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原子结构与性质

AP 化学 · 第 1 主题

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Atomic Structure and Properties

A chemical equation counts particles. Two of this react with one of that. But atoms are far too small to count, and there is no instrument that will hand you a…

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讲义 词汇表 词汇测验 1
1.1

摩尔与摩尔质量
大纲
Learning ObjectiveEssential Knowledge

1.1.A
Calculate quantities of a substance or its relative number of particles using dimensional analysis and the mole concept.

  • 1.1.A.1 One cannot count particles directly while performing laboratory work. Thus, there must be a connection between the masses of substances reacting and the actual number of particles undergoing chemical changes.
  • 1.1.A.2 Avogadro's number ($N_{\mathrm{A}} = 6.022 \times 10^{23}\ \mathrm{mol}^{-1}$) provides the connection between the number of moles in a pure sample of a substance and the number of constituent particles (or formula units) of that substance.
  • 1.1.A.3 Expressing the mass of an individual atom or molecule in atomic mass units (amu) is useful because the average mass in amu of one particle (atom or molecule) or formula unit of a substance will always be numerically equal to the molar mass of that substance in grams. Thus, there is a quantitative connection between the mass of a substance and the number of particles that the substance contains.
    • Equation: $n = m/M$

来源:美国大学理事会 AP 课程与考试说明

因为原子太小无法计数,化学家以摩尔(moles)计数。一摩尔是阿伏伽德罗常数(Avogadro's number)个粒子,$N_A=6.022\times10^{23}$。摩尔质量(molar mass)(每摩尔的克数,从周期表读出)在质量和摩尔之间转换:

$$n=\frac{m}{M}.$$
摩尔是实验室(你称的克)和方程(反应的粒子)之间的桥梁。

摩尔是枢纽:在质量、粒子、气体体积和浓度之间转换
摩尔是枢纽:在质量、粒子、气体体积和浓度之间转换

Worked example. $36.0\ \text{g}$ 的水($M=18.0\ \text{g/mol}$)里有多少摩尔,以及多少分子?

$$n=\frac{m}{M}=\frac{36.0}{18.0}=2.0\ \text{mol},\qquad N=n\,N_A=2.0\times6.022\times10^{23}=1.2\times10^{24}\ \text{molecules}.$$

探索

Link mass, moles and molar mass

Molar mass $M$ is the bridge between the mass you weigh and the number of moles: $m = M \times n$. Because $M$ is fixed for a substance, mass is proportional to moles — double the moles, double the mass.

词汇表 训练
英文 中文 拼音
moles 摩尔 mó ěr
Avogadro's number 阿伏伽德罗常数 ā fú gā dé luó cháng shù
molar mass 摩尔质量 mó ěr zhì liàng
练习卷
1.2

元素的质谱
大纲
Learning ObjectiveEssential Knowledge

1.2.A
Explain the quantitative relationship between the mass spectrum of an element and the masses of the element's isotopes.

  • 1.2.A.1 The mass spectrum of a sample containing a single element can be used to determine the identity of the isotopes of that element and the relative abundance of each isotope in nature.
  • 1.2.A.2 The average atomic mass of an element can be estimated from the weighted average of the isotopic masses using the mass of each isotope and its relative abundance.
    • Exclusion Statement: Interpreting mass spectra of samples containing multiple elements or peaks arising from species other than singly charged monatomic ions will not be assessed on the AP Exam.

来源:美国大学理事会 AP 课程与考试说明

质谱法

一台质谱仪(mass spectrometer)按质量分开原子,给出一个质谱(mass spectrum):在每个同位素(isotope)(相同元素,不同中子数)处有峰,峰高显示它们的相对丰度(relative abundance)。元素的平均原子质量是它同位素质量的丰度加权平均。

相对原子质量是同位素的丰度加权平均
相对原子质量是同位素的丰度加权平均
氯的质谱:两个丰度不同的同位素
氯的质谱:两个丰度不同的同位素

Worked example. 氯是 $75.8\%$ 氯-35 和 $24.2\%$ 氯-37。它的平均原子质量是

$$A_r=(35)(0.758)+(37)(0.242)=26.5+8.95=35.5.$$
平均值更接近 $35$,因为那个同位素更丰富——这就是为什么周期表值是 $35.5$,不是一个整数。

探索

Explore isotopes — same element, different mass

Keep the protons fixed but change the neutrons to build the two chlorine isotopes ($^{35}$Cl and $^{37}$Cl). Same element, different mass — exactly the peaks a mass spectrum shows.

