LC Physics and Chemistry cheat sheet

Newton's second law: F_net = ma; use component form F_x = ma_x, F_y = ma_y with a chosen positive direction stated explicitly.

Kinematic equations apply only for constant acceleration: v = u + at; s = ut + ½at²; v² = u² + 2as.

Momentum p = mv is conserved in any collision or explosion with no external net force; kinetic energy is conserved only in elastic collisions.

Projectile motion: horizontal velocity constant; vertical acceleration g ≈ 9.8 m/s² downward; time of flight from vertical motion alone.

Circular motion: centripetal acceleration a = v²/r directed toward the centre; centripetal force is the net inward force, not a new force.

Hooke's law F = kx up to the limit of proportionality; elastic potential energy stored = ½kx².

Work done W = Fs cosθ; power P = W/t = Fv; efficiency = useful output energy ÷ total input energy × 100%.

Moments: for equilibrium about a pivot, sum of clockwise moments = sum of anticlockwise moments; sum of forces also zero.

Specific heat capacity: Q = mcΔT; specific latent heat: Q = mL, with no temperature change during a phase change.

Thermal energy flows spontaneously from higher to lower temperature only; temperature is a measure of average kinetic energy of particles.

Pressure law and gas laws: pV = nRT; at constant T, p₁V₁ = p₂V₂; at constant V, p₁/T₁ = p₂/T₂ with T in kelvin.

Absolute zero is 0 K = −273 °C; always convert to kelvin before using gas-law ratios.

Conduction requires a temperature gradient and is fastest in metals (free electrons); convection requires a fluid and gravity-driven density differences; radiation needs no medium.

Internal energy = total kinetic + potential energy of particles; it rises with temperature and during melting/boiling even at constant temperature.

Thermal equilibrium: two bodies in contact reach the same temperature; net heat transfer then becomes zero.

Ideal-gas kinetic theory: pressure arises from particle collisions with walls; average kinetic energy is proportional to absolute temperature.

Wave equation v = fλ; frequency is set by the source and does not change on refraction; speed and wavelength change.

Transverse waves oscillate perpendicular to propagation (light); longitudinal waves oscillate parallel (sound).

Refraction: light bending toward the normal when entering a denser medium (n = c/v, Snell's law n₁sinθ₁ = n₂sinθ₂).

Total internal reflection occurs only when light travels from denser to less dense medium and the angle of incidence exceeds the critical angle: sin C = 1/n.

Sound needs a medium; it travels faster in solids than gases and cannot travel through a vacuum.

Diffraction is greatest when the gap or obstacle is comparable to the wavelength; this is why sound bends around corners but light does not noticeably.

For a converging lens, 1/f = 1/u + 1/v; real images are inverted and can be projected; virtual images are upright.

Superposition: waves meeting in phase reinforce (constructive), in antiphase cancel (destructive); path difference of half a wavelength gives cancellation.

Ohm's law V = IR applies to ohmic conductors at constant temperature; filament lamps are non-ohmic because resistance rises with temperature.

Series: same current, voltages add, R_total = R₁ + R₂. Parallel: same voltage, currents add, 1/R_total = 1/R₁ + 1/R₂.

Electrical power P = VI = I²R = V²/R; energy transferred E = Pt.

Charge Q = It; one coulomb is one ampere-second; conventional current flows from positive to negative terminal.

Magnetic force on a current-carrying wire F = BIL sinθ; on a moving charge F = qvB sinθ; direction by Fleming's left-hand rule.

Electromagnetic induction (Faraday): an emf is induced only when magnetic flux through a circuit changes; Lenz's law gives the direction opposing the change.

Transformers: V_s/V_p = N_s/N_p; ideal transformer has equal input and output power (V_pI_p = V_sI_s).

Electric field between parallel plates is uniform: E = V/d; field lines run from positive to negative plate.

Photoelectric effect: photoelectrons are emitted only if incident photon energy hf exceeds the work function φ; maximum kinetic energy = hf − φ.

Photon energy E = hf = hc/λ; intensity controls the number of photoelectrons, not their maximum kinetic energy.

Line spectra arise from electrons falling between discrete energy levels: photon energy equals the energy-level difference.

Half-life: after n half-lives, remaining fraction = (1/2)ⁿ; activity and count rate decay exponentially.

Nuclear notation: mass number A = protons + neutrons, atomic number Z = protons; isotopes have the same Z but different A.

Alpha decay reduces A by 4 and Z by 2; beta-minus decay keeps A constant and increases Z by 1; gamma emission changes neither.

Mass–energy equivalence E = mc²; mass defect in a nucleus appears as binding energy.

Wave–particle duality: electrons diffract through a crystal lattice, showing wave behaviour; light shows particle behaviour in the photoelectric effect.

Ionic bonding: metal transfers electrons to non-metal; high melting points; conduct only when molten or aqueous because ions must be mobile.

Covalent bonding: shared electron pairs between non-metals; simple molecular substances have weak intermolecular forces and low melting points.

Giant covalent structures (diamond, silicon dioxide) have very high melting points; graphite conducts because of delocalised electrons between layers.

Metallic bonding: positive ions in a sea of delocalised electrons; explains conductivity, malleability and ductility.

Polarity: a bond is polar when electronegativity difference is significant; a molecule is polar only if bond dipoles do not cancel by symmetry.

Intermolecular forces increase in strength: induced dipole < permanent dipole < hydrogen bonding (N–H, O–H, F–H).

