📌 Density = mass ÷ volume = 12.450 g ÷ 4.50 mL = 2.766666… g/mL. Significant figures rule for division: the answer carries the same sig figs as the LEAST precise measurement. 4.50 mL has 3 sig figs (mass has 5), so the answer rounds to 3 sig figs: 2.77 g/mL.

📌 Electron: −1 charge, mass ≈ 1/1836 of a proton. Protons are +1 charge with mass ≈ 1 amu. Neutrons have no charge, mass ≈ 1 amu. The nucleus is not a particle — it's the dense central region containing protons and neutrons.

📌 Calcium forms Ca²⁺ (Group 2). Chlorine forms Cl⁻ (Group 17). To balance the +2 charge, you need TWO Cl⁻ ions per one Ca²⁺ → formula CaCl₂. The subscripts cross-cross from the charges: Ca²⁺ + Cl⁻ → Ca₁Cl₂ = CaCl₂. Net charge of the formula unit is 0.

📌 The proposed explanation describes a MECHANISM supported by repeated experimental and observational evidence — that's a scientific theory. A law would describe a pattern without explaining why (e.g., 'limestone erodes faster in industrial areas'). A hypothesis is a TENTATIVE proposal not yet tested. Common student error: thinking 'theory' means 'guess.' In science it means well-tested explanation.

📌 Atoms emit only specific wavelengths because electrons can only occupy discrete (quantized) energy levels. When an electron drops from a higher level to a lower level, it emits a photon whose energy equals the difference between those levels. Each element has a unique pattern of energy levels, producing a unique emission spectrum — the basis of atomic emission spectroscopy.

📌 Magnesium (a metal, group 2) transfers its two valence electrons to oxygen (a nonmetal, group 16), producing Mg²⁺ and O²⁻ ions. The opposite charges attract → ionic bond. Rule of thumb: metal + nonmetal with large electronegativity difference → ionic. Two nonmetals → covalent.

📌 Isotopes are atoms of the SAME element (same proton count, so both are carbon) with DIFFERENT neutron counts. Carbon-12 has 6 neutrons, carbon-14 has 8. Ions differ in electrons. Allotropes (graphite, diamond) are different molecular structures, not different atoms.

📌 In a controlled experiment, the independent variable (water temperature) is the ONLY thing that changes between trials. All other conditions — sugar mass, water volume, stirring, container — must stay constant. Otherwise, you can't attribute the observed effect to temperature.

📌 Balanced: 4 Al + 3 O₂ → 2 Al₂O₃. Start by balancing aluminum: 2 Al₂O₃ contains 4 Al, so you need 4 Al on the left. Then balance oxygen: 2 Al₂O₃ contains 6 O atoms; since O₂ provides 2 O per molecule, you need 3 O₂. Always balance metals/nonmetals first and leave free elements (like O₂) for last.