📚 Solubility Curves and Their Applications | 溶解度曲线及其应用
In chemistry, solubility tells us how much of a substance can dissolve in a given amount of solvent at a particular temperature. A solubility curve is a graph that shows how this limit changes as temperature changes. It is one of the most useful tools in both laboratory work and industrial chemistry.
在化学中，溶解度指在特定温度下，一种物质在给定溶剂中最多能溶解的量。溶解度曲线是用图形表示这种“溶解上限”如何随温度变化。它是实验化学与工业化学中最重要的工具之一。
1. What Is Solubility? | 什么是溶解度？
Solubility is defined as the maximum mass of solute that dissolves in 100 g of water to form a saturated solution at a given temperature. The solute may be a solid, liquid or gas, and the solvent is usually water.
溶解度定义为：在给定温度下，当100 g水形成饱和溶液时所溶解的溶质最大质量。溶质可以是固体、液体或气体，溶剂通常是水。
Solubility (g/100 g H₂O) = (mass of solute ÷ mass of water) × 100
This equation is only meaningful when the solution is exactly saturated. If the solution is unsaturated, the value calculated is simply the amount that was dissolved, not the solubility.
这个公式只有在溶液恰好饱和时才有意义。如果溶液未饱和，计算出的数值只是实际溶解量，而不是溶解度。
2. Introducing Solubility Curves | 溶解度曲线介绍
A solubility curve is a plot of solubility (on the y-axis) against temperature (on the x-axis). Each point on the curve represents a saturated solution at that temperature.
溶解度曲线是以温度为横坐标、溶解度为纵坐标作图。曲线上的每个点都代表该温度下的饱和溶液。
For example, the data below show how the solubilities of two common salts change with temperature:
例如，下表显示两种常见盐的溶解度如何随温度变化：
| Temperature (°C) | 0 | 20 | 40 | 60 | 80 | 100 |
|---|---|---|---|---|---|---|
| KNO₃ (g/100 g H₂O) | 13.3 | 31.6 | 63.9 | 110.0 | 169.0 | 246.0 |
| NaCl (g/100 g H₂O) | 35.7 | 36.0 | 36.6 | 37.3 | 38.4 | 39.8 |
Notice that KNO₃ has a steeply rising curve, while NaCl has a very flat curve. The shape of the curve determines how each substance can be separated and purified.
注意 KNO₃ 曲线上升非常明显，而 NaCl 曲线非常平缓。曲线的形状决定了这两种物质如何被分离和提纯。
3. How to Read a Solubility Curve | 如何读溶解度曲线
To find the solubility at a given temperature, draw a vertical line from the temperature on the x-axis up to the curve, then read across to the y-axis.
要查找某温度下的溶解度，可从横坐标上该温度画一条竖线，与曲线相交，再从交点水平对应到纵坐标。
At 40°C, the solubility of KNO₃ is 63.9 g per 100 g of water.
在40°C时，KNO₃的溶解度为每100 g水63.9 g。
At 20°C, the solubility of NaCl is 36.0 g per 100 g of water.
在20°C时，NaCl的溶解度为每100 g水36.0 g。
If you know the solubility and the volume of water, you can calculate the maximum mass of solute that can dissolve. Similarly, if you know the desired mass of solute, you can calculate the minimum mass of water needed to dissolve it completely.
如果已知溶解度和水的质量，就可以计算能溶解的最大溶质质量。同理，如果已知所需溶质质量，也可以计算出完全溶解它所需的最少水量。
4. Saturated, Unsaturated and Supersaturated Solutions | 判断饱和、不饱和与过饱和溶液
The position of a point relative to the solubility curve tells us about the state of a solution.
一个点相对于溶解度曲线的位置，可以告诉我们溶液的状态。
A point below the curve represents an unsaturated solution; more solute could still dissolve.
曲线下方的点代表不饱和溶液；仍可继续溶解更多溶质。
A point exactly on the curve represents a saturated solution.
恰好落在曲线上的点代表饱和溶液。
A point above the curve represents a supersaturated solution, which is unstable. It can be made by cooling a saturated solution very carefully, and any disturbance may cause rapid crystallisation.
曲线上方的点代表过饱和溶液，它不稳定。可通过小心冷却饱和溶液得到，任何扰动都可能引发快速结晶。
For example, at 40°C, 50 g of KNO₃ in 100 g of water is unsaturated because the curve shows a solubility of 63.9 g. But at 0°C, 20 g of KNO₃ in 100 g of water is already supersaturated because the curve shows only 13.3 g can dissolve.
