📚 SQA Higher Chemistry Formula & Theorem Quick Reference Guide | SQA Higher 化学公式定理速查手册
This guide compiles all the essential formulas, relationships, and key theorems you need for the SQA Higher Chemistry course. Each entry includes the standard notation, a brief explanation, and an example of how the equation is applied in typical exam questions. Use this as your last-minute summary sheet or as a structured checklist while you revise.
本手册汇集了 SQA Higher 化学课程中所有重要的公式、关系式和定理。每个条目都包含标准符号、简要说明以及在典型考题中的应用示例。你可以将其作为考前最后一刻的速查页，或在复习时用作结构化的核对清单。
1. The Mole and Mass Relationship | 物质的量与质量关系
The mole is the central unit in chemistry linking the microscopic world of atoms to the macroscopic world of grams. The fundamental equation n = m / M allows conversion between mass and amount of substance.
物质的量是化学的核心单位，它将微观的原子世界与宏观的质量联系起来。基本公式 n = m / M 可实现质量与物质的量之间的转换。
Here n is the amount in moles (mol), m is the mass in grams (g), and M s of H₂O = (2 × 1.0) + 16.0 = 18.0 g mol⁻¹. If you have 36.0 g of water, then n = 36.0 / 18.0 = 2.00 mol.
其中 n 是物质的量（摩尔，mol），m 是质量（克，g），M 是摩尔质量（每摩尔克数，g mol⁻¹）。M 通过将化学式中所有原子的相对原子质量相加得到。例如，H₂O 的摩尔质量 = (2 × 1.0) + 16.0 = 18.0 g mol⁻¹。若有 36.0 g 水，则 n = 36.0 / 18.0 = 2.00 mol。
n = m / M
Always pay attention to diatomic gases like O₂, N₂, F₂, Cl₂: their M is twice the atomic mass. In a calculation involving gases, linking to the molar volume or ideal gas equation is a common next step.
务必注意双原子气体如 O₂、N₂、F₂、Cl₂：其 M 是原子质量的两倍。在涉及气体的计算中，下一步通常会与摩尔体积或理想气体方程联系。
2. Concentration and Volume of Solutions | 溶液的浓度与体积
Concentration expresses how much solute is dissolved in a given volume of solution. The key relationship is n = c × V, where V is in litres (dm³) and c is in mol dm⁻³ (often written as mol/L or M).
浓度表示在一定体积溶液中溶有多少溶质。关键关系式为 n = c × V，其中 V 以升（dm³）为单位，c 的单位为 mol dm⁻³（常写作 mol/L 或 M）。
.200 × (500/1000) = 0.100 mol. This simple formula underpins titration calculations, where c₁V₁ = c₂V₂ is used for neutralisation reactions when the stoichiometry is 1:1.
若体积以 cm³ 给出，需除以 1000 转换为 dm³。对于 500 cm³、0.200 mol dm⁻³ NaCl 溶液，n = 0.200 × (500/1000) = 0.100 mol。这个简单公式构成了滴定计算的基础，当化学计量比为 1:1 时，可使用 c₁V₁ = c₂V₂ 计算中和反应。
n = cV and c₁V₁ = c₂V₂ (for 1:1 reactions)
In the SQA exam, you may need to find the concentration in g dm⁻³: simply multiply c (mol dm⁻³) by M to get mass concentration, or use mass conc = m / V ctly. Be careful with units: cm³ → dm³ conversion is often a source of avoidable mistakes.
在 SQA 考试中，你可能需要求出以 g dm⁻³ 为单位的浓度：只需将 c (mol dm⁻³) 乘以 M 得到质量浓度，或直接使用 质量浓度 = m / V。注意单位换算：cm³ → dm³ 的转换常是可避免的失分点。
3. Molar Volume of Gases and the Ideal Gas Equation | 气体摩尔体积与理想气体方程
At standard temperature and pressure (STP: 0 °C, 1 atm), one mole of any gas occupies approximately 22.4 dm³. SQA often uses a molar volume of 22.4 dm³ mol⁻¹ for calculations at STP. In some problems, you may need to use the ideal gas equation when conditions differ from STP.
在标准温度和压力下（STP: 0 °C, 1 atm），1 mol 任何气体占据约 22.4 dm³。SQA 在处理 STP 下的计算时通常采用摩尔体积 22.4 dm³ mol⁻¹。当条件偏离 STP 时，你可能需要使用理想气体方程。
The ideal gas law pV = nRT re to pascals (1 atm = 101 325 Pa; SQA sometimes uses 1 atm = 101 kPa or 101.3 kPa), and volume to m³ (1 m³ = 1000 dm³).
