Standard Methods of Solution Preparation | 溶液配制的标准方法

📚 Standard Methods of Solution Preparation | 溶液配制的标准方法

A standard solution is a solution whose concentration is accurately known. In IGCSE Science, you must be able to prepare standard solutions from a solid solute or by diluting a concentrated stock solution, and you must use the correct apparatus and calculations.

标准溶液是浓度准确已知的溶液。在 IGCSE 科学课程中，你需要掌握用固体溶质配制标准溶液，或通过稀释浓储备液配制标准溶液的方法，并会使用正确的仪器和计算方法。

1. What Is a Solution? | 什么是溶液？

A solution is a homogeneous mixture formed when a solute dissolves in a solvent. The solute is the substance that dissolves, and the solvent is the liquid that does the dissolving. In aqueous solutions, water is the solvent.

溶液是溶质溶解在溶剂中形成的均一混合物。溶质是被溶解的物质，溶剂是进行溶解的液体。在水溶液中，水是溶剂。

In IGCSE practical work, the solute is often a solid such as sodium hydroxide, anhydrous sodium carbonate, or a soluble salt. When the solution has a known concentration, it is called a standard solution.

在 IGCSE 实验中，溶质通常是固体，例如氢氧化钠、无水碳酸钠或可溶性盐。当溶液的浓度已知时，就称为标准溶液。

2. Concentration Units in IGCSE Science | IGCSE 科学中的浓度单位

Concentration tells us how much solute is dissolved in a given volume of solution. The two main units used in Cambridge IGCSE Science are grams per cubic decimetre and moles per cubic decimetre.

浓度表示在一定体积的溶液中含有多少溶质。剑桥 IGCSE 科学中使用的两个主要单位是克每立方分米和摩尔每立方分米。

Unit \| 单位	What it measures \| 表示内容	Typical use \| 典型用途
g/dm³	Mass of solute per cubic decimetre of solution	Solubility, simple salt solutions
mol/dm³	Amount of solute in moles per cubic decimetre	Titration, quantitative reactions

The two units are linked by the molar mass. To convert a concentration in g/dm³ to mol/dm³, divide by the molar mass, Mᵣ: concentration (mol/dm³) = concentration (g/dm³) ÷ Mᵣ.

这两个单位通过摩尔质量联系起来。将 g/dm³ 转换为 mol/dm³ 时，除以摩尔质量 Mᵣ：浓度 (mol/dm³) = 浓度 (g/dm³) ÷ Mᵣ。

3. Apparatus and Reagents for Standard Solutions | 配制标准溶液的仪器与试剂

Accurate preparation of a standard solution requires clean, appropriate apparatus. The key items include a digital balance, a clean beaker, a glass stirring rod, a funnel, a volumetric flask of the exact required volume, a wash bottle with distilled water, and a dropping pipette.

准确配制标准溶液需要干净、合适的仪器。主要仪器包括电子天平、干净的烧杯、玻璃搅拌棒、漏斗、所需准确体积的容量瓶、装有蒸馏水的洗瓶和滴管。

The volumetric flask is the most important piece of apparatus because it is calibrated to contain a precise volume at a specified temperature. Its long narrow neck allows the meniscus to be read accurately against the graduation mark.

容量瓶是最重要的仪器，因为它经过校准，可以在特定温度下容纳精确体积。其细长的瓶颈使弯月面能够对准刻度线准确读数。

Use a volumetric flask, never a beaker or conical flask, for the final exact volume.

最终定容时使用容量瓶，绝不要使用烧杯或锥形瓶。
Use distilled or deionised water to avoid introducing impurities.

使用蒸馏水或去离子水，以避免引入杂质。
Use a dropping pipette to add the final few drops of water near the mark.

接近刻度线时使用滴管逐滴加入最后几滴水。

4. Method A: Preparing a Standard Solution from a Solid Solute | 方法 A：用固体溶质配制标准溶液

This is the standard method used when the solute is a pure solid with a known formula. The goal is to dissolve a known mass and make up the solution to an exact volume in a volumetric flask.

这是溶质为已知化学式的纯固体时使用的标准方法。目标是溶解已知质量，并在容量瓶中定容至准确体积。

Step 1: Calculate the required mass of solute. Weigh it accurately in a weighing boat or on a balance paper. Step 2: Transfer the solid into a clean beaker and dissolve it in a small amount of distilled water, stirring with a glass rod.

