📚 Acid-Base Indicators and Titration Analysis | 酸碱指示剂与滴定分析
Acid-base titration is one of the most important practical techniques in A-Level chemistry. To obtain reliable results, you must understand how acid-base indicators work and how to choose the correct indicator for a given titration. This article explains the theory underlying indicators, the shapes of titration curves, and the reasoning behind indicator selection.
酸碱滴定是 A-Level 化学中最核心的实验技术之一。要想获得可靠的结果，你必须理解酸碱指示剂的工作原理，并学会为特定滴定选择合适的指示剂。本文讲解指示剂背后的理论、滴定曲线的形状以及指示剂选择的逻辑。
1. What Are Acid-Base Indicators? | 什么是酸碱指示剂？
Acid-base indicators are weak organic acids or weak bases that show different colours in their protonated and deprotonated forms. Because their colour depends on the concentration of hydrogen ions, they can be used to detect the end point of a titration.
酸碱指示剂是弱的有机酸或有机碱，它们在质子化和去质子化形态下呈现不同颜色。由于它们的颜色依赖于氢离子浓度，因此可用于指示滴定的终点。
Litmus is a natural indicator that turns red in acid and blue in alkali.
石蕊是天然指示剂，在酸中变红，在碱中变蓝。
Phenolphthalein is colourless in acid and pink in alkali.
酚酞在酸性溶液中无色，在碱性溶液中呈粉红色。
Methyl orange is red in acid and yellow in alkali.
甲基橙在酸性溶液中呈红色，在碱性溶液中呈黄色。
Not every indicator is suitable for every titration, as we will see when we examine titration curves.
并非任何指示剂都适用于所有滴定，这一点在我们讨论滴定曲线时会更为清楚。
2. How Indicators Work: The Weak Acid Model | 指示剂的工作原理：弱酸模型
For simplicity, we treat a typical indicator as a weak acid with the formula HIn. The acid form has one colour, while the conjugate base In⁻ has a different colour.
为简单起见，我们把典型指示剂看作一种弱酸，分子式写作 HIn。酸式形态呈现一种颜色，共轭碱 In⁻ 呈现另一种颜色。
The weak acid dissociation equilibrium is:
HIn(aq) ⇌ H⁺(aq) + In⁻(aq)
The equilibrium constant for this dissociation is:
KIn = [H⁺][In⁻] / [HIn]
If acid is added to the solution, the concentration of H⁺ increases. According to Le Chatelier's principle, the equilibrium shifts to the left, making the HIn form dominate and giving the colour of the acid form. If alkali is added, OH⁻ removes H⁺ to form water, so the equilibrium shifts to the right and the In⁻ colour predominates.
如果向溶液中加酸，H⁺ 浓度增大。根据勒夏特列原理，平衡向左移动，HIn 占据主导，显示出酸式的颜色。如果加碱，OH⁻ 与 H⁺ 结合成水，平衡向右移动，于是 In⁻ 的颜色占主导。
3. The Henderson-Hasselbalch Equation and pH Range | Henderson-Hasselbalch方程与变色范围
From the expression for KIn, we can rearrange to obtain the Henderson-Hasselbalch equation for the indicator:
pH = pKIn + log([In⁻] / [HIn])
The eye cannot detect a colour change until the ratio [In⁻]/[HIn] changes by about a factor of 10. In other words, the acid colour is clearly seen when [In⁻]/[HIn] is less than about 1:10, and the base colour is clearly seen when this ratio is greater than about 10:1.
人眼只有在 [In⁻]/[HIn] 的比值大约变化十倍时才能察觉到颜色变化。换句话说，当 [In⁻]/[HIn] 小于约 1:10 时，酸式颜色清晰可见；当该比值大于约 10:1 时，碱式颜色清晰可见。
Substituting these limiting ratios into the equation gives the useful rule:
pH range of indicator = pKIn ± 1
Thus an indicator changes colour over a range of about 2 pH units centred on its pKIn value. For example, methyl orange has pKIn close to 3.4, which explains its observed range of about 3.1 to 4.4.
因此，指示剂的变色范围约为以其 pKIn 为中心的两个 pH 单位。例如，甲基橙的 pKIn 接近 3.4，这就解释了它大约为 3.1 到 4.4 的变色范围。
4. Common Indicators and Their Colour Changes | 常见指示剂及其颜色变化
The table below summarises the indicators most commonly used in acid-base titrations at this level.
下表总结了现阶段酸碱滴定中最常用的一些指示剂。
| Indicator | Colour in acid | Colour in alkali | pH range | pKIn (approx.) |
| Methyl orange | Red | Yellow | 3.1 – 4.4 | 3.4 |
| Phenolphthalein | Colourless | Pink | 8.2 – 10.0 | 9.3 |
| Litmus | Red | Blue | 5.0 – 8.0 | 6.5 |
Litmus is rarely used in quantitative titration because its colour change is broad and harder to observe sharply. Phenolphthalein and methyl orange are preferred because their transitions are sharp when used with the correct type of titration.