词汇表 训练
英文 中文 拼音
mass spectrometer 质谱仪 zhì pǔ yí
mass spectrum 质谱 zhì pǔ
isotope 同位素 tóng wèi sù
relative abundance 相对丰度 xiāng duì fēng dù
练习卷
1.3

纯净物的元素组成
大纲
Learning ObjectiveEssential Knowledge

1.3.A
Explain the quantitative relationship between the elemental composition by mass and the empirical formula of a pure substance.

  • 1.3.A.1 Some pure substances are composed of individual molecules, while others consist of atoms or ions held together in fixed proportions as described by a formula unit.
  • 1.3.A.2 According to the law of definite proportions, the ratio of the masses of the constituent elements in any pure sample of that compound is always the same.
  • 1.3.A.3 The chemical formula that lists the lowest whole number ratio of atoms of the elements in a compound is the empirical formula.

来源:美国大学理事会 AP 课程与考试说明

一个化合物的百分组成(percent composition)是每个元素的质量分数。从它你通过把每个元素的质量转换成摩尔并除以最小的来求实验式(empirical formula)(原子的最简整数比)。分子式(molecular formula)是实验式的一个整数倍,从摩尔质量求出。

求实验式:质量到摩尔、除以最小的、读比
求实验式:质量到摩尔、除以最小的、读比

Worked example. 一个化合物按质量是 $40.0\%$ C、$6.7\%$ H 和 $53.3\%$ O。假设 $100\ \text{g}$,把每个质量转换成摩尔并除以最小的:

$$\text{C}:\frac{40.0}{12}=3.33,\quad \text{H}:\frac{6.7}{1}=6.7,\quad \text{O}:\frac{53.3}{16}=3.33 \;\xrightarrow{\div 3.33}\; 1:2:1,$$
所以实验式是 $\text{CH}_2\text{O}$。若摩尔质量是 $180\ \text{g/mol}$($=6\times30$),分子式会是 $\text{C}_6\text{H}_{12}\text{O}_6$ ——葡萄糖。

词汇表 训练
英文 中文 拼音
percent composition 百分组成 bǎi fēn zǔ chéng
empirical formula 实验式 shí yàn shì
molecular formula 分子式 fēn zǐ shì
练习卷
1.4

混合物的组成
大纲
Learning ObjectiveEssential Knowledge

1.4.A
Explain the quantitative relationship between the elemental composition by mass and the composition of substances in a mixture.

  • 1.4.A.1 Pure substances contain atoms, molecules, or formula units of a single type. Mixtures contain atoms, molecules, or formula units of two or more types, whose relative proportions can vary.
  • 1.4.A.2 Elemental analysis can be used to determine the relative numbers of atoms in a substance and to determine its purity.

来源:美国大学理事会 AP 课程与考试说明

与一个纯化合物不同,一个混合物(mixture)有可变的组成——它的各部分保持它们自己的身份。用每个组分的质量或摩尔分数来描述一个混合物;这些不遵循一个固定的公式。光谱学(像 PES 或吸收)能测量每个组分存在多少。

词汇表 训练
英文 中文 拼音
mixture 混合物 hùn hé wù
练习卷
1.5

原子结构与电子排布
大纲
Learning ObjectiveEssential Knowledge

1.5.A
Represent the ground-state electron configuration of an atom of an element or its ions using the Aufbau principle.

