📚 4 The pH Scale | 4. pH标度
The pH scale is a cornerstone of acid-base chemistry, quantifying the acidity or basicity of an aqueous solution. It is a logarithmic expression of the hydrogen ion concentration, offering a convenient way to compare the corrosive power of battery acid, the neutrality of pure water, and the alkalinity of household cleaners. For IB and Cambridge Chemistry students, mastery of pH is essential for understanding equilibria, titrations, and the behaviour of buffers in biological systems.
pH标度是酸碱化学的基石，用来定量描述水溶液的酸性或碱性。它通过氢离子浓度的对数来简洁地表达从电池酸的强腐蚀性到纯水的中性，再到家用清洁剂的碱性。对于学习IB和剑桥化学课程的学生来说，掌握pH是理解化学平衡、滴定以及生物体系中缓冲行为的关键。
1. What is pH? | 什么是pH?
The pH of a solution is defined as the negative logarithm (base 10) of the hydrogen ion concentration, expressed in mol dm-3. Mathematically, pH = – ithmic scale, each change of one pH unit corresponds to a tenfold change in [H⁺]. The term 'p' comes from the German 'Potenz', meaning power or exponent, and 'H' stands for hydrogen.
溶液的pH定义为氢离子浓度（以mol dm-3为单位）的负对数（以10为底）。数学表达式为pH = –log[H⁺]。由于是对数标度，pH每变化一个单位，[H⁺]就改变十倍。'p'来源于德语'Potenz'，意为幂或指数，'H'代表氢。
In water, a small number of molecules undergo autoprotolysis: 2H₂O ⇌ H₃O⁺ + OH⁻. The hydronium ion H₃O⁺ is often simplified as H⁺. Thus pH is directly linked to the equilibrium constant for water.
水中有少量分子发生自耦电离：2H₂O ⇌ H₃O⁺ + OH⁻。水合氢离子H₃O⁺通常简写为H⁺。因此pH与水的离子积常数直接相关。
2. The pH Scale and Its Range | pH标度及其范围
Under standard conditions (25 ℃ ts pH is less than 7, neutral at pH = 7, and basic (alkaline) if its pH is greater than 7.
在标准条件（25 ℃）下，pH标度通常从0到14，不过极浓的强酸或强碱可以超出这个范围。pH小于7的溶液是酸性的，pH等于7为中性，pH大于7则为碱性。
| Substance | Approximate pH | Nature |
|---|---|---|
| Stomach acid (HCl) | 1.0–2.0 | Strongly acidic |
| Lemon juice | 2.2–2.4 | Acidic |
| Vinegar | 2.5–3.0 | Acidic |
| Black coffee | 5.0 | Weakly acidic |
| Pure water | 7.0 | Neutral |
| Blood | 7.35–7.45 | Weakly basic |
| Baking soda solution | 8.3 | Basic |
| Household ammonia | 11.0–12.0 | Strongly basic |
more acidic than one with pH = 4, and a hundred times more acidic than a pH = 5 solution.
上表展示了常见物质在pH标度上的分布。注意pH = 3的溶液比pH = 4的溶液酸性强十倍，比pH = 5的溶液酸性强一百倍。
3. Calculating pH from Hydrogen Ion Concentration | 由氢离子浓度计算pH
The equation pH = –log[H⁺] allows direct calculation when [H⁺] is known. For pure water at 25 ℃, [H⁺] = 1.0 × 10⁻⁷ mol dm-3, giving pH = –log(1.0 × 10⁻⁷) = 7.00. Similarly, a 0.10 mol dm-3 l solution, being a strong acid, fully dissociates to give [H⁺] = 0.10 = 1.0 × 10⁻¹ mol dm-3, so its pH = 1.00.
公式pH = –log[H⁺]可在已知[H⁺]时直接计算。25 ℃下的纯水，[H⁺] = 1.0 × 10⁻⁷ mol dm-3，因此pH = –log(1.0 × 10⁻⁷) = 7.00。类似地，0.10 mol dm-3的HCl溶液是强酸，完全解离得到[H⁺] = 0.10 = 1.0 × 10⁻¹ mol dm-3，所以其pH = 1.00。
ields a decimal pH. For example, a sample of acid rain might have [H⁺] = 2.5 × 10⁻⁵ mol dm-3. Then pH = –(2.5 × 10⁻⁵) ≈ 4.60. The calculation can be reversed to find [H⁺] from pH using [H⁺] = 10⁻pH.
