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Gen Chem Equations
| Question | Answer |
|---|---|
| What is Beer's Law? | A = εℓc A = absorbance ε = molar absorptivity (M⁻¹·cm⁻¹) ℓ = path length (cm) c = concentration of solution (mol/L) |
| Molarity Formula | M = moles of solute / liters of solution (mol/L) |
| Molality Formula | m = moles of solute / kilograms of solvent |
| Dilution Formula | M₁V₁ = M₂V₂ M₁ = molarity of initial solution V₁ = volume of initial solution M₂ = molarity of final solution V₂ = volume of final solution |
| Normality | N = n × M N = normality n = number of mole equivalents (number of H⁺ or OH⁻ ions per molecule) M = molarity |
| Mole Fraction | X_A = moles A / total moles |
| Raoult's Law (Vapor Pressure Depression) | P_A = X_A × P°_A P_A = vapor pressure of the solution after solute is added X_A = mole fraction of the solvent P°_A = pure vapor pressure of the solvent |
| Boiling Point Elevation | ΔT_b = k_b × i × m ΔT_b = change in boiling point temperature (increase) k_b = solvent's boiling point elevation constant i = van't Hoff factor (number of particles solute dissociates into) m = molality |
| Freezing Point Depression | ΔT_f = −k_f × i × m ΔT_f = change in freezing point temperature (decrease) k_f = solvent's freezing point depression constant i = van't Hoff factor m = molality Note: negative sign indicates a decrease in freezing point |
| Osmotic Pressure | Π = iMRT Π = osmotic pressure (atm) i = van't Hoff factor M = molarity (mol/L) R = universal gas constant (0.0821 L·atm·K⁻¹·mol⁻¹) T = temperature (must be in Kelvin) |
| Pressure | P = F/A |
| Boyle's Law | P₁V₁ = P₂V₂ |
| Charles's Law | V₁/T₁ = V₂/T₂ |
| Avogadro's Law | V₁/n₁ = V₂/n₂ |
| Gay-Lussac's Law | P₁/T₁ = P₂/T₂ |
| Combined Gas Law | P₁V₁/n₁T₁ = P₂V₂/n₂T₂ |
| Celsius to Kelvin | K = 273 + °C |
| Ideal Gas Law | PV = nRT |
| Gas constant (atm) | R = 0.0821 L·atm/mol·K |
| Gas constant (kPa) | R = 8.314 L·kPa/mol·K |
| STP molar volume | 1 mol of any gas at STP = 22.4 L |
| Dalton's Law | P_total = P₁ + P₂ + P₃ + … |
| Partial pressure | P₁ = X₁ × P_total |
| Gas density | ρ = m/V = PM/RT |
| Graham's Law of Effusion | r₁/r₂ = √(M₂/M₁) |
| Volume | 1 L = 1,000 mL = 1,000 cm³ |
| formula for standard enthalpy of reaction | ΔH°reaction = Σn·ΔH°f(products) − Σm·ΔH°f(reactants), where n and m are moles. Elements in their standard state have ΔH°f = 0. |
| What is the equation for change in enthalpy? | ΔH = H(products) − H(reactants) |
| What are the two work equations? | ΔE = q + w and w = −PΔV |
| What is the heat formula for a substance not undergoing a phase change? | q = mCΔT |
| What is the heat formula for a substance undergoing a phase change? | q = mΔH(fus/vap) |
| What are the two bomb calorimetry equations? | q(cal) = CΔT and q(rxn) = −q(cal) |
| What is the bond enthalpy equation for ΔH°(rxn)? | ΔH°(rxn) = ΣΔH°(bonds broken) − ΣΔH°(bonds formed) |
| What is the entropy change equation for a reaction? | ΔS(rxn) = Σ(n · S(products)) − Σ(m · S(reactants)) |
| What is the Gibbs Free Energy equation? | ΔG = ΔH − TΔS (T in Kelvin; under standard conditions: ΔG° = ΔH° − TΔS°) |
| What is the system/surroundings heat relationship? | q(system) + q(surroundings) = 0, therefore q(system) = −q(surroundings) |