  • 1.5.A.1 The atom is composed of negatively charged electrons and a positively charged nucleus that is made of protons and neutrons.
  • 1.5.A.2 Coulomb's law is used to calculate the force between two charged particles.
    • Equation: $F_{coulombic} \propto \dfrac{q_1 q_2}{r^2}$
  • 1.5.A.3 In atoms and ions, the electrons can be thought of as being in "shells (energy levels)" and "subshells (sublevels)," as described by the ground-state electron configuration. Inner electrons are called core electrons, and outer electrons are called valence electrons. The electron configuration is explained by quantum mechanics, as delineated in the Aufbau principle and exemplified in the periodic table of the elements.
    • Exclusion Statement: The assignment of quantum numbers to electrons in subshells of an atom will not be assessed on the AP Exam.
  • 1.5.A.4 The relative energy required to remove an electron from different subshells of an atom or ion or from the same subshell in different atoms or ions (ionization energy) can be estimated through a qualitative application of Coulomb's law. This energy is related to the distance from the nucleus and the effective (shield) charge of the nucleus.

来源:美国大学理事会 AP 课程与考试说明

一个原子是一个微小的原子核(nucleus)(质子和中子),被在壳层(shells)和亚层(subshells)(s、p、d、f)里的电子围绕。电子排布(electron configuration)列出电子如何填充这些,最低能量优先(例如 $1s^2\,2s^2\,2p^6$)。最外层、最高能量的电子——价电子(valence electrons)——控制化学。库仑定律(Coulomb's law)解释它们的能量:更接近原子核、被更少屏蔽的电子被更紧地束缚。

一个原子:一个微小的质子和中子的原子核,电子在壳层里
一个原子:一个微小的质子和中子的原子核,电子在壳层里
一排九个燃烧的皿,每一簇火焰都是不同的鲜艳颜色——深红、橙、黄、绿、蓝、紫
焰色试验:每种金属离子给出自己的颜色,因为热激发它的电子,当电子落回时,它们发出特定波长的光

Worked example. 写硫($Z=16$)的电子排布。按顺序填充亚层直到 $16$ 个电子被放置:$1s^2\,2s^2\,2p^6\,3s^2\,3p^4$。$3s$ 和 $3p$ 电子(总共六个)是价电子,所以硫倾向于获得两个电子来完成它的八隅体。

The periodic table organises elements by atomic structure — electron configuration explains the patterns
The periodic table organises elements by atomic structure — electron configuration explains the patterns
探索

Explore how electrons fill the shells

Change the atomic number $Z$ and watch the electrons fill the shells lowest-energy-first (the Aufbau principle 构造原理). The outermost electrons are the valence electrons that drive bonding.

词汇表 训练
英文 中文 拼音
nucleus 原子核 yuán zǐ hé
electron configuration 电子排布 diàn zi pái bù
valence electrons 价电子 jià diàn zi
练习卷
1.6

光电子能谱
大纲
Learning ObjectiveEssential Knowledge

1.6.A
Explain the relationship between the photoelectron spectrum of an atom or ion and:
i. The ground-state electron configuration of the species.
ii. The interactions between the electrons and the nucleus.

  • 1.6.A.1 The energies of the electrons in a given shell can be measured experimentally with photoelectron spectroscopy (PES). The position of each peak in the PES spectrum is related to the energy required to remove an electron from the corresponding subshell, and the relative height of each peak is (ideally) proportional to the number of electrons in that subshell.

来源:美国大学理事会 AP 课程与考试说明

光电子能谱(photoelectron spectroscopy)(PES)测量从每个亚层移除电子所需的能量。每个峰是一个亚层:它的位置给出结合能(束缚得多紧)而它的高度给出其中电子的数量。PES 数据让你直接读一个元素的电子排布并确认壳层结构。

连续电离能通过大的跳跃揭示壳层结构
连续电离能通过大的跳跃揭示壳层结构
氖的光电子能谱:每个亚层一个峰,高度由电子数设定
氖的光电子能谱:每个亚层一个峰,高度由电子数设定
词汇表 训练
英文 中文 拼音
Photoelectron spectroscopy 光电子能谱 guāng diàn zi néng pǔ
练习卷
1.7

周期性变化趋势
大纲
Learning ObjectiveEssential Knowledge

1.7.A
Explain the relationship between trends in atomic properties of elements and electronic structure and periodicity.

