South 고등학교 2학년 Matter and Energy
Chapters: 4
1. Three states of matter
Ideal gas law · Partial pressure and mole fraction · Liquids and intermolecular forces · Crystalline and amorphous solids
- Perfect Gas Equation PV = nRT and Work in Compressing a Gas – A gas is made of countless tiny molecules flying about. Their hits on the walls make pressure. For a low-density gas, three simple laws hold: at fixed temperature, P × V stays constant (Boyle); at fixed pressure, V grows in step with kelvin temperature (Charles); at the same P and T, equal volumes hold equal numbers of molecules (Avogadro). Put together they give the perfect gas equation PV = nRT = N k T. One mole holds Avogadro's number, 6.022 × 10²³, of particles. Pushing a piston in does work on the gas; the work equals the area under the P–V graph, and at fixed temperature W = nRT ln(V₁/V₂).
- Gas Laws: How Pressure, Volume and Temperature Are Linked – Gas pressure comes from particles hitting the walls. For a fixed amount of gas: Boyle's law P₁V₁ = P₂V₂ (constant T); Charles's law V₁/T₁ = V₂/T₂ (constant P); pressure (Gay-Lussac's) law P₁/T₁ = P₂/T₂ (constant V). Temperature must be in kelvin. Combined: P₁V₁/T₁ = P₂V₂/T₂. Dalton's law: in a mixture, total pressure = sum of partial pressures, and each partial pressure = mole fraction × total pressure.
- Intermolecular Forces – Intermolecular forces are weak attractions BETWEEN molecules. From weakest to strongest (for similar-size molecules): London dispersion < dipole–dipole < hydrogen bond. Stronger forces mean higher melting and boiling points, higher viscosity and surface tension, and they decide what dissolves in what.
- The Solid State – In a solid the particles sit close together and only vibrate in place, so a solid keeps its shape. In crystalline solids the particles repeat in a regular pattern; in amorphous solids (like glass) they do not. The smallest repeating box is the unit cell. Simple cubic holds 1 particle, body-centred cubic 2 and face-centred cubic 4. By the bonds holding them, crystals are ionic, covalent network, molecular or metallic.
2. Properties of solutions
Special properties of water · Concentration units · Osmosis and colligative properties
- Water: The Small Molecule That Makes Life Possible – A water molecule (H₂O) is bent and polar: oxygen is slightly negative and the hydrogens slightly positive. Because of this, water molecules stick together with hydrogen bonds. These bonds explain why water dissolves many substances, stores a lot of heat, takes a lot of energy to evaporate, sticks together (cohesion) and to surfaces (adhesion), and why ice floats. Living things also use water as a reactant, for transport and to keep cells firm. Mineral salts dissolved in water supply ions like Na⁺, K⁺, Ca²⁺, Fe²⁺ and phosphate.
- Solutions: Types, Concentration and Henry's Law – A solution is an even mix of two or more substances. The part in bigger amount is the solvent, the smaller part is the solute. We tell 'how strong' a solution is with concentration terms: mass %, volume %, ppm, mole fraction, molarity (per litre of solution) and molality (per kg of solvent). Solids usually dissolve more when hot. Gases dissolve more when their pressure is high (Henry's law, p = KH·x) and less when it is hot.
- Colligative Properties: Counting Particles, Not Their Type – Colligative properties depend only on HOW MANY solute particles are in the solution, not on what they are. There are four: relative lowering of vapour pressure (Δp/p° = x₂), elevation of boiling point (ΔTb = Kb·m), depression of freezing point (ΔTf = Kf·m) and osmotic pressure (π = CRT). We use them to find molar mass. Salts that split into ions (NaCl) or molecules that pair up (acetic acid in benzene) give abnormal molar masses, fixed with the van 't Hoff factor i.
3. Spontaneity of chemical change
Enthalpy · Hess's law · Entropy and Gibbs energy
- Enthalpy, Calorimetry and Hess's Law – Enthalpy H = U + pV. At constant pressure the heat taken in or given out equals ΔH; at constant volume it equals ΔU. We measure ΔU in a sealed bomb calorimeter and ΔH in an open cup calorimeter, using q = C ΔT or q = m c ΔT. For gases, ΔH = ΔU + Δn_g RT. The reaction enthalpy ΔrH is negative for exothermic and positive for endothermic reactions, and ΔrH° = ΣΔfH°(products) − ΣΔfH°(reactants). Hess's law: the total enthalpy change is the same whether a reaction happens in one step or many, so thermochemical equations can be added like algebra.
- Spontaneity, Entropy and Gibbs Energy – A spontaneous process happens by itself, without outside help (it may be fast or slow). ΔH alone cannot predict it: ice melts on its own although it takes in heat. Entropy S measures how spread out energy and matter are; ΔS = q_rev/T. Second law: for any spontaneous change, ΔS_total = ΔS_system + ΔS_surroundings > 0; at equilibrium it is zero. Third law: a perfect crystal at 0 K has zero entropy. Gibbs energy G = H − TS combines both: at constant T and p, ΔG = ΔH − TΔS, and ΔG < 0 means spontaneous, ΔG = 0 means equilibrium. It links to the equilibrium constant by ΔG° = −RT ln K = −2.303 RT log K.
4. Reaction rates
Rate and concentration · First-order half-life · Collision theory and activation energy · Temperature and catalysts
- Rate of a Chemical Reaction – The rate of a reaction tells how fast a reactant is used up or a product is made, per unit time. Rate = −Δ[R]/Δt = +Δ[P]/Δt (unit mol L⁻¹ s⁻¹). The rate law, rate = k[A]^x[B]^y, is found by experiment; x + y is the order. Molecularity is the number of particles that collide in one elementary step.
- Integrated Rate Equations: Zero and First Order – Integrated rate equations link concentration with time. Zero order: [R] = [R]₀ − kt (straight line), t½ = [R]₀/2k. First order: k = (2.303/t) log([R]₀/[R]), ln[R] falls in a straight line with slope −k, and t½ = 0.693/k, which does not depend on the starting amount.
- Temperature, Activation Energy, Catalysts and Collision Theory – Reactant molecules must climb an energy hill, the activation energy Ea, to become products. The Arrhenius equation k = A e^(−Ea/RT) shows that a small rise in temperature lets many more molecules cross, so k rises fast. A catalyst gives a lower hill without changing ΔH. Collision theory: molecules react only when they collide with enough energy and the right orientation.
- Catalysts: Speeding Up Reactions Without Being Used Up – A catalyst is a substance that makes a chemical reaction faster but is not used up; its mass and chemical nature are the same at the end. It works by giving the reaction a different route with a lower activation energy. Manganese dioxide speeds up the breakdown of hydrogen peroxide into water and oxygen. Enzymes are catalysts in living things.