⁺或OH⁻。
A salt from a weak acid and a strong base, such as sodium ethanoate, gives a basic solution. The ethanoate ion hydrolyses:
由弱酸和强碱生成的盐，如乙酸钠，其溶液呈碱性。乙酸根离子发生水解：
CH₃COO⁻ + H₂O ⇌ CH₃COOH + OH⁻
The equilibrium constant for this hydrolysis is Kb = Kw / Ka. Since Ka of ethanoic acid is small, Kb is not negligible, and OH⁻ is produced.
该水解反应的平衡常数Kb = Kw / Ka。由于乙酸的Ka较小，Kb不可忽略，因此会产生OH⁻。
Conversely, a salt from a strong acid and a weak base, such as ammonium chloride, gives an acidic solution. Salts from strong acids and strong bases, such as NaCl, do not hydrolyse and remain neutral at 25 °C.
相反，由强酸和弱碱生成的盐，如氯化铵，其溶液呈酸性。由强酸和强碱生成的盐，如NaCl，不发生水解，在25 °C时保持中性。
9. Buffer Solutions and pH Control | 缓冲溶液与pH控制
A buffer solution resists changes in pH when small amounts of acid or base are added. It contains a weak acid and its conjugate base, or a weak base and its conjugate acid. Blood is a natural buffer system based on H₂CO₃ / HCO₃⁻.
缓冲溶液在加入少量酸或碱时能抵抗pH变化。它含有弱酸及其共轭碱，或弱碱及其共轭酸。血液就是基于H₂CO₃ / HCO₃⁻的天然缓冲体系。
For an acidic buffer made from HA and A⁻, the Henderson-Hasselbalch equation is used:
对于由HA和A⁻组成的酸性缓冲溶液，可使用Henderson-Hasselbalch方程：
pH = pKa + log₁₀([A⁻] / [HA])
When [A⁻] = [HA], pH = pKa. Adding a small amount of H⁺ shifts the equilibrium to convert A⁻ into HA; adding OH⁻ converts HA into A⁻. The ratio [A⁻]/[HA] changes only slightly, so pH remains nearly constant.
当[A⁻] = [HA]时，pH = pKa。加入少量H⁺会使平衡移动，将A⁻转化为HA；加入OH⁻则将HA转化为A⁻。比值[A⁻]/[HA]仅发生微小变化，因此pH几乎不变。
To prepare a buffer with a desired pH, choose a weak acid whose pKa is close to that pH and adjust the ratio of salt to acid. Buffer capacity depends on the total concentration of the acid-conjugate base pair.
要配制特定pH的缓冲溶液，应选择pKa接近所需pH的弱酸，并调节盐与酸的比例。缓冲容量取决于酸-共轭碱对的总浓度。
10. pH Indicators and Titrations | pH指示剂与滴定
Indicators are weak acids whose conjugate base has a different colour. For a typical indicator HIn, the equilibrium is HIn ⇌ H⁺ + In⁻. When pH changes, the ratio of [In⁻]/[HIn] changes, producing a colour change over a narrow pH range.
指示剂是共轭碱具有不同颜色的弱酸。常见指示剂HIn存在平衡：HIn ⇌ H⁺ + In⁻。当pH变化时，[In⁻]/[HIn]的比值会改变，从而在较窄的pH范围内产生颜色变化。
| Indicator | Colour change range | Use in titration |
| Methyl orange | 3.1 – 4.4 | Strong acid into weak base |
| Phenolphthalein | 8.2 – 10.0 | Strong base into weak acid |
In an acid-base titration, pH changes dramatically near the equivalence point. The indicator must change colour within the steep section of the titration curve. Choosing the wrong indicator leads to inaccurate results.
在酸碱滴定中，接近等当点时pH发生急剧变化。指示剂的变色范围必须落在滴定曲线陡峭段内。选择错误的指示剂会导致不准确的结果。
11. Applications and Biological Importance | 应用与生物学意义
The pH scale has practical importance in medicine, agriculture and industry. Enzymes in the human body work best within narrow pH ranges; for example, pepsin in the stomach functions optimally around pH 2, while trypsin in the intestine prefers pH around 8.
pH标度在医学、农业和工业中具有实际意义。人体内的酶只在较窄的pH范围内发挥最佳活性：例如，胃中的胃蛋白酶在pH约为2时活性最高，而肠道中的胰蛋白酶则偏好pH约为8的环境。
Soils with extreme pH are unsuitable for most crops: acidic soils are often treated with limestone (CaCO₃) to raise pH. Aquaculture and fish farming also monitor pH closely because fish are sensitive to even small shifts in water acidity.
pH极端不适的土壤不适合大多数农作物：通常用石灰石CaCO₃处理酸性土壤以提高pH。水产养殖也密切监测pH，因为鱼类对水中酸性的微小变化都非常敏感。
From laboratory calculations to real-world systems, the pH scale connects the microscopic concentration of H⁺ to macroscopic outcomes. Mastering pH, pOH, Kw and Ka gives you the tools to analyse any acid-base equilibrium you meet in IB Chemistry.
从实验室计算到现实系统，pH标度将微观的H⁺浓度与宏观结果联系起来。掌握pH、pOH、Kw和Ka，将使你具备分析IB化学中任何酸碱平衡的能力。
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