📚 Ideal Gases | 理想气体
An ideal gas is a simplified model that helps chemists predict and explain the behaviour of real gases under many conditions. Although no gas is truly ideal, the concept provides a powerful foundation for understanding pressure, volume, temperature, and the amount of gas. In IB Chemistry S1.5, you will learn to apply the ideal gas equation, convert units accurately, and explore why real gases deviate from ideality.
理想气体是一个简化的模型，帮助化学家预测和解释真实气体在许多条件下的行为。虽然不存在真正理想的气体，但这一概念为理解压强、体积、温度和气体物质的量提供了强有力的基础。在IB化学S1.5中，你将学习运用理想气体状态方程，准确换算单位，并探索真实气体偏离理想状态的原因。
1. What Is an Ideal Gas? | 什么是理想气体？
An ideal gas is a hypothetical gas composed of point-like particles that have no volume themselves and exert no attractive or repulsive forces on each other. Collisions between particles, and between particles and the container walls, are perfectly elastic, meaning kinetic energy is conserved. This model allows the behaviour of a gas to be described by a simple mathematical relationship between pressure, volume, temperature, and amount.
理想气体是一种假想气体，由自身没有体积、彼此之间不存在吸引或排斥力的点状粒子组成。粒子之间以及粒子与容器壁之间的碰撞是完全弹性的，意味着动能守恒。这个模型使得气体的行为可以用压强、体积、温度和物质的量之间的简单数学关系来描述。
Real gases approximate ideal behaviour when their particles are far apart and moving at high speeds – typically at low pressure and high temperature. Under these conditions, the volume of the particles themselves is negligible compared with the total volume of the container, and intermolecular forces are too weak to influence the motion significantly.
当真实气体的粒子相距很远且高速运动时——通常在低压和高温下——会接近理想行为。在这些条件下，粒子自身的体积与容器总体积相比可以忽略，而且分子间力过于微弱，不足以显著影响运动。
2. Kinetic Molecular Theory Assumptions | 气体分子运动论假设
The kinetic molecular theory provides the microscopic foundation for the ideal gas model. The following assumptions are made for an ideal gas:
气体分子运动论为理想气体模型提供了微观基础。对理想气体作出以下假设：
(i) Particle volume is negligible. Gas particles are considered as points that occupy no volume. The total volume of the container is essentially the space available for particle motion.
(i) 粒子体积可忽略。气体粒子被视为不占体积的质点。容器的总体积基本上就是粒子可以运动的空间。
(ii) No intermolecular forces. There are no attractive or repulsive forces between particles, except during collisions. Particles travel in straight lines between collisions.
(ii) 没有分子间力。粒子之间不存在吸引或排斥力，碰撞瞬间除外。粒子在两次碰撞之间沿直线运动。
(iii) Random, constant motion. Gas particles are in perpetual, random motion in all directions. Their kinetic energy depends only on the absolute temperature.
(iii) 无规则持续运动。气体粒子处于永不停息、朝各个方向的无规则运动中。它们的动能仅取决于绝对温度。
(iv) Elastic collisions. All collisions – between particles as well as between particles and the walls – are perfectly elastic. No kinetic energy is lost; it may be transferred between particles, but the total kinetic energy stays constant at constant temperature.
(iv) 弹性碰撞。所有碰撞——粒子之间以及粒子与器壁之间的碰撞——都是完全弹性的。动能没有损失；它可以在粒子之间转移，但在恒温下总动能保持不变。
(v) Average kinetic energy is proportional to Kelvin temperature. The average translational kinetic energy of particles is directly proportional to the absolute temperature: Ek ∝ T. At a given temperature, all ideal gas particles have the same average kinetic energy regardless of their identity.