当氢离子浓度不是10的整数次幂时，可用计算器求得带小数的pH。例如，某酸雨样品[H⁺] = 2.5 × 10⁻⁵ mol dm-3，则pH = –log(2.5 × 10⁻⁵) ≈ 4.60。也可反过来，由pH求[H⁺]：[H⁺] = 10⁻pH。
4. Relationship Between pH and pOH | pH与pOH的关系
Water has an ion product Kw = [H⁺][OH⁻]. At 25 ℃, Kw = 1.0 × 10⁻¹⁴ mol² dm-6. Taking the negative logarithm gives pKw = –log Kw = 14.00. Consequently, pOH is defined as pOH = –log[OH⁻], and the relationship pH + pOH = pKw = 14.00 holds at 25 ℃. This makes it easy to interconvert pH and pOH.
水具有离子积Kw = [H⁺][OH⁻]。25 ℃时，Kw = 1.0 × 10⁻¹⁴ mol² dm-6。取负对数得到pKw = –log Kw = 14.00。由此定义pOH = –log[OH⁻]，且25 ℃时满足pH + pOH = pKw = 14.00。这使得pH与pOH可以方便地相互换算。
For instance, if a sodium hydroxide solution has [OH⁻] = 0.01 mol dm-3, pOH = –log(0.01) = 2.0, hence pH = 14.0 – pendent: at higher temperatures, Kw increases and neutral pH becomes slightly less than 7.
例如，某氢氧化钠溶液的[OH⁻] = 0.01 mol dm-3，pOH = –log(0.01) = 2.0，所以pH = 14.0 – 2.0 = 12.0。这一关系依赖于温度：温度升高时Kw增大，中性pH略低于7。
5. Strong and Weak Acids and Bases | 强酸和弱酸、强碱和弱碱
A strong acid, such as HCl or HNO₃, dissociates completely in water, meaning [H⁺] equals the initial acid concentration. A weak acid, like ethanoic acid CH₃COOH, dissociates only partially: CH₃COOH ⇌ CH₃COO⁻ + H⁺. Therefore, two solutions with the same concentration can have very different pH values.
强酸（如HCl或HNO₃）在水中完全解离，因此[H⁺]等于酸的初始浓度。弱酸（如乙酸CH₃COOH）仅部分解离：CH₃COOH ⇌ CH₃COO⁻ + H⁺。所以，相同浓度的两种溶液pH值可能差异很大。
For a 0.10 mol dm-3 HCl solution, [H⁺] = 0.10 mol dm-3, pH = 1.0. For 0.10 mol dm-3 CH₃COOH, which is about 1.3% dissociated, [H⁺] ≈ 1.3 × 10⁻³ mol dm-3 ≈ 2.9. Weak bases, like ammonia NH₃, behave similarly, setting up an equilibrium NH₃ + H₂O ⇌ r pH (closer to neutral) than an equally concentrated solution of a strong base like NaOH.
0.10 mol dm-3 HCl溶液中，[H⁺] = 0.10 mol dm-3，pH = 1.0。而对0.10 mol dm-3 CH₃COOH，解离度约为1.3%，[H⁺] ≈ 1.3 × 10⁻³ mol dm-3，pH ≈ 2.9。弱碱（如氨NH₃）表现类似，建立平衡NH₃ + H₂O ⇌ NH₄⁺ + OH⁻，其pH比同浓度强碱（如NaOH）低得多，更接近中性。
6. Measuring pH | pH的测量
continuous colour spectrum from pH 0 to 14, allowing a rough estimate to about ±1 pH unit.
测定溶液pH有多种方法。酸碱指示剂（如石蕊、酚酞和甲基橙）会在其特征pH范围内变色。通用指示剂是多种指示剂的混合物，可在pH 0–14范围内呈现连续的颜色谱，能粗略估计pH，误差约±1个单位。
For precise measurements, a pH meter is used. It consists of a glass electrode sensitive to H⁺ ions and a reference electrode. The potential difference between them is proportional to pH. Before use, the meter must be calibrated with buffer solutions of known pH, typically pH 4.00, 7.00, and 10.00.