步骤一：计算所需溶质质量。用称量舟或称量纸准确称量。步骤二：将固体转移至干净的烧杯中，用少量蒸馏水溶解，并用玻璃棒搅拌。

Step 3: Pour the solution into the volumetric flask through a funnel. Rinse the beaker, stirring rod and funnel with distilled water, and transfer these washings to the flask. This ensures all solute is transferred.

步骤三：将溶液通过漏斗倒入容量瓶中。用蒸馏水冲洗烧杯、搅拌棒和漏斗，并将洗涤液一并转移到容量瓶中。这样可以确保所有溶质都被转移。

Step 4: Add distilled water until the level is just below the graduation mark. Use a dropping pipette to add water drop by drop until the bottom of the meniscus rests exactly on the mark. Step 5: Stopper the flask and invert it several times to mix the solution thoroughly.

步骤四：加入蒸馏水至液面略低于刻度线。用滴管逐滴加水，直到弯月面底部恰好与刻度线齐平。步骤五：盖上瓶塞，将容量瓶倒转数次，使溶液充分混匀。

5. Calculation of Mass of Solute from Concentration | 由浓度计算所需溶质质量

Before preparing a standard solution, you must calculate the mass of solid solute needed. The useful formula is: mass (g) = concentration (mol/dm³) × volume (dm³) × molar mass (g/mol).

配制标准溶液前，必须先计算所需固体溶质的质量。有用的公式为：质量 (g) = 浓度 (mol/dm³) × 体积 (dm³) × 摩尔质量 (g/mol)。

m = c × V × Mᵣ

Worked example: Prepare 250 cm³ of 0.100 mol/dm³ sodium hydroxide solution. Mᵣ(NaOH) = 40 g/mol. Convert 250 cm³ to dm³: 250 ÷ 1000 = 0.250 dm³. Then m = 0.100 × 0.250 × 40 = 1.00 g.

例题：配制 250 cm³ 0.100 mol/dm³ 氢氧化钠溶液。Mᵣ(NaOH) = 40 g/mol。将 250 cm³ 换算为 dm³：250 ÷ 1000 = 0.250 dm³。则 m = 0.100 × 0.250 × 40 = 1.00 g。

If the solute is a hydrated salt such as CuSO₄·5H₂O, include the water of crystallisation in the molar mass. This is a common IGCSE examination point.

如果溶质是水合盐，例如 CuSO₄·5H₂O，计算摩尔质量时必须将结晶水包含在内。这是 IGCSE 考试中常见的考点。

6. Method B: Dilution of a Stock Solution | 方法 B：稀释储备液

A stock solution is a concentrated solution of known concentration. Dilution is used when a less concentrated standard solution is required, such as a dilute acid or alkali for a titration.

储备液是浓度已知的浓溶液。当需要较稀的标准溶液时，例如滴定用的稀酸或稀碱，就采用稀释法。

The dilution equation is based on the fact that the amount of solute in moles does not change when water is added. The commonly used formula is:

稀释公式基于这样一个事实：加水时溶质的物质的量不变。常用的公式为：

c₁V₁ = c₂V₂

where c₁ and V₁ are the concentration and volume of the stock solution, and c₂ and V₂ are the concentration and volume of the diluted solution.

其中 c₁ 和 V₁ 是储备液的浓度和体积，c₂ 和 V₂ 是稀释后溶液的浓度和体积。

Steps: Use a pipette filler and a clean pipette to measure the required volume of stock solution. Transfer it into a clean volumetric flask. Add distilled water until the volume reaches the graduation mark, then stopper and invert several times to mix.

步骤：使用洗耳球和干净的移液管量取所需体积的储备液。将其转移至干净的容量瓶中。加入蒸馏水至刻度线，然后盖上瓶塞并倒转数次混匀。

Worked example: To prepare 100 cm³ of 0.500 mol/dm³ HCl from 2.00 mol/dm³ HCl, V₁ = c₂V₂ ÷ c₁ = (0.500 × 100) ÷ 2.00 = 25.0 cm³. Therefore, pipette 25.0 cm³ of the stock acid into a 100 cm³ volumetric flask and make up to the mark.

