Key Formulas & Equations
Core Concepts
Mole & Avogadro's Number
The mole is the SI unit for amount of substance. One mole contains exactly 6.022×10²³ particles (atoms, molecules, ions). The molar mass of an element (g/mol) equals its atomic mass in amu.
Acid-Base Equilibria
Brønsted-Lowry: acids donate H⁺, bases accept H⁺. The strength of an acid is measured by Ka (acid dissociation constant). Strong acids (HCl, H₂SO₄) fully dissociate; weak acids (CH₃COOH) partially dissociate, establishing equilibrium.
Le Chatelier's Principle
When a system at equilibrium is disturbed (concentration, temperature, or pressure change), the system shifts to counteract the disturbance and re-establish equilibrium. Adding reactant shifts right; increasing temperature shifts in the endothermic direction.
Thermochemistry
Study of heat energy in chemical reactions. Exothermic reactions release heat (ΔH < 0); endothermic reactions absorb heat (ΔH > 0). Hess's Law: the enthalpy change of a reaction is the sum of enthalpy changes of its steps.
Electrochemistry
Interconversion of chemical and electrical energy. In galvanic cells, spontaneous redox reactions produce electricity. In electrolytic cells, electrical energy drives non-spontaneous reactions. The anode is where oxidation occurs; the cathode is where reduction occurs.
Chemical Kinetics
The study of reaction rates. Rate depends on concentration, temperature, catalysts, and surface area. The rate law expresses this relationship. Reaction mechanisms describe the elementary steps through which a reaction proceeds.
Worked Examples
Example 1: Ideal Gas Law
Problem: 2.0 mol of gas at 1.5 atm occupies what volume at 300 K? (R = 0.0821 L·atm/(mol·K))
Step 1: PV = nRT → V = nRT/P
Step 2: V = (2.0)(0.0821)(300)/(1.5) = 49.26/1.5
Step 3: V = 32.84 L
Answer: The volume is approximately 32.8 L.
Example 2: pH Calculation
Problem: Calculate the pH of 0.01 M HCl solution.
Step 1: HCl is a strong acid → fully dissociates: [H⁺] = 0.01 M
Step 2: pH = -log[H⁺] = -log(0.01) = -log(10⁻²)
Step 3: pH = 2
Answer: The pH is 2 (strongly acidic).
Example 3: Stoichiometry
Problem: How many grams of H₂O form from 4.0 g of H₂ in 2H₂ + O₂ → 2H₂O? (H=1, O=16)
Step 1: Moles of H₂ = 4.0 g / 2.02 g/mol = 1.98 mol
Step 2: Mole ratio: 2 mol H₂ : 2 mol H₂O = 1:1
Step 3: Moles of H₂O = 1.98 mol
Step 4: Mass H₂O = 1.98 × 18.02 = 35.7 g
Answer: Approximately 35.7 grams of water are produced.
Example 4: Gibbs Free Energy
Problem: Determine if a reaction is spontaneous at 298 K with ΔH = -50 kJ/mol and ΔS = -100 J/(mol·K).
Step 1: Convert ΔS to kJ: ΔS = -0.100 kJ/(mol·K)
Step 2: ΔG = ΔH - TΔS = -50 - (298)(-0.100) = -50 + 29.8
Step 3: ΔG = -20.2 kJ/mol
Answer: ΔG < 0, so the reaction is spontaneous at 298 K.
Practice Problems
Problem 1
What is the molarity of a solution containing 0.5 mol NaCl in 2.0 L?
Answer: M = 0.5/2.0 = 0.25 M
Problem 2
Calculate ΔG for a reaction with ΔH = 80 kJ and ΔS = 200 J/K at 400 K.
Answer: ΔG = 80 - (400)(0.200) = 80 - 80 = 0 kJ (at equilibrium)
Problem 3
A first-order reaction has k = 0.05 s⁻¹. What is its half-life?
Answer: t₁/₂ = 0.693/0.05 = 13.86 s
Problem 4
Balance the equation: C₃H₈ + O₂ → CO₂ + H₂O
Answer: C₃H₈ + 5O₂ → 3CO₂ + 4H₂O
Problem 5
What is the empirical formula of a compound that is 40% C, 6.7% H, 53.3% O?
Answer: Moles: C=40/12=3.33, H=6.7/1=6.7, O=53.3/16=3.33. Ratio ≈ 1:2:1 → CH₂O
Problem 6
At equilibrium, [A] = 0.2 M, [B] = 0.3 M for A ⇌ B. What is Kc?
Answer: Kc = [B]/[A] = 0.3/0.2 = 1.5