物质与混合物的性质

Intermolecular forces 分子间作用力 (IMFs) are attractions between molecules – much weaker than bonds, but they set melting/boiling points. The main types are listed below; their relative strengths depend on the particles and conditions:

• London dispersion forces 伦敦色散力: present in all molecules; they arise from Coulombic attraction between temporary, fluctuating dipoles, and are stronger for larger, more polarizable electron clouds - often the strongest net force between large molecules.
• Dipole–dipole 偶极-偶极: between polar molecules. Their strength depends on the size of the dipoles and their relative orientation - a $\delta+$ end lining up with a neighbour's $\delta-$ end attracts, so these act in addition to dispersion and make polar molecules stickier than nonpolar ones of similar size.
• Hydrogen bonding 氢键: a strong dipole force when H is bonded to N, O, or F.
• Ion–dipole 离子-偶极: between an ion and a polar molecule (the ion pulls on the oppositely-charged end of the dipole). Their strength depends on ion charge, ion size and the molecular dipole. They help stabilize dissolved ions, although not every ionic solid dissolves readily in water - each $\text{Na}^+$ is surrounded by the $\delta-$ oxygen ends of water molecules.

The whole ladder is understood qualitatively by looking at the sign of the partial charges: a larger or better-aligned partial charge, or a full ionic charge, gives a stronger attraction. Stronger IMFs mean higher boiling points and lower vapor pressure. This is why water ($18\ \text{g/mol}$, hydrogen-bonded) boils at $100\,{}^{\circ}\text{C}$ while methane ($16\ \text{g/mol}$, dispersion only) boils at $-162\,{}^{\circ}\text{C}$.

A solid's properties reflect the particles and forces holding it: ionic, covalent-network (a 3D network like diamond, very hard and high-melting; graphite is a layered exception — high-melting but soft, because its 2D layers slide over one another), metallic, and molecular solids (held by weak IMFs, soft, low-melting). Matching a solid's properties to its structure is a common exam task.

Metallic solids conduct electricity and heat and are malleable 可锻的 and ductile 可延展的, all because their free valence electrons 自由价电子 move easily and let the metal ions slide past one another without breaking the bonding. Solids are also either crystalline 晶体 (particles in a regular, repeating 3-D arrangement) or amorphous 非晶体 (no long-range order, like glass).

The three states differ in how tightly particles are held. Rising temperature raises average kinetic energy; when it overcomes the attractions, the substance melts or boils. Gases are mostly empty space, so they are compressible and fill their container.

An ideal gas obeys

linking pressure, volume, moles, and absolute temperature. Use it to find any one quantity from the others, or (holding some constant) to predict how a gas responds to a change.

Worked example. How many moles of gas fill a $2.0\ \text{L}$ container at $300\ \text{K}$ and $1.5\ \text{atm}$? Using $R=0.0821\ \text{L atm/(mol K)}$,

Always use kelvin for $T$ and match the units of $R$ to your pressure and volume.

Kinetic molecular theory 分子运动论 explains gas behavior: particles are tiny, in constant random motion, with negligible volume and no attractions, and collisions are elastic. Temperature is proportional to average kinetic energy, so at a given temperature lighter molecules move faster (Graham's law of effusion).

Real gases deviate from ideal behavior at high pressure and low temperature, where molecules are close enough that their real volume and their attractions matter. Attractions lower the pressure below ideal; molecular volume raises it.

A solution 溶液 is a homogeneous mixture of a solute 溶质 dissolved in a solvent 溶剂. Concentration is usually molarity 摩尔浓度:

Dilution conserves moles: $M_1V_1=M_2V_2$.

Worked example. What volume of water must you add to $50\ \text{mL}$ of $6.0\ \text{M}$ HCl to make it $2.0\ \text{M}$? The moles of HCl are unchanged, so $M_1V_1=M_2V_2$ gives the final volume $V_2=\dfrac{M_1V_1}{M_2}=\dfrac{6.0\times50}{2.0}=150\ \text{mL}$. You therefore add $150-50=100\ \text{mL}$ of water.

A particulate diagram shows the solute and solvent particles. For an ionic solute, show it fully dissociated into separate ions surrounded by solvent; count particles to reason about concentration and conductivity.

Because a mixture's components keep their properties, physical methods separate them: filtration (by particle size), distillation (by boiling point), and chromatography 色谱法 (by how strongly each component sticks to a stationary phase versus moving with a solvent).

Solubility 溶解度 is how much solute dissolves. "Like dissolves like" is a useful guide: polar solutes often dissolve in polar solvents, and nonpolar solutes in nonpolar solvents. It is not a guarantee, especially for ionic solids. Both interaction energies and entropy affect dissolution.

Spectroscopy 光谱学 studies how matter absorbs or emits light. Different regions of the electromagnetic spectrum probe different changes: microwaves (rotation), infrared (bond vibrations), ultraviolet–visible (electron transitions). The light absorbed reveals structure.

Light is carried by photons 光子, each with energy $E=h\nu=\dfrac{hc}{\lambda}$. Higher frequency (shorter wavelength) means higher energy. A molecule absorbs a photon only when its energy matches an allowed energy gap.

The Beer–Lambert law 比尔-朗伯定律 relates how much light a solution absorbs to its concentration:

where $A$ is absorbance, $\varepsilon$ the molar absorptivity, $b$ the path length, and $c$ the concentration. Since $A$ is proportional to $c$, measuring absorbance is a fast way to find an unknown concentration.

Worked example. A dye has molar absorptivity $\varepsilon=2000\ \text{L/(mol cm)}$; in a $1.0\ \text{cm}$ cell a sample reads absorbance $A=0.40$. Its concentration is $c=\dfrac{A}{\varepsilon b}=\dfrac{0.40}{2000\times1.0}=2.0\times10^{-4}\ \text{M}$. Because $A\propto c$, a solution twice as concentrated would read $A=0.80$ – the basis of a calibration curve.

Common mistakes.

• Using °C in $PV=nRT$. Convert to kelvin first ($T/\text{K}=t/{}^{\circ}\text{C}+273$); at $0\,{}^{\circ}\text{C}$ the Celsius value would give a volume of zero.
• Saying a hydrogen bond is a bond between the H and the O inside one water molecule. That O–H is a covalent bond; the hydrogen bond is the attraction from that H to a lone pair on a neighbouring molecule.
• Saying any molecule containing H can hydrogen-bond. The H must be bonded to N, O or F; the H atoms in $\text{CH}_4$ cannot.
• Assuming dispersion forces are always the weakest. Between large, highly polarizable molecules, dispersion can outweigh the dipole–dipole forces of a smaller polar molecule.
• Using $V_2$ as the volume of water to add in a dilution. $M_1V_1=M_2V_2$ gives the final volume; subtract the starting volume to find the water added.
• Saying real gases deviate most at low pressure and high temperature. Deviations are largest at high pressure and low temperature, where the particles are close and slow enough for their volume and attractions to matter.
• Reading a higher absorbance as a more dilute solution. In $A=\varepsilon bc$, absorbance is proportional to concentration.

• Intermolecular forces (dispersion, dipole–dipole and hydrogen bonding) affect boiling points — they are much weaker than the bonds inside a molecule.
• Boiling breaks the forces between molecules, not the covalent bonds within them.
• Use $PV=nRT$ with temperature in kelvin and $R$ matched to your pressure/volume units.
• For solutions use molarity $M=\text{mol}/\text{L}$; dilution conserves moles, so $M_1V_1=M_2V_2$.
• "Like dissolves like" is a guide; check the particular solute and solvent.