例题：用 2.00 mol/dm³ HCl 配制 100 cm³ 0.500 mol/dm³ HCl，V₁ = c₂V₂ ÷ c₁ = (0.500 × 100) ÷ 2.00 = 25.0 cm³。因此，用移液管量取 25.0 cm³ 储备酸至 100 cm³ 容量瓶中，并定容至刻度。

7. Serial Dilution and Its Uses | 连续稀释及其应用

Serial dilution is a stepwise dilution of a substance in solution. Each dilution step uses the same dilution factor, for example a 1:10 dilution repeated several times. The concentration decreases exponentially.

连续稀释是对溶液中的物质进行逐步稀释。每一步使用相同的稀释倍数，例如重复进行 1:10 稀释。浓度呈指数级下降。

This technique is used in biology and chemistry when a very low concentration is needed, such as in measuring bacterial growth, enzyme activity, or calibrating a colorimeter.

当需要极低浓度时，例如在测量细菌生长、酶活性或校准比色计时，会使用该技术。

To prepare a serial dilution, take 1.0 cm³ of the starting solution and add 9.0 cm³ of distilled water to make a 10⁻¹ dilution. Mix well, then take 1.0 cm³ of this new solution and add 9.0 cm³ of water to make a 10⁻² dilution. Repeat as required.

配制连续稀释液时，取 1.0 cm³ 初始溶液，加入 9.0 cm³ 蒸馏水，得到 10⁻¹ 稀释液。充分混匀后，取 1.0 cm³ 该新溶液加入 9.0 cm³ 水，得到 10⁻² 稀释液。根据需要重复操作。

8. Factors Affecting Accuracy of Solution Preparation | 影响溶液配制准确度的因素

To prepare a standard solution accurately, you must control several factors. The most important are reading the meniscus correctly, transferring all solute, using clean apparatus, and using a balance that is properly zeroed.

要准确配制标准溶液，必须控制几个因素。最重要的是正确读取弯月面、转移全部溶质、使用干净的仪器以及使用已正确归零的天平。

Read the bottom of the meniscus at eye level. If the eye is above or below the mark, parallax error will occur and the volume will be incorrect.

读取弯月面底部时视线应与刻度线保持水平。如果眼睛高于或低于刻度线，就会产生视差误差，使体积不准确。

If the solute is not completely transferred from the beaker to the volumetric flask, the solution will be less concentrated than expected. Rinsing with distilled water and adding the washings avoids this transfer error.

如果溶质没有从烧杯完全转移到容量瓶中，溶液的浓度就会低于预期。用蒸馏水冲洗并将洗涤液加入容量瓶可以避免这种转移误差。

Temperature also matters because glassware is calibrated at a fixed temperature, often 20 °C. Very hot or cold solutions can change the volume of the flask slightly.

温度也很重要，因为玻璃仪器通常在固定温度（通常为 20 °C）下校准。过热或过冷的溶液会使容量瓶体积发生微小变化。

9. Safety in Solution Preparation | 溶液配制的安全事项

Solution preparation often involves handling acids, alkalis, toxic salts, or corrosive solids. You must always wear eye protection and, where required, gloves and a laboratory coat.

配制溶液经常涉及酸、碱、有毒盐或腐蚀性固体。必须始终佩戴护目镜，并在必要时戴手套和穿实验服。

When diluting concentrated acids, always add acid to water, never water to acid. Adding water to concentrated acid can cause violent boiling and splashing of corrosive liquid.

稀释浓酸时，一定要将酸加入水中，切勿将水加入酸中。将水加入浓酸会引起剧烈沸腾和腐蚀性液体飞溅。

Work in a well-ventilated area or a fume cupboard when using volatile or toxic substances such as concentrated ammonia or barium chloride. Check hazard symbols and read the safety data sheet before starting.

使用挥发性或有毒物质（如浓氨水或氯化钡）时，应在通风良好的区域或通风橱中操作。开始前应检查危险标志并阅读安全数据表。

Dispose of waste solutions as directed by your teacher. Never pour hazardous chemicals down the sink unless specifically instructed.

