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Decay sequence: 100 g → 50 g (1 half-life) → 25 g (2 half-lives). Two half-lives = 12 hours → half-life = 12 ÷ 2 = 6 hours. Correct answer: C.

ACS objectives stress half-life calculations, exponential decay equations, and their applications in dating, medicine, and nuclear safety.

At equilibrium, Gibbs free energy change (ΔG) equals zero, meaning no net driving force. Reactions still occur, but forward and reverse rates are equal. ACS objectives stress linking ΔG and equilibrium constants. This principle is key for analyzing chemical systems and predicting outcomes.

NH₃ has three bonding pairs and one lone pair around nitrogen, resulting in trigonal pyramidal geometry. CO₂ is linear, CH₄ is tetrahedral, and BF₃ is trigonal planar. ACS objectives stress predicting molecular geometry using VSEPR theory. This skill helps explain polarity, reactivity, and physical properties of molecules.

Boyle’s Law states that pressure and volume are inversely proportional at constant temperature and amount of gas. Mathematically: P × V = constant, or P ∝ 1/V. Doubling pressure halves volume if temperature is held constant. This principle derives from kinetic molecular theory: when volume decreases, gas particles collide more frequently with container walls, increasing pressure. ACS exam objectives stress understanding gas laws, their mathematical derivations, and their use in problem-solving. Mastery of these concepts prepares students to apply ideal gas behavior in laboratory conditions, real gas corrections, and gas stoichiometry calculations. Boyle’s Law is foundational in physics, chemistry, and applications like scuba diving and industrial gas storage.

Step 1: Convert hydrogen mass to moles.

Hydrogen molar mass (H₂) = 2.0 g/mol.

Moles H₂ = 4.00 ÷ 2.0 = 2.00 mol.

Step 2: Apply stoichiometry.

Balanced equation shows 2 moles H₂ → 2 moles H₂O.

Therefore, 2.00 mol H₂ → 2.00 mol H₂O.

Step 3: Convert moles of H₂O to grams.

Molar mass H₂O = 18.0 g/mol.

2.00 × 18.0 = 36.0 g.

This exercise highlights stoichiometric principles: balanced equations provide mole ratios, which are essential for mass-to-mass conversions. ACS exam objectives emphasize correct use of molar masses, coefficients, and unit conversions, as these underpin laboratory applications such as yield calculations and limiting reagent analysis. Accuracy in such calculations is central to real-world chemistry, from industrial processes to environmental monitoring.