理想气体定律 pV = nRT 将压力（Pa）、体积（m³）、物质的量（mol）和温度（K）联系起来。R = 8.31 J K⁻¹ mol⁻¹。务必把温度转换为开尔文（K = °C + 273），压力转换为帕斯卡（1 atm = 101325 Pa；SQA 有时使用 1 atm = 101 kPa 或 101.3 kPa），体积转换为 m³（1 m³ = 1000 dm³）。
pV = nRT
At STP: V = n × 22.4 dm³. For a quick volume calculation under STP, use this direct proportionality. The ideal gas equation appears in Higher when you are required to determine the molar mass of a volatile liquid or to analyse a reaction producing gas under non-standard conditions.
在 STP 下：V = n × 22.4 dm³。对于 STP 下的快速体积计算，可直接使用此比例关系。当需要测定挥发性液体的摩尔质量或分析非标准条件下产生气体的反应时，理想气体方程会在 Higher 考试中出现。
4. Enthalpy Change – Experimental Determination | 焓变 – 实验测定
Enthalpy change (ΔH) is most commonly measured using a simple calorimeter. The heat absorbed or released by the solution is calculated using q = m c ΔT, where m is the mass of the solution (usually water, with density 1 g cm⁻³), c is the specific heat capacity (4.18 J g⁻¹ K⁻¹ for water), and ΔT is the temperature change.
焓变 (ΔH) 通常使用简单量热计测定。溶液吸收或放出的热量用 q = m c ΔT 计算，其中 m 为溶液的质量（通常是水，密度为 1 g cm⁻³），c 为比热容（水的 c = 4.18 J g⁻¹ K⁻¹），ΔT 为温度变化。
Then ΔH is found by dividing the heat change by the number of moles of the limiting reactant: ΔH = –q / n (with a negative sign when the reaction is exothermic, giving a negative ΔH). The minus sign is essential to convert heat released by the reaction (positive q) into a negative enthalpy change. Make sure to convert q from J to kJ if the answer requires kJ mol⁻¹.
然后通过热效应除以限制反应物的物质的量求得 ΔH：ΔH = –q / n（放热反应 q 为正值，加上负号后 ΔH 为负值）。这个负号对于将反应放出的热量（正 q）转化为负的焓变至关重要。如果答案要求以 kJ mol⁻¹ 为单位，请务必将 q 从 J 转换为 kJ。
q = m c ΔT and ΔH = –q / n
SQA Higher expects you to handle calorimetry data, calculate the enthalpy of neutralisation, solution, or combustion, and comment on sources of error such as heat loss to the surroundings. Remember to use the mass of the solution that actually absorbs the heat, not the mass of the solid unless it is the medium.
SQA Higher 要求你处理量热数据，计算中和焓、溶解焓或燃烧焓，并讨论误差来源如向环境散热。记得使用实际吸收热量的溶液质量，而不是固体的质量，除非固体是导热介质。
5. Hess's Law – Indirect Determination of Enthalpy Change | 盖斯定律 – 间接测定焓变
Hess's Law states that the total enthalpy change for a reaction is independent of the route taken. This allows you to calculate an unknown ΔH by combining known enthalpy changes of related reactions using a thermochemical cycle.
盖斯定律指出，一个反应的总焓变与所采取的途径无关。这使得我们可以通过构建热化学循环，结合相关反应的已知焓变来计算未知的 ΔH。
The most common approach uses standard enthalpies of formation: ΔH° = ΣΔHf°(products) – ΣΔHf°(reactants). Alternatively, a cycle can be constructed using enthalpies of combustion. SQA exams often present data in a table and ask you to calculate a target ΔH using the cycle method, carefully noting the direction of arrows and signs.
最常用的方法采用标准生成焓：ΔH° = ΣΔHf°(产物) – ΣΔHf°(反应物)。或者，也可利用燃烧焓构建循环。SQA 试题常以表格呈现数据，要求你通过循环法计算目标 ΔH，需注意箭头的方向和符号。
ΔH° = Σ ΔHf°(products) – Σ ΔHf°(reactants)
When using the cycle, write the target equation at the top and alternative routes below. Remember that going against an arrow reverses the sign of ΔH. Also, be mindful of multiplying ΔH values by stoichiometric coefficients. Practice building cycles for both formation and combustion data.