按照老师的指示处理废液。除非特别要求，切勿将危险化学品倒入水槽。

10. Common Errors and How to Avoid Them | 常见错误及避免方法

One common error is forgetting to rinse the beaker and funnel after transferring the solution. This leaves solute behind and makes the solution too dilute. Always add the washings to the volumetric flask.

一个常见错误是转移溶液后忘记冲洗烧杯和漏斗。这会使溶质残留，导致溶液浓度偏低。一定要将洗涤液加入容量瓶。

Another error is overfilling the volumetric flask. If the meniscus is above the mark, the solution is too dilute, and it cannot be corrected by removing liquid with a pipette because some solute may be removed. You must discard and start again.

另一个错误是容量瓶定容过量。如果弯月面超过刻度线，溶液浓度会偏低，而且不能用移液管吸出液体来纠正，因为可能同时吸出溶质。必须弃去重配。

Using a measuring cylinder instead of a volumetric flask for the final volume also reduces accuracy. A measuring cylinder has a much larger tolerance than a volumetric flask.

最后定容时使用量筒代替容量瓶也会降低准确度。量筒的允许误差远大于容量瓶。

Reading the meniscus when the flask is not at eye level causes parallax error. Keep the graduation mark at eye level and read the bottom of the meniscus.

读取弯月面时容量瓶未与眼睛保持水平会导致视差误差。应使刻度线与眼睛齐平，并读取弯月面底部。

11. Practice Calculations for IGCSE | IGCSE 典型计算练习

Practice is essential for mastering solution preparation calculations. Here are two typical IGCSE questions.

练习对于掌握溶液配制计算至关重要。以下是两道典型的 IGCSE 题目。

Question 1: Calculate the mass of anhydrous sodium carbonate, Na₂CO₃, needed to prepare 500 cm³ of 0.0500 mol/dm³ solution. Mᵣ(Na₂CO₃) = 106 g/mol.

问题 1：计算配制 500 cm³ 0.0500 mol/dm³ 溶液所需无水碳酸钠 Na₂CO₃ 的质量。Mᵣ(Na₂CO₃) = 106 g/mol。

Answer: V = 500 ÷ 1000 = 0.500 dm³. Mass = 0.0500 × 0.500 × 106 = 2.65 g.

答案：V = 500 ÷ 1000 = 0.500 dm³。质量 = 0.0500 × 0.500 × 106 = 2.65 g。

Question 2: What volume of 3.00 mol/dm³ sulfuric acid is needed to prepare 250 cm³ of 0.120 mol/dm³ H₂SO₄ by dilution?

问题 2：用稀释法配制 250 cm³ 0.120 mol/dm³ H₂SO₄，需要多少体积的 3.00 mol/dm³ 硫酸？

Answer: V₁ = c₂V₂ ÷ c₁ = (0.120 × 250) ÷ 3.00 = 10.0 cm³. Measure 10.0 cm³ of the concentrated acid and make up to 250 cm³ with distilled water.

答案：V₁ = c₂V₂ ÷ c₁ = (0.120 × 250) ÷ 3.00 = 10.0 cm³。量取 10.0 cm³ 浓酸，加蒸馏水定容至 250 cm³。

12. Summary and Exam Tips | 总结与考试提示

Standard solution preparation is a core practical skill in IGCSE Science. Remember the two main methods: dissolving a weighed solid and diluting a stock solution. Both require a volumetric flask for the final exact volume.

标准溶液的配制是 IGCSE 科学中的核心实验技能。记住两种主要方法：溶解称量好的固体和稀释储备液。两种方法都需要容量瓶来进行最终定容。

Always convert cm³ to dm³ by dividing by 1000. Use the formula m = c × V × Mᵣ for solid solutes and c₁V₁ = c₂V₂ for dilutions. Show your working clearly in calculations.

始终将 cm³ 除以 1000 换算为 dm³。固体溶质使用公式 m = c × V × Mᵣ，稀释使用公式 c₁V₁ = c₂V₂。计算时清晰写出步骤。

In exam or practical papers, pay attention to the meniscus, rinsing of apparatus, and safety when using concentrated acids. These are frequent sources of marks.

在考试或实验卷中，注意弯月面读数、仪器的冲洗以及使用浓酸时的安全问题。这些都是常见的得分点。

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Standard Methods of Solution Preparation | 溶液配制的标准方法