| Rate Expressions | Rate = Δ[A]/Δt Rate = −Δ[A]/Δt = −Δ[B]/Δt = Δ[C]/Δt Rate = −(1/a)Δ[A]/Δt = −(1/b)Δ[B]/Δt = (1/c)Δ[C]/Δt = (1/d)Δ[D]/Δt |
| Rate Law | Rate = k[A]ᵐ[B]ⁿ Units of k: M¹⁻ⁿ·s⁻¹ (where n = overall reaction order) |
| Integrated Rate Laws | Zero-order: [A]t = −kt + [A]₀ First-order: ln[A]t = −kt + ln[A]₀ Second-order: 1/[A]t = kt + 1/[A]₀ |
| Integrated Rate Law Graphs & Slopes | Zero-order: [A] vs. t — slope = −k First-order: ln[A] vs. t — slope = −k Second-order: 1/[A] vs. t — slope = +k |
| Rate Constant (k) Units by Order | Zero-order: M·s⁻¹ First-order: s⁻¹ Second-order: M⁻¹·s⁻¹ |
| Half-Life Equations | Zero-order: t½ = [A]₀ / 2k First-order: t½ = 0.693 / k Second-order: t½ = 1 / k[A]₀ |
| Arrhenius Equation | k = Ae^(−Eₐ/RT) |
| pH and H+ | pH = −log[H⁺] [H⁺] = 10^−pH |
| pOH and OH- | pOH = −log[OH⁻] [OH⁻] = 10^−pOH |
| pH + pOH = | 14 (at 25°C) |
| Ka = | [H₃O⁺][A⁻] / [HA] |
| Kb = | [HB⁺][OH⁻] / [B] |
| Kw = | [H⁺][OH⁻] = 1×10⁻¹⁴ (at 25°C) Kw = Ka × Kb |
| pKa = | −log(Ka) |
| pKb = | −log(Kb) |
| pKa + pKb = | 14 |
| Henderson-Hasselbalch | pH = pKa + log([A⁻]/[HA]) weak acid (HA) and its conjugate base (A⁻) pOH = pKb + log([HB⁺]/[B]) conjugate acid (HB) and weak base (B) |
| When [A⁻] = [HA]: | pH = pKa |
| When [HB⁺] = [B]: | pOH = pKb |
| Titration | NtVt = NaVa Nt: Normality of the titrant (known concentration) Vt: Volume of the titrant used to reach the equivalence point. Na: Normality of the analyte (the solution with an unknown concentration) Va: Volume of the analyte being titrated. |
| At equivalence point: | moles OH⁻ = moles H⁺ for normality |
| At half equivalence point: | pH = pKa |
| log(1) = | 0 |
| log(10) = | 1 |
| log(100) = | 2 |
| Kp = | (Pc)^c(Pd)^d / (Pa)^a(Pb)^b (pressure-based) |
| Q = | [C]^c[D]^d / [A]^a[B]^b (reaction quotient, same form as Keq) |
| Keq = | [C]^c[D]^d / [A]^a[B]^b (for aA + bB ⇌ cC + dD) |
| Kc = | [C]^c[D]^d / [A]^a[B]^b (concentration-based) |
| GIBBS FREE ENERGY & EQUILIBRIUM | ΔG° = −RT ln(Keq) R = 8.314 J·mol⁻¹·K⁻¹ T = temperature in Kelvin |
| SOLUBILITY | Ksp = [cation]^m[anion]^n (coefficients become exponents) Qsp = [cation]^m[anion]^n (same form as Ksp, at any point) Example: PbI₂ → Ksp = [Pb²⁺][I⁻]² |
| Standard Cell Potential | E°cell = E°reduction + E°oxidation |
| Oxidation Potential from Reduction Potential | E°oxidation = −E°reduction |
| Gibbs Free Energy and Cell Potential | ΔG° = −nFE°cell where: n = moles of electrons transferred F = Faraday's constant (96,500 C/mol e⁻) E°cell = standard cell potential |
| Electrolysis / Electroplating | (I × tₛ) / (n × F) = moles of product deposited where: I = current (amps) tₛ = time (seconds) n = moles of electrons transferred F = Faraday's constant (96,500 C/mol e⁻) |
| Faraday's constant (F) = | 96,500 C/mol e⁻ |
| 1 Ampere = | 1 coulomb/second |
| 1 Volt = | 1 joule/coulomb |
| Number of Neutrons | neutrons = A − Z |
| Einstein's Mass-Energy / Binding Energy | E = Δmc² |
| Alpha Decay | ᴬ𝓩X → ᴬ⁻⁴𝓩₋₂Y + ⁴₂α |
| Beta Plus / Positron Decay | ᴬ𝓩X → ᴬ𝓩₋₁Y + ⁰₊₁β⁺ |
| Beta Minus Decay | ᴬ𝓩X → ᴬ𝓩₊₁Y + ⁰₋₁β⁻ |
| Electron Capture | ᴬ𝓩X + ⁰₋₁e → ᴬ𝓩₋₁Y |
| Gamma Decay | ᴬ𝓩X* → ᴬ𝓩X + γ |
| Radioactive Half-Life | Mf = Mi × (1/2)ⁿ Mf = final mass Mi = initial mass n = number of half-lives |
| Number of Half-Lives | n = total time elapsed ÷ half-life duration |
Created by:
smurtab