例如，在40°C时，100 g水中溶解50 g KNO₃是不饱和的，因为曲线上显示溶解度为63.9 g。但在0°C时，100 g水中溶解20 g KNO₃已属于过饱和，因为曲线上显示只能溶解13.3 g。
5. Calculating Mass of Solute and Mass of Crystals | 计算溶质质量与晶体质量
Once the solubility is known from the curve, calculations involving different masses of water become straightforward.
一旦从曲线读出了溶解度，涉及不同水量或溶质质量的计算就变得很简单。
mass of solute = (solubility ÷ 100) × mass of water
When a hot saturated solution is cooled, the solubility decreases. Some solute must therefore leave the solution as solid crystals.
当热的饱和溶液被冷却时，溶解度下降，因此部分溶质会以固体晶体形式析出。
mass of crystals formed = mass of solute in hot solution - mass of solute that remains dissolved in the cool solution
Remember to use the same mass of water in both parts of the calculation.
务必在前后两个部分中使用相同的水的质量。
6. Trends Across the Curve | 溶解度随温度的变化趋势
Most solid solutes become more soluble as temperature increases, because the dissolving process is often endothermic. According to Le Chatelier's principle, increasing temperature favours an endothermic change, so more solute dissolves.
大多数固体溶质的溶解度随温度升高而增大，因为溶解过程通常是吸热的。根据勒夏特列原理，升温有利于吸热过程，因此更多溶质会溶解。
Steep curves: KNO₃, NH₄Cl and many nitrate salts dissolve much more easily when heated.
陡峭曲线：KNO₃、NH₄Cl以及许多硝酸盐升温时溶解度显著增大。
Flat curves: NaCl is almost unaffected by temperature, so heating cannot dissolve much more salt.
平缓曲线：NaCl几乎不受温度影响，因此加热不能明显溶解更多食盐。
Negative curves: Ce₂(SO₄)₃ and Li₂CO₃ become less soluble as temperature rises, because their dissolution is exothermic.
反向曲线：Ce₂(SO₄)₃和Li₂CO₃的溶解度随温度升高而下降，因为它们的溶解过程放热。
7. Recrystallisation: Purification by Cooling | 重结晶：冷却提纯
Recrystallisation is a purification technique that uses solubility curves to remove impurities from a solid product.
重结晶是一种利用溶解度曲线从固体产物中除去杂质的提纯技术。
First, dissolve the impure solid in the minimum volume of hot solvent so that it forms a saturated solution. Then filter the hot solution to remove insoluble impurities. Finally, cool the filtrate; as the temperature falls, the solubility drops sharply, and pure crystals begin to form.
首先，用最少量的热溶剂溶解不纯固体，使其形成饱和溶液。然后趁热过滤，除去不溶性杂质。最后冷却滤液；随着温度下降，溶解度急剧降低，纯晶体开始析出。
Because the impurities are present in much smaller quantities, they usually remain below their saturation point and stay dissolved in the mother liquor. The purified crystals can then be collected by filtration and dried.
因为杂质的量很少，通常仍低于其饱和点，所以留在母液中。纯晶体可经过滤收集并干燥。
8. Fractional Crystallisation: Separating Two Solutes | 分步结晶：分离两种溶质
When a mixture contains two soluble solids, a solubility curve can tell us whether they can be separated by fractional crystallisation.
当混合物含有两种可溶性固体时，溶解度曲线可以帮助判断能否用分步结晶法分离。
The method works best when one solute has a steep solubility curve and the other has a flat curve. A hot concentrated solution of the mixture is cooled slowly. The solute with the steep curve reaches saturation first and crystallises out, while the solute with the flat curve remains dissolved.
这种方法最适合一种溶质曲线陡峭、另一种曲线平缓的情况。将混合物的热浓溶液缓慢冷却，曲线陡峭的溶质首先达到饱和并结晶析出，而曲线平缓的溶质仍留在溶液中。
A classic example is separating KNO₃ and NaCl. On cooling, KNO₃ crystals form because its solubility falls from about 169 g at 80°C to about 32 g at 20°C, while NaCl hardly changes. The crystals can be filtered off, and the process may be repeated to increase purity.