使用循环时，将目标方程式写在顶部，替代路径写在下方。记住，逆箭头方向会使 ΔH 的符号反转。同时，注意将 ΔH 值乘以化学计量系数。针对生成和燃烧数据多练习构建循环。
6. Rate of Reaction – Calculating Average and Instantaneous Rate | 反应速率 – 计算平均速率与瞬时速率
Reaction rate is defined as the change in concentration of a reactant or product per unit time. The average rate over a time interval Δt is given by rate = –Δ[R]/Δt for a reactant, or +Δ[P]/Δt for a product.
反应速率定义为单位时间内反应物或产物浓度的变化。对于反应物，在时间间隔 Δt 内的平均速率为 rate = –Δ[R]/Δt；对于产物，则为 +Δ[P]/Δt。
To find the rate at a particular instant from a concentration–time graph, draw a tangent to the curve at that time and calculate its gradient. The instantaneous rate is the absolute value of that gradient (for a reactant, drop the negative sign). SQA often provides graphs of volume of gas evolved vs. time, and you calculate the initial rate or rate at a specific time.
要从浓度-时间图求某一时刻的瞬时速率，可在该时刻作曲线的切线并计算其斜率。瞬时速率即为该斜率的绝对值（对于反应物，去掉负号）。SQA 常提供气体产生体积-时间图，要求计算初始速率或特定时间的速率。
Average rate = Δ[product]/Δt or –Δ[reactant]/Δt
The units of rate are typically mol dm⁻³ s⁻¹ (or mol L⁻¹ s⁻¹). If the change is measured in mass or volume, convert to concentration when required, but gradient calculations can sometimes be done directly using the raw data, with appropriate units.
速率的单位通常为 mol dm⁻³ s⁻¹（或 mol L⁻¹ s⁻¹）。如果变化以质量或体积测量，在需要时可转换为浓度，但有时亦可直接利用原始数据进行斜率计算，并附加适当单位。
7. Equilibrium Constant (Kc) | 平衡常数 (Kc)
For a reversible reaction at equilibrium at a given temperature, the equilibrium constant Kc is expressed in terms of concentrations. For the general reaction aA + bB ⇌ cC + dD, Kc = [C]ᵓ[D]ᵈ / [A]ᵃ[B]ᵇ, where square brackets denote concentration in mol dm⁻³ and the powers are the stoichiometric coefficients.
对于在给定温度下达到平衡的可逆反应，平衡常数 Kc 用浓度表示。对于一般反应 aA + bB ⇌ cC + dD，Kc = [C]ᵓ[D]ᵈ / [A]ᵃ[B]ᵇ，方括号表示浓度（mol dm⁻³），指数为化学计量系数。
Kc is temperature-dependent; its value indicates the position of equilibrium. A large Kc means the equilibrium lies to the right (more products). To calculate Kc, you need equilibrium concentrations, which can be found from initial amounts and the stoichiometric change using a RICE (or ICE) table.
Kc 与温度有关；其值指示平衡位置。Kc 值大表明平衡向右（产物更多）。要计算 Kc，需要平衡浓度，可通过初始量和利用 RICE（或 ICE）表从化学计量变化求得。
Kc = [C]ᵓ[D]ᵈ / [A]ᵃ[B]ᵇ
SQA Higher will ask you to write the expression, calculate Kc from given data, or predict the effect of changing conditions. Remember: solids and pure liquids are not included in the expression; only aqueous or gaseous species appear. A catalyst does not affect the value of Kc.
SQA Higher 会要求你写出表达式，根据给定数据计算 Kc，或预测条件变化的影响。记住：固体和纯液体不写入表达式，只有水相或气相物种出现。催化剂不影响 Kc 的值。
8. pH and the Ionic Product of Water | pH 与水的离子积
The pH of an aqueous solution is defined as pH = –log₁₀[H⁺] (or more precisely pH = –log₁₀[H₃O⁺]), where [H⁺] is in mol dm⁻³. Likewise, pOH = –log₁₀[OH⁻], and at 25 °C, pH + pOH = 14 because of the ionic product of water, Kw = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴ mol² dm⁻⁶.
水溶液的 pH 定义为 pH = –log₁₀[H⁺]（更精确地，pH = –log₁₀[H₃O⁺]），其中 [H⁺] 单位为 mol dm⁻³。类似地，pOH = –log₁₀[OH⁻]，在 25 °C 下，由于水的离子积 Kw = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴ mol² dm⁻⁶，因此 pH + pOH = 14。
To find [H⁺] from pH, use [H⁺] = 10⁻pH. For strong monoprotic acids, [H⁺] equals the acid concentration. For strong bases such as NaOH, [OH⁻] equals the base concentration, and you find pOH first, then pH. For weak acids and bases, you would need Ka or Kb, but that is typically Advanced Higher; Higher focuses on strong acids and bases and dilution calculations.