石蕊很少用于定量滴定，因为它的变色范围宽，且颜色变化较难精确判断。酚酞和甲基橙因在正确的滴定类型中变色敏锐，因此更为常用。
5. Titration Curves: Strong Acid + Strong Base | 滴定曲线：强酸+强碱
A titration curve is a graph of pH against the volume of titrant added. For a strong acid such as HCl titrated with a strong base such as NaOH, the curve has a characteristic shape.
滴定曲线是 pH 对加入滴定剂体积的图。以 HCl 这类强酸滴定 NaOH 这类强碱时，曲线具有明显的特征形状。
Initial pH is low, often about 1 for a 0.100 mol dm⁻³ strong acid.
初始 pH 很低，对于 0.100 mol dm⁻³ 强酸通常约为 1。
As alkali is added, pH rises slowly at first.
加入碱后，pH 起初缓慢上升。
Near the equivalence point, the pH changes very rapidly, from about 3 to about 11 within one or two drops.
接近等当点时，pH 变化非常剧烈，通常一两滴之内便从约 3 升至约 11。
The equivalence point for a strong acid-strong base titration is exactly pH 7.
强酸强碱滴定的等当点恰好是 pH 7。
After the equivalence point, the pH levels off at a high value.
越过等当点后，pH 在高值处趋于平缓。
Because the vertical portion of the curve covers a wide pH range, both methyl orange and phenolphthalein can be used successfully for this titration.
由于曲线垂直段覆盖了很大的 pH 范围，甲基橙和酚酞都可以用于这类滴定。
6. Titration Curves: Weak Acid + Strong Base | 滴定曲线：弱酸+强碱
When a weak acid such as ethanoic acid, CH₃COOH, is titrated with a strong base such as NaOH, the curve differs in two important ways.
当用 NaOH 等强碱滴定乙酸的弱酸时，曲线有两个重要不同之处。
The initial pH is higher than that of a strong acid of the same concentration because the weak acid is only partially dissociated.
初始 pH 高于同浓度强酸，因为弱酸只是部分电离。
There is a buffer region around the half-neutralisation point, where the curve is relatively flat.
在半中和点附近存在缓冲区域，曲线相对平坦。
The equivalence point is above pH 7, typically around pH 8 – 9, because the conjugate base (e.g. CH₃COO⁻) hydrolyses and produces hydroxide ions.
等当点高于 pH 7，通常在 pH 8 – 9 左右，因为共轭碱（如 CH₃COO⁻）会发生水解并产生氢氧根离子。
point exactly, [CH₃COOH] = [CH₃COO⁻], so the Henderson-Hasselbalch equation simplifies to:
pH = pKa
This provides a convenient experimental method for estimating the Ka of a weak acid.
这为实验测定弱酸的 Ka 提供了简便方法。
For this titration, phenolphthalein is suitable because its pH range (8.2 – 10.0) matches the steep part of the curve around the equivalence point. Methyl orange would change colour too early and give a large error.
这种滴定中酚酞适用，因为它的变色范围 (8.2 – 10.0) 与等当点附近的陡峭段吻合。甲基橙则会过早变色，带来较大误差。
7. Titration Curves: Strong Acid + Weak Base | 滴定曲线：强酸+弱碱
When a strong acid such as HCl is titrated with a weak base such as ammonia, NH₃, the equivalence point lies on the acidic side of pH 7.
当用 HCl 等强酸滴定 NH₃ 等弱碱时，等当点位于 pH 7 的酸性一侧。
The conjugate acid NH₄⁺ hydrolyses to produce H⁺ ions:
NH₄⁺(aq) ⇌ NH₃(aq) + H⁺(aq)
The pH at the equivalence point is usually between 5 and 6.
等当点 pH 通常在 5 到 6 之间。
The vertical section is narrower than for a strong acid-strong base titration.
垂直段比强酸强碱滴定更窄。
Methyl orange is a suitable indicator because it changes colour in the pH range 3.1 – 4.4, which lies on the vertical portion of the curve.
甲基橙适用，因为它在 3.1 – 4.4 的 pH 范围内变色，正好位于曲线的垂直段。
Phenolphthalein is not suitable because it changes colour at a pH well above the equivalence point.
酚酞不适用，因为它变色时的 pH 远高于等当点。
This is why students must select the indicator based on the shape of the titration curve, not just on habit.
这就是为什么选择指示剂必须依据滴定曲线的形状，而不是仅凭习惯。
8. Choosing the Correct Indicator | 选择正确的指示剂
The key rule for choosing an indicator is that the pH range of the indicator should overlap the steep, vertical section of the titration curve that contains the equivalence point.
选择指示剂的关键规则是：指示剂的 pH 范围应与滴定曲线中包含等当点的陡峭垂直段重叠。
| Titration type | pH at equivalence point | Suitable indicator(s) |
| Strong acid + strong base | 7 | Methyl orange or phenolphthalein |
| Weak acid + strong base | > 7 | Phenolphthalein |
| Strong acid + weak base | < 7 | Methyl orange |
| Weak acid + weak base | ~ 7 | No sharp end point; use pH meter |
For a weak acid-weak base titration, the pH changes gradually through the equivalence point, so no single indicator gives a sharp colour
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