  • 1.7.A.1 The organization of the periodic table is based on patterns of recurring properties of the elements, which are explained by patterns of ground-state electron configurations and the presence of completely or partially filled shells (and subshells) of electrons in atoms.
    • Exclusion Statement: Writing the electron configuration of elements that are exceptions to the aufbau principle will not be assessed on the AP Exam.
  • 1.7.A.2 Trends in atomic properties within the periodic table (periodicity) can be predicted by the position of the element on the periodic table and qualitatively understood using Coulomb's law, the shell model, and the concepts of shielding and effective nuclear charge. These properties include:
    • i. Ionization energy
    • ii. Atomic and ionic radii
    • iii. Electron affinity
    • iv. Electronegativity.
  • 1.7.A.3 The periodicity (in 1.7.A.2) is useful to predict/estimate values of properties in the absence of data.

来源:美国大学理事会 AP 课程与考试说明

周期表上的趋势由核电荷(nuclear charge)和屏蔽(shielding)决定:

电负性在一个周期上升而在一个族下降
电负性在一个周期上升而在一个族下降
  • 原子半径(atomic radius)在一个周期上减小(更强的拉力)而在一个族上增大(更多壳层)。
  • 电离能(ionization energy)(移除一个电子的能量)横向增大、向下减小——与半径相反。
  • 电负性(electronegativity)(对共享电子的拉力)横向和向上增大,朝向氟。
周期趋势:半径、电离能和电负性如何横向和向下变化
周期趋势:半径、电离能和电负性如何横向和向下变化
探索

Explore atomic radius across a period

Step across Period 3 and watch the atomic radius shrink — each added proton raises the effective nuclear charge and pulls the same shell in tighter.

词汇表 训练
英文 中文 拼音
Atomic radius 原子半径 yuán zi bàn jìng
Ionization energy 电离能 diàn lí néng
Electronegativity 电负性 diàn fù xìng
练习卷
1.8

价电子与离子化合物
大纲
Learning ObjectiveEssential Knowledge

1.8.A
Explain the relationship between trends in the reactivity of elements and periodicity.

  • 1.8.A.1 The likelihood that two elements will form a chemical bond is determined by the interactions between the valence electrons and nuclei of elements.
  • 1.8.A.2 Elements in the same column of the periodic table tend to form analogous compounds.
  • 1.8.A.3 Typical charges of atoms in ionic compounds are governed by the number of valence electrons and predicted by their location on the periodic table.

来源:美国大学理事会 AP 课程与考试说明

原子获得、失去或共享价电子以达到稳定的排布。金属(低电离能)失去电子形成阳离子(cations);非金属获得电子形成阴离子(anions)。带相反电荷的离子吸引成一个离子化合物(ionic compound),它的公式平衡电荷使整体呈中性。例如,铝($3+$)和氧化物($2-$)结合成 $\text{Al}_2\text{O}_3$,所以 $+6$ 和 $-6$ 抵消。

探索

Watch an ionic bond form by electron transfer

A metal gives up its valence electron(s) and a non-metal takes them, so both reach a full shell. The atoms become oppositely charged ions that attract — that electrostatic pull is the ionic bond.

词汇表 训练
英文 中文 拼音
cations 阳离子 yáng lí zi
anions 阴离子 yīn lí zi
ionic compound 离子化合物 lí zi huà hé wù
练习卷
1.8

考试技巧
  • 用摩尔作为枢纽:用 $n=m/M$ 转换克↔摩尔,用阿伏伽德罗常数转换摩尔↔粒子。
  • 相对原子质量是同位素的丰度加权平均——它更接近更丰富的那个,不是中间。
  • 对于一个实验式,把每个元素的质量变成摩尔并除以最小的;放大到整数。
  • 从核电荷和屏蔽读周期趋势:原子半径在一个周期上减小、电离能和电负性横向(和向上)增大。
  • 按能量顺序填充电子排布;外层价电子控制化学。

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