Hydrogen bonding explains water's anomalously high boiling point and ice being less dense than liquid water.

Dot-and-cross diagrams must show outer electrons only; total electrons shown equals the sum of the valence electrons.

One mole contains 6.02 × 10²³ particles (Avogadro constant); n = m/M and n = N/N_A.

Molar gas volume at standard conditions is about 22.4 dm³ (r.t.p. often taken as 24 dm³); n = V/22.4 for a gas at STP.

Concentration c = n/V in mol/dm³; moles = concentration × volume in dm³ (divide cm³ by 1000 first).

Limiting reactant: calculate moles of each reactant, divide by stoichiometric coefficients; the smallest quotient is limiting.

Percentage yield = actual yield ÷ theoretical yield × 100%; atom economy = molar mass of desired product ÷ total molar mass of reactants × 100%.

Empirical formula from percentage composition: divide each percentage by atomic mass, then divide by the smallest ratio.

Balanced equations conserve atoms and charge; ionic equations cancel spectator ions.

Molar mass of a gas can be found from density: M = mRT/pV.

pH = −log[H⁺]; [H⁺] = 10^(−pH); strong acids ionise completely, weak acids only partially.

Neutralisation: acid + base → salt + water; acid + carbonate → salt + water + carbon dioxide.

Kw at 25 °C = [H⁺][OH⁻] = 1 × 10⁻¹⁴; pH + pOH = 14 in aqueous solution at 25 °C.

Le Chatelier: raising temperature shifts equilibrium in the endothermic direction; raising pressure shifts toward the side with fewer gas moles.

A catalyst increases the rate of both forward and reverse reactions equally and does not shift equilibrium position.

Equilibrium constant Kc depends only on temperature; a large Kc means products predominate at equilibrium.

Buffer solutions resist pH change; an acidic buffer contains a weak acid with its conjugate base in comparable amounts.

Titration equivalence point: moles of acid and base react in the ratio of their balanced equation, not necessarily 1:1.

Homologous series share a general formula and similar reactions; each member differs by CH₂.

Alkanes undergo substitution with halogens under UV light via free-radical mechanism (initiation, propagation, termination).

Alkenes undergo electrophilic addition; the C=C double bond is attacked by Br₂, HBr or H₂O, and bromine water decolourises.

Markovnikov's rule: in HBr addition, the hydrogen adds to the carbon already carrying more hydrogens.

Alcohols: primary oxidise to aldehydes then carboxylic acids; secondary to ketones; tertiary resist oxidation.

Carboxylic acids plus alcohols form esters (esterification) with a concentrated acid catalyst; esters have characteristic sweet smells.

Nucleophilic substitution of halogenoalkanes: primary favour SN2 (one step), tertiary favour SN1 (carbocation intermediate).

Isomers have the same molecular formula but different structural or spatial arrangements; structural isomers differ in connectivity.

Exothermic reactions release heat (ΔH negative); endothermic absorb heat (ΔH positive).

Bond breaking absorbs energy; bond forming releases energy; ΔH ≈ energy in bonds broken − energy in bonds formed.

Hess's law: the enthalpy change of a reaction is independent of route, so ΔH can be found by summing known steps.

Standard enthalpy of formation is the enthalpy change when one mole of a compound forms from its elements in standard states.

Calorimetry: heat gained by water Q = mcΔT; enthalpy change per mole = Q ÷ moles reacted.

Activation energy is the minimum energy needed for a successful collision; it is lowered by a catalyst.

ΔH of combustion can be calculated from enthalpies of formation: ΔH = ΣΔHf(products) − ΣΔHf(reactants).

Energy-level diagrams show reactants, products and activation energy; the difference between reactant and product levels is ΔH.

Rate increases with concentration, temperature, surface area and catalyst presence; rate = change in amount ÷ time.

Collision theory: reaction requires collisions with energy ≥ activation energy and correct orientation.

Temperature raises rate mainly by increasing the fraction of molecules with energy above activation energy, not just collision frequency.

Oxidation is loss of electrons (increase in oxidation number); reduction is gain of electrons (decrease in oxidation number).

Oxidation numbers: free elements 0; oxygen usually −2; hydrogen +1; sum equals the overall charge of the ion or molecule.

In a redox reaction, the oxidising agent is reduced and the reducing agent is oxidised.

Electrolysis: oxidation at the anode (positive in electrolysis), reduction at the cathode; electrons flow through the external circuit.

Electrochemical cell: oxidation at the anode (negative terminal), reduction at the cathode; the more reactive metal is the negative electrode.

Titration: rinse burette with the solution it will contain, use a white tile, read the bottom of the meniscus at eye level, and take concordant results.

Measuring rates: collect gas in a syringe or over water, or measure mass loss; plot volume or mass against time and take the tangent for initial rate.

Testing for gases: hydrogen pops with a lit splint; oxygen relights a glowing splint; carbon dioxide turns limewater milky; chlorine bleaches damp litmus.

Flame tests: lithium crimson, sodium yellow, potassium lilac, calcium brick-red, copper blue-green.

Precipitation tests: chloride with silver nitrate gives white precipitate; sulfate with barium chloride gives white precipitate (acidify first).

Calorimetry practical: use a polystyrene cup, measure temperature change, and account for heat loss by insulation and a lid.

Uncertainty: percentage error = (uncertainty ÷ measured value) × 100%; use the smallest scale division as the reading uncertainty.

Safety and validity: identify independent, dependent and control variables; repeat readings and calculate a mean to reduce random error.