(v) 平均动能与开氏温度成正比。粒子的平均平动动能与绝对温度成正比：Ek ∝ T。在给定温度下，所有理想气体粒子不论种类如何，具有相同的平均动能。
3. The Ideal Gas Equation and Its Terms | 理想气体状态方程及其术语
The relationship between pressure, volume, amount, and temperature for an ideal gas is summarised in the ideal gas equation:
理想气体的压强、体积、物质的量和温度之间的关系总结于理想气体状态方程：
PV = nRT
Here, P is the pressure of the gas, V is the volume, n is the amount of gas in moles, T is the absolute temperature in kelvin (K), and R is the universal gas constant. The equation shows that, for a fixed amount of gas, the product PV is directly proportional to T.
其中，P 是气体的压强，V 是体积，n 是气体的物质的量（摩尔），T 是绝对温度（开尔文，K），R 是摩尔气体常数。该方程表明，对于固定量的气体，PV 乘积与 T 成正比。
known, for example: n = PV / RT, or T = PV / nR. It combines the empirical gas laws (Boyle's, Charles's, and Avogadro's laws) into a single expression.
理想气体状态方程可以重新排列，以在其他变量已知时求解任一变量，例如：n = PV / RT，或 T = PV / nR。它将经验气体定律（波义耳定律、查理定律和阿伏伽德罗定律）结合到一个表达式中。
4. The Gas Constant R and Unit Conversions | 气体常数R与单位换算
The value of the gas constant R R = 8.31 kPa dm³ mol⁻¹ K⁻¹ when P is in kilopascals (kPa) and V in cubic decimetres (dm³).
气体常数 R 的数值取决于压强和体积所用的单位。在IB计算中，最常用的是 R = 8.31 J mol⁻¹ K⁻¹（压强以帕斯卡 Pa、体积以立方米 m³ 为单位）。这等价于 R = 8.31 kPa dm³ mol⁻¹ K⁻¹（压强以千帕 kPa、体积以立方分米 dm³ 为单位）。
tm mol⁻¹ K⁻¹ when pressure is measured in atmospheres (atm) and volume in litres (L). The table below summarises the most useful forms of R for IB Chemistry:
另一个常用值是 R = 0.08206 L atm mol⁻¹ K⁻¹（压强用大气压 atm，体积用升 L）。下表总结了IB化学中最有用的 R 值形式：
| P unit | V unit | R value |
|---|---|---|
| Pa | m³ | 8.314 J mol⁻¹ K⁻¹ |
| kPa | dm³ | 8.314 kPa dm³ mol⁻¹ K⁻¹ |
| atm | L (dm³) | 0.08206 L atm mol⁻¹ K⁻¹ |
+ 273). Volumes must be expressed in a unit consistent with the R value you select, and pressures must match that unit system.
解题时，必须将温度换算为开尔文，即摄氏度加上 273（K = °C + 273）。体积单位必须与你选择的 R 值一致，压强单位也必须与之匹配。
5. Molar Volume at Standard Temperature and Pressure (STP) | 标准状况下的摩尔体积
One useful application of the ideal gas equation is the calculation of the molar volume – the volume occupied by one mole of an ideal gas at a specified temperature and pressure. Under standard temperature and pressure (STP) defined in the IB syllabus as 273 K and 100 kPa, the molar volume of an ideal gas is:
理想气体状态方程的一个有用的应用是计算摩尔体积——即一摩尔理想气体在指定温度和压强下占据的体积。在IB大纲定义的标准状况（STP）下，即 273 K 和 100 kPa，理想气体的摩尔体积为：
Vm = RT / P = (8.314 × 273) / 100 = 22.7 dm³ mol⁻¹
Some data books still quote the older STP of 273 K and 1 atm (101.3 kPa), which gives a molar volume of 22.4 dm³ mol⁻¹. In IB examinations, use the STP condition given in the question, but remember the current recommended standard is 100 kPa and 22.7 dm³ mol⁻¹.
一些数据手册仍引用旧版STP（273 K，1 atm，即101.3 kPa），得出摩尔体积为 22.4 dm³ mol⁻¹。在IB考试中，请使用题目给出的STP条件，但要记住当前推荐的标准是 100 kPa 和 22.7 dm³ mol⁻¹。
This molar volume relationship is extremely useful for converting between amount of gas and volume in stoichiometry problems at STP.