从 pH 求 [H⁺]，使用 [H⁺] = 10⁻pH。对于强一元酸，[H⁺] 等于酸浓度。对于强碱如 NaOH，[OH⁻] 等于碱浓度，先求出 pOH，再求 pH。对于弱酸和弱碱，你需要 Ka 或 Kb，但这通常是 Advanced Higher 的内容；Higher 侧重强酸强碱以及稀释计算。
pH = –log₁₀[H⁺] [H⁺] = 10⁻pH
The pH scale is logarithmic: a change of one pH unit means a tenfold change in [H⁺]. Always give pH values to one or two decimal places as appropriate. SQA expects you to handle dilution problems: if you dilute an acid, [H⁺] decreases, so pH increases; for a base, dilution lowers [OH⁻], pOH increases, and therefore pH decreases.
pH 标度是对数的：改变一个 pH 单位意味着 [H⁺] 变化十倍。pH 值通常保留一位或两位小数。SQA 要求你处理稀释问题：稀释酸，[H⁺] 降低，pH 升高；稀释碱，[OH⁻] 降低，pOH 升高，因此 pH 降低。
9. Standard Electrode Potentials and Cell EMF | 标准电极电势与电池电动势
The electrochemical cell combines two half-cells. The standard electrode potential E° measures the tendency of a species to be reduced. The cell EMF (E°cell) under standard conditions is given by E°cell = E°right – E°left, where the left-hand electrode is the one at which oxidation occurs (anode, electron source) and the right-hand electrode is where reduction occurs (cathode, electron sink).
电化学电池由两个半电池组成。标准电极电势 E° 衡量物质被还原的倾向。标准条件下的电池电动势 (E°cell) 由 E°cell = E°右 – E°左 给出，其中左侧电极发生氧化（阳极，电子源），右侧电极发生还原（阴极，电子接收端）。
SQA data book provides a list of standard reduction potentials. To calculate E°cell, choose two half-equations, decide which is reduction (more positive E°) and which is oxidation (reverse the more negative one). Then apply the formula. The cell EMF must be positive for a spontaneous reaction. A common task is to predict whether a reaction is feasible: a positive E°cell indicates thermodynamic feasibility under standard conditions, although kinetic factors may affect actual occurrence.
SQA 数据手册提供标准还原电势列表。计算 E°cell 时，选择两个半反应，判断哪一个为还原（E° 更正的），哪一个为氧化（将较负者逆转）。然后应用公式。电池电动势必须为正，反应才能自发进行。常见考题是判断反应是否可行：E°cell 为正表明标准条件下热力学可行，尽管动力学因素可能影响实际发生。
E°cell = E°reduction – E°oxidation
Do not multiply the E° values by stoichiometric coefficients. E° is an intensive property. Also, in Higher, standard conditions mean 298 K, 1 mol dm⁻³ ion concentrations, and 101 kPa pressure for gases.
切勿将 E° 值乘以化学计量系数。E° 是强度性质。此外，在 Higher 课程中，标准条件指 298 K、1 mol dm⁻³ 离子浓度、气体压力 101 kPa。
10. Faraday's Laws of Electrolysis | 法拉第电解定律
Electrolysis calculations link the quantity of electricity passed to the amount of substance produced. The quantity of charge Q (in coulombs) is Q = I × t, where I is current in amperes (A) and t is time in seconds (s). One faraday (F) is the charge on one mole of electrons, 96 500 C mol⁻¹.
电解计算将通入的电量与生成的物质的量联系起来。电荷量 Q（单位库仑）的计算公式为 Q = I × t，其中 I 为电流（安培，A），t 为时间（秒，s）。1 法拉第 (F) 是 1 mol 电子的电荷量，为 96 500 C mol⁻¹。
posit 1 mol of Ag(s) from Ag⁺ + e⁻ → Ag, 1 mol of electrons is needed; to form 1 mol of Cu(s) from Cu²⁺ + 2e⁻ → Cu, 2 mol of electrons are needed. The mass produced is then m = n × M.
