📌 q = m × c × ΔT, where q is heat, m is mass, c is specific heat, and ΔT is temperature change. q = 50.0 g × 4.18 J/(g·°C) × (80.0 − 20.0) °C = 50.0 × 4.18 × 60.0 = 12,540 J. Always compute ΔT as final minus initial; positive ΔT means heat absorbed, negative means heat released.

📌 17,190 years ÷ 5,730 years per half-life = 3 half-lives. After each half-life, the remaining amount halves. So 100 g → 50 g (1st) → 25 g (2nd) → 12.5 g (3rd). General formula: remaining = initial × (1/2)ⁿ, where n is the number of half-lives elapsed. This is the basis of radiocarbon dating for fossils up to ~50,000 years old.

📌 Moles = mass ÷ molar mass = 88.0 g ÷ 44.0 g/mol = 2.00 mol. The mole bridge: grams ↔ moles ↔ particles. To go from grams to moles, ALWAYS divide by molar mass. Multiplying (the common error in distractor D) gives an unreasonable answer.

📌 Charles's Law (constant pressure): V₁/T₁ = V₂/T₂. Rearranging: V₂ = V₁ × (T₂/T₁) = 4.0 L × (400 K / 200 K) = 8.0 L. Doubling the absolute temperature (in Kelvin) doubles the volume at constant pressure. Always use Kelvin — converting from °C would give wildly wrong answers.

📌 Kinetic Molecular Theory assumes ideal gas particles (1) have negligible volume relative to the container, (2) experience no intermolecular forces, (3) move in random straight-line motion, (4) undergo elastic collisions (no energy lost), and (5) have average kinetic energy proportional to absolute temperature. Real gases deviate at high pressure and low temperature.

📌 Moles = mass ÷ molar mass = 36.0 g ÷ 18.0 g/mol = 2.00 mol. Repeat after me: grams → moles is ALWAYS division by molar mass. Multiplying produces an unreasonably huge answer (option D shows that error).

📌 When the surroundings (the beaker, your hand) get colder, the system absorbed heat from them → endothermic. The energy went INTO breaking apart the ionic lattice of NH₄NO₃ during dissolution. This is the principle behind instant cold packs — they use NH₄NO₃ dissolving in water for emergency cooling.

📌 For dilute aqueous solutions (density ≈ 1 g/mL), parts per million ≈ mg per kg of solvent ≈ mg per liter. So 5 mg/L ≈ 5 ppm. Pattern: ppm = (mass of solute in g ÷ mass of solution in g) × 10⁶. Used for trace concentrations like water-quality testing (e.g., 'fluoride at 1 ppm in tap water').

📌 Gamma rays are pure electromagnetic radiation (like light, but much higher energy) — no mass, no charge. Alpha particles are helium nuclei (mass 4, charge +2). Beta particles are high-speed electrons (mass ~0, charge −1). Neutrons have mass 1 and no charge but are usually not classified with the three main decay types. Gamma rays often accompany alpha or beta decay as the nucleus releases excess energy.