这一摩尔体积关系在STP下进行物质的量与气体体积之间的化学计量换算时极其有用。
6. Applying the Ideal Gas Equation: Worked Examples | 理想气体方程的应用：计算示例
The ideal gas equation can be used to determine any missing variable when the other three are known. It also links with the mole concept to find the molar mass of a gas.
当其他三个变量已知时，理想气体状态方程可用于求算任一未知变量。它也与摩尔概念相联系，可用来求气体的摩尔质量。
Example 1: Calculate the volume occupied by 0.500 mol of an ideal gas at 295 K and 150 kPa.
示例1：计算 0.500 mol 理想气体在 295 K 和 150 kPa 下占据的体积。
.314 kPa dm³ mol⁻¹ K⁻¹ because P is in kPa, so V = (0.500 × 8.314 × 295) / 150 ≈ 8.17 dm³.
使用 V = nRT / P。因为 P 用 kPa，选择 R = 8.314 kPa dm³ mol⁻¹ K⁻¹，得 V = (0.500 × 8.314 × 295) / 150 ≈ 8.17 dm³。
Example 2: A sample of a volatile liquid with mass 0.352 g is vaporised in a flask. The vapour occupies 127 cm³ at 372 K and 101 kPa. Determine its molar mass.
示例2：质量为 0.352 g 的易挥发液体试样在烧瓶中气化。蒸气在 372 K 和 101 kPa 下占据 127 cm³。求其摩尔质量。
× 372) ≈ 0.00414 mol. Then molar mass M = mass / n = 0.352 g / 0.00414 mol ≈ 85.0 g mol⁻¹.
先换算体积为 dm³：127 cm³ = 0.127 dm³。使用 n = PV / RT = (101 × 0.127) / (8.314 × 372) ≈ 0.00414 mol。然后摩尔质量 M = mass / n = 0.352 g / 0.00414 mol ≈ 85.0 g mol⁻¹。
7. The Combined Gas Law | 组合气体定律
), the ideal gas equation reduces to the combined gas law, which describes the relationship when a sample undergoes changes in pressure, volume, and temperature:
对于固定量的气体（n 不变），理想气体状态方程可简化为组合气体定律，它描述气体样品经历压强、体积和温度变化时的关系：
P₁V₁ / T₁ = P₂V₂ / T₂
dition 1 by the state at condition 2, keeping n and R constant. It is extremely useful when a gas sample moves from one set of conditions to another, for example when a balloon rises and both pressure and temperature change.
该方程直接由 PV = nRT 推导而来，将状态1的表达式除状态2的表达式，保持 n 和 R 不变。当气体样品从一组条件变化到另一组条件时，例如气球上升导致压强和温度同时变化时，该方程非常有用。
pecial cases where one variable is held constant, the combined gas law simplifies to Boyle's law (P₁V₁ = P₂V₂ at constant T and n), Charles' at constant P and n), or the pressure-temperature law (P₁/T₁ = P₂/T₂ at constant V and n).
在其中一个变量保持不变的特殊情况下，组合气体定律可简化为波义耳定律（恒 T、恒 n 时 P₁V₁ = P₂V₂）、查理定律（恒 P、恒 n 时 V₁/T₁ = V₂/T₂）或压强–温度定律（恒 V、恒 n 时 P₁/T₁ = P₂/T₂）。
8. Ideal Gas Mixtures and Partial Pressures | 理想气体混合物与分压
In a mixture of ideal gases that do not react, each gas behaves independently and exerts its own pressure as if it alone occupied the whole container. The total pressure is the sum of the partial pressures of the components. For an ideal gas mixture, the partial pressure of gas A is proportional to its mole fraction:
在互不反应的理想气体混合物中，每种气体独立地起作用，并如同单独占据整个容器一样施加其自身的压强。总压等于各组分分压之和。对于理想气体混合物，气体 A 的分压与其摩尔分数成正比：
P(A) = x(A) × Ptotal
where the mole fraction x(A) = n(A) / ntotal Published by TutorHao | IB Chemistry Revision Series | aleveler.com
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