通过的电子物质的量为 n(e⁻) = Q / F。要求产物的物质的量，需利用半反应中的化学计量比。例如，从 Ag⁺ + e⁻ → Ag 沉积 1 mol Ag(s) 需要 1 mol 电子；而从 Cu²⁺ + 2e⁻ → Cu 生成 1 mol Cu(s) 需要 2 mol 电子。然后生成的质量为 m = n × M。
Q = I t n(e⁻) = Q / 96500 n(product) = n(e⁻) / (e⁻ per ion)
ermine Avogadro’s constant from electrolysis data, assuming you know the charge on one electron (1.60 × 10⁻¹⁹ C).
确保时间以秒为单位；若以分钟给出，需乘以 60。法拉第常数在 SQA 数据手册中给出。Higher 可能要求你根据电解数据确定阿伏伽德罗常数，假设已知一个电子的电荷（1.60 × 10⁻¹⁹ C）。
11. Bond Enthalpy Calculations | 键能计算
Mean bond enthalpies can be used to estimate the enthalpy change of a reaction in the gas phase. The general rule is ΔH ≈ Σ (bond enthalpies of bonds broken) – Σ (bond enthalpies of bonds formed). This is an application of Hess's Law, breaking all reactant bonds (endothermic, positive) and forming all product bonds (exothermic, negative).
平均键能可用于估算气相反应的焓变。一般规则为 ΔH ≈ Σ (断裂键的键能总和) – Σ (形成键的键能总和)。这是盖斯定律的应用，断裂反应物所有化学键（吸热，正值），形成产物所有化学键（放热，负值）。
f bonds. For example, for combustion of methane: CH₄ + 2O₂ → CO₂ + 2H₂O. Bonds broken: 4 C–H and 2 O=O; bonds formed: 2 C=O and 4 O– lt will be an approximation because mean bond enthalpies are averages from many compounds.
画出完整的结构式，计算键的类型和数目。例如，甲烷燃烧：CH₄ + 2O₂ → CO₂ + 2H₂O。断裂键：4 个 C–H 和 2 个 O=O；形成键：2 个 C=O 和 4 个 O–H。使用手册中的数据代入公式。由于平均键能是来自许多化合物的平均值，结果仅为估算值。
ΔH ≈ Σ E(bonds broken) – Σ E(bonds formed)
SQA may ask you to calculate ΔH using bond enthalpies and then compare with a value obtained from standard enthalpies of formation or combustion, discussing why they differ (mean bond enthalpies vs exact specific values). Remember that bond enthalpies are positive energies required to break a bond; forming a bond releases the same amount of energy.
SQA 可能要求你使用键能计算 ΔH，然后与由标准生成焓或燃烧焓得到的值比较，并讨论为何存在差异（平均键能 vs 精确特定值）。记住，键能是断裂一个键所需的正能量；形成键则释放等量能量。
12. Radioactive Decay and Half-Life | 放射性衰变与半衰期
Radioisotopes decay with first-order kinetics. The half-life t½ is constant and independent of the initial amount. The relationship between decay constant λ and half-life is λ = ln 2 / t½, which comes from the exponential decay law N = N₀ e–λt.
放射性同位素以一级动力学衰变。半衰期 t½ 是常数，与初始量无关。衰变常数 λ 与半衰期的关系为 λ = ln 2 / t½，源自指数衰变定律 N = N₀ e–λt。
ds: plotting ln(activity) or ln(counts) against time gives a straight line with gradient = – graph or using the equation. The number of half-lives elapsed can also be calculated from n = total time / t½, and the fraction remaining is (½)ⁿ.
在 Higher 中，你可能使用图解法：将 ln(活度) 或 ln(计数) 对时间作图得到直线，斜率为 –λ。然后可直接从图确定半衰期或使用公式计算。已过去的半衰期数目也可由 n = 总时间 / t½ 计算，剩余分数为 (½)ⁿ。
λ = ln 2 / t½ and Fraction remaining = (½)n
Use the SQA data book for nuclear equations; note that alpha decay reduces mass number by 4 and atomic number by 2, while beta decay increases atomic number by 1 with no change in mass number. Radioisotopes are used in medical imaging, carbon dating, and industrial thickness monitoring – contextual questions often appear.
使用 SQA 数据手册查看核反应方程；注意 α 衰变质量数减少 4、原子序数减少 2，而 β 衰变原子序数增加 1、质量数不变。放射性同位素用于医学成像、碳定年和工业厚度监测——情境题常会出现。
Published by TutorHao | Chemistry Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
或截图后用「扫一扫 → 相册」选择本图