若要精确测量，则使用pH计。它由一个对H⁺敏感的玻璃电极和一个参比电极构成，两极间的电位差与pH成正比。使用前必须用已知pH的缓冲溶液（通常为pH 4.00、7.00和10.00）对pH计进行校准。
7. Acid-Base Indicators | 酸碱指示剂
Acid-base indicators are themselves weak acids or weak bases, where the undissociated form (HIn) has a different colour from the dissociated form (In⁻). The equilibrium HIn ⇌ H⁺ + In⁻ shifts according to the pH of the solution, causing a colour change over a specific pH interval, typically pKa ± 1.
酸碱指示剂本身也是弱酸或弱碱，其未解离型（HIn）与解离型（In⁻）颜色不同。平衡HIn ⇌ H⁺ + In⁻随溶液pH移动，从而在特定的pH区间（通常是pKa ± 1）内发生颜色变化。
| Indicator | Colour in acid (low pH) | Colour in alkali (high pH) | pH range |
|---|---|---|---|
| Methyl orange | Red | Yellow | 3.1 – 4.4 |
| Bromothymol blue | Yellow | Blue | 6.0 – 7.6 |
| Phenolphthalein | Colourless | Pink | 8.2 – 10.0 |
Selecting the right indicator for a titration depends on the pH change near the equivalence point. For a strong acid–strong base titration, the pH jumps from about 3 to 11, so both methyl orange and phenolphthalein are suitable. However, for a weak acid–strong base titration, the equivalence point is above 7, making phenolphthalein the better choice.
滴定中选择合适的指示剂取决于等当点附近的pH突跃。强酸–强碱滴定时，pH从约3突变至11，因此甲基橙和酚酞都适用。但弱酸–强碱滴定的等当点高于7，宜选用酚酞。
8. pH Titration Curves | pH滴定曲线
on curve. The shape of the curve reveals the nature of the acid and base. In a strong acid– ry sharp vertical rise at the equivalence point (pH = 7), before levelling off at high pH.
连续记录pH随滴定剂加入体积的变化，即得pH滴定曲线。曲线的形状揭示了酸和碱的性质。强酸–强碱滴定的曲线从低pH开始，缓慢上升，随后在等当点（pH = 7）出现一条几乎垂直的突跃，再趋于高pH。
For a weak acid (e.g. CH₃COOH) titrated with a strong base (NaOH), the initial pH is higher, the curve has a buffer region with a gentle slope, and the equivalence point lies above 7 (about pH 8.7) due to the hydrolysis of the acetate ion. A weak base–strong acid curve shows an equivalence point below 7. The faint vertical portion in weak–weak titrations makes indicator detection unreliable; such titrations are rarely performed.
弱酸（如CH₃COOH）用强碱（NaOH）滴定时，起始pH稍高，曲线有一段缓冲区间（斜率平缓），等当点由于乙酸根离子的水解而高于7（约pH 8.7）。弱碱–强酸滴定的等当点则低于7。弱酸–弱碱滴定的垂直突跃极弱，指示剂无法准确判断，因此很少采用。
9. Buffer Solutions | 缓冲溶液
A buffer solution resists changes in pH upon addition of small amounts of acid or base, or upon dilution. It consists of a weak acid and its conjugate base (e.g. CH₃COOH / CH₃COO⁻) or a weak base and its conjugate acid (e.g. NH₃ / NH₄⁺). The equilibrium between the two species consumes added H⁺ or OH⁻, stabilising the pH.
缓冲溶液能在加入少量酸或碱、或者稀释时抵抗pH的变化。它由弱酸与其共轭碱（如CH₃COOH / CH₃COO⁻）或弱碱与其共轭酸（如NH₃ / NH₄⁺）组成。两组分间的平衡会消耗外来H⁺或OH⁻，从而稳定pH。
The Henderson–Hasselbalch equation, pH = pKa + log([A⁻]/[HA]), quantitatively predicts buffer pH. A buffer works best when the desired pH is within 1 unit of the pKa of the weak acid, and when the concentrations of the conjugate pair are similar. Biological systems use buffers extensively: the carbonic acid–hydrogencarbonate system maintains blood pH at about 7.4.
亨德森–哈塞尔巴尔赫方程pH = pKa + log([A⁻]/[HA])可定量预测缓冲液的pH。当所需的pH在弱酸pKa的±1范围内，且共轭对浓度相近时，缓冲能力最强。生物体系广泛运用缓冲系统：碳酸–碳酸氢根体系将血液pH维持在约7.4。
10. Real-world
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