IB CCEA Chemistry: Calculation Drill | IB CCEA 化学：计算题专项训练

📚 IB CCEA Chemistry: Calculation Drill | IB CCEA 化学：计算题专项训练

Calculation questions form a significant part of both IB and CCEA Chemistry examinations. Mastering these quantitative skills is essential for achieving top grades. This article provides a structured drill covering the most common calculation topics, with clear steps and key equations to help you build confidence and accuracy.

计算题在 IB 和 CCEA 化学考试中都占有相当大的比重。掌握定量计算技巧是取得高分的关键。本文提供一套结构化的专项训练，涵盖最常见的计算题型，配合清晰的解题步骤和关键公式，帮助同学们提升信心与准确率。

1. Moles and Molar Mass | 物质的量与摩尔质量

The mole is the central unit in chemistry. The number of moles (n) is calculated by dividing the mass (m) by the molar mass (M):

n = m / M

Always ensure that mass is in grams (g) and molar mass is in g mol⁻¹. For elements, molar mass is the relative atomic mass (Ar); for compounds, it is the sum of the Ar values of all atoms in the formula. For water (H₂O), M = 2×1.01 + 16.00 = 18.02 g mol⁻¹. Make sure you can correctly work out the molar mass of any substance before attempting further calculations.

务必确保质量单位为克 (g)，摩尔质量单位为 g mol⁻¹。对于元素，摩尔质量即相对原子质量 (Ar)；对于化合物，则是化学式中所有原子相对原子质量的总和。例如水 (H₂O) 的摩尔质量 M = 2×1.01 + 16.00 = 18.02 g mol⁻¹。在进行后续计算前，确保能正确计算出任何物质的摩尔质量。

Remember to convert all masses to grams, and never use the mass in kilograms when applying this formula unless you adjust the value of M to kg mol⁻¹. In IB and CCEA papers, you will often be given the mass of a sample and asked to find moles, or vice versa.

切记将所有质量转换为克，除非将摩尔质量相应调整为 kg mol⁻¹，否则不要直接使用千克数值代入公式。在 IB 和 CCEA 考试中，经常会给出样品质量要求计算物质的量，或进行反向计算。

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2. Empirical and Molecular Formulae | 经验式与分子式

To determine an empirical formula, convert the percentage composition or mass of each element to moles by dividing by the respective atomic mass. Then divide all mole values by the smallest number of moles to obtain the simplest whole-number ratio. If the ratio is, for example, 1 : 1.5 : 1, multiply all by 2 to get integers.

要确定经验式，将各元素的质量分数或质量除以相应的原子质量，得到物质的量。再将所有摩尔值除以其中最小的摩尔数，得到最简整数比。若得到如 1 : 1.5 : 1 的比例，则全体乘以 2 得到整数比。

The empirical formula mass is calculated from this simplest formula. The molecular formula is found by: n = (molar mass of compound) / (empirical formula mass). Then multiply the subscripts in the empirical formula by this integer n.

经验式质量由该最简式算出。分子式由下式得到：n = (化合物的摩尔质量) / (经验式质量)。再将经验式中的下标乘以该整数 n 即为分子式。

Molecular formula = (Empirical formula)ₙ

A common mistake is to round mole ratios too aggressively. Use sensible rounding (e.g., 2.02 ≈ 2, but 2.5 must be doubled). Always check that your empirical formula mass makes sense before determining the multiplier.

常见错误是过度四舍五入摩尔比。应合理取整（如 2.02 ≈ 2，但 2.5 必须翻倍处理）。在确定倍数前，务必检查经验式质量是否合理。

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3. Stoichiometry and Limiting Reactants | 化学计量学与限量反应物

Using a balanced chemical equation, mole ratios allow us to calculate the amount of reactants consumed and products formed. First, ensure the equation is properly balanced: for every species, the number of atoms matches on both sides. The coefficients give the stoichiometric ratio.

利用配平的化学方程式，通过物质的量之比可以计算反应物消耗量与产物生成量。首先确保方程式已正确配平：每种元素的原子数在两侧相等。系数即为化学计量比。

To identify the limiting reactant, calculate the moles of each reactant available. Divide each by its stoichiometric coefficient; the reactant giving the smaller value is limiting. All product calculations must then be based on this limiting reactant’s moles and the mole ratio from the equation.

要识别限量反应物，先计算每种反应物的可用物质的量。将各物质的量除以其化学计量数，所得值较小的即为限量反应物。所有产物计算必须基于该限量反应物的物质的量以及方程式给出的摩尔比。

Pay attention to units when masses are provided. Convert fully to moles before comparing. In many IB and CCEA questions, you will need to state which reactant is in excess and by how many moles. Always show your logic clearly.

当给出质量时注意单位转换，先全部转换为物质的量再进行比较。IB 和 CCEA 试题中常要求指出哪种反应物过量以及过量的物质的量，务必清晰展示推理过程。

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4. Titration Calculations | 滴定计算

Titration problems often rely on the relationship between the reacting solutions:

c₁V₁ / n₁ = c₂V₂ / n₂

where c is concentration (mol dm⁻³), V is volume, and n is the stoichiometric coefficient from the balanced equation. Volumes must be in consistent units; if using cm³, keep both in cm³, but safer is to convert to dm³ (divide by 1000).

滴定计算常依赖反应溶液间的关系式：c₁V₁ / n₁ = c₂V₂ / n₂，其中 c 为浓度 (mol dm⁻³)，V 为体积，n 为配平方程式中的化学计量数。体积单位需一致；若用 cm³ 则保持两者均为 cm³，但更安全的做法是转换为 dm³ (除以 1000)。

For a typical acid–base titration, work out the moles of the known substance first from its volume and concentration, then use the mole ratio to find the moles of the unknown. Finally divide by the volume of the unknown to get its concentration. Record burette readings to ±0.05 cm³, and select concordant titres (within 0.10 cm³).

典型的酸碱滴定中，先由已知溶液的体积与浓度求出其物质的量，再利用摩尔比求出未知物的物质的量，最后除以未知物的体积得到其浓度。记录滴定管读数精确至 ±0.05 cm³，并选取吻合的滴定值（相差 ≤0.10 cm³）。

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5. Gas Laws and Ideal Gas Equation | 气体定律与理想气体状态方程

The ideal gas equation is used to relate pressure, volume, temperature and moles:

PV = nRT

where P = pressure in pascals (Pa), V = volume in m³, n = moles, R = 8.31 J K⁻¹ mol⁻¹, and T = temperature in kelvin (K). Always convert temperature: T(K) = T(°C) + 273.15. If pressure is given in kPa, multiply by 1000 to get Pa; if volume is in dm³, divide by 1000 to get m³.

理想气体状态方程用于关联压强、体积

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