经典的例子是分离 KNO₃ 和 NaCl。冷却时，KNO₃ 晶体析出，因为其溶解度从80°C时约169 g降至20°C时约32 g，而 NaCl 几乎不变。滤出晶体后，可重复操作以提高纯度。
9. Everyday and Industrial Applications | 生活与工业应用
Solubility curves are not just an exam topic; they have real industrial uses.
溶解度曲线不只是考试内容，它们在工业中具有实际用途。
Salt production: Seawater is evaporated in shallow ponds so that NaCl crystallises when the water becomes saturated.
食盐生产：海水在浅池中蒸发，当水达到饱和时 NaCl 结晶析出。
Pharmaceutical industry: Drugs are purified by recrystallisation to remove unwanted impurities and control crystal size.
制药工业：药物通过重结晶提纯，以除去杂质并控制晶体大小。
Fertiliser production: Chemicals such as potassium nitrate are recovered from solution by cooling crystallisation.
化肥生产：硝酸钾等化学品通过冷却结晶从溶液中回收。
Sugar refining: Sugar is crystallised from concentrated sugar solutions after careful temperature adjustment.
蔗糖精制：通过精确调节温度，从浓缩糖液中结晶出蔗糖。
10. Solubility of Gases: A Different Curve | 气体溶解度：不同的曲线
Gas solubility behaves differently from most solids. As temperature increases, the solubility of a gas in water decreases.
气体溶解度与大多数固体不同。温度升高时，气体在水中的溶解度下降。
When water is heated, gas molecules gain kinetic energy and escape from the surface more easily. This is why dissolved oxygen in warm water is lower than in cold water, which can affect fish and aquatic life.
水受热时，气体分子获得动能，更容易从表面逸出。这就是为什么温水中的溶解氧比冷水中低，可能影响鱼类和水生生物。
Pressure also matters: the higher the gas pressure above the liquid, the more gas dissolves, according to Henry's law. Carbonated drinks are bottled under high CO₂ pressure and go flat when opened because the pressure drops.
压力也很重要：根据亨利定律，液面上方气体压力越高，溶解的气体越多。碳酸饮料在高压下罐装 CO₂，开瓶后压力降低，因此会跑气变淡。
11. Common Misconceptions and Exam Tips | 常见误区与考试技巧
Many students lose marks because of small but predictable mistakes.
许多学生因为一些小而常见的错误丢分。
"All solids become more soluble when heated" is false. Ce₂(SO₄)₃ and Li₂CO₃ are exceptions.
“所有固体升温时都会更易溶解”是错误的。Ce₂(SO₄)₃ 和 Li₂CO₃ 就是例外。
Solubility is always stated per 100 g of water, not per 100 g of solution. Read the axis label carefully.
溶解度总是以每100 g水计，而不是每100 g溶液。仔细阅读坐标轴标注。
Adding more water does not change the solubility value; it changes how much solute is needed to make the solution saturated.
加入更多水不会改变溶解度数值；只会改变达到饱和所需溶质的质量。
A saturated solution at a high temperature may become unsaturated when cooled if its solubility actually increases with cooling, as happens with Ce₂(SO₄)₃.
高温下的饱和溶液冷却后可能变为不饱和，如果这种溶质的溶解度随温度降低而增大，例如 Ce₂(SO₄)₃。
Always show working and include units. When reading graph values, use a ruler and check whether the required unit is g/100 g of water or another scale.
解题时一定要写出过程并带上单位。读图时使用直尺，并确认题目要求的是每100 g水还是其他单位。
12. Worked Example with Graph | 结合图形的例题
Use the following solubility data for KNO₃ to solve a typical cooling crystallisation problem.
试用以下 KNO₃ 溶解度数据求解一道典型的冷却结晶问题。
At 70°C, solubility = 138 g / 100 g H₂O. At 30°C, solubility = 45 g / 100 g H₂O.
Suppose 100 g of water is used to prepare a saturated solution of KNO₃ at 70°C. What mass of crystals forms when the solution is cooled to 30°C?
假设用100 g水在70°C配制 KNO₃ 饱和溶液。将该溶液冷却到30°C时，会析出多少克晶体？
At 70°C, the mass of KNO₃ that dissolves is 138 g. At 30°C, only 45 g of KNO₃ can remain dissolved in 100 g of water. Therefore:
在70°C时，溶解的 KNO₃ 质量为138 g。在30°C时，100 g水中只能保留45 g KNO₃ 溶解。因此：
mass of crystals = 138 g - 45 g = 93 g
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