which of the following solutions containing one mole per dm$^3$ of the compound would have the lowest PH?

Analyze the question: We need the solution with the lowest pH. The lower the pH, the higher the hydrogen ion concentration [H⁺], so we are looking for the most acidic solution.

Concept: pH = -log[H⁺]. Strong acids ionize completely in water, giving a high [H⁺]. Weak acids ionize only partially. Neutral salts give a pH of about 7, and salts of a weak acid with a strong base are slightly alkaline.

Solution: Compare each option at 1 mol/dm³:

• A. Ethanoic acid (CH₃COOH): a weak acid, only slightly ionized. [H⁺] ≈ √(Ka × C) = √(1.8×10⁻⁵ × 1) ≈ 4.2×10⁻³ M, so pH ≈ 2.4.
• B. Hydrochloric acid (HCl): a strong acid, completely ionized. [H⁺] = 1 M, so pH = 0.
• C. Sodium chloride (NaCl): a salt of a strong acid and a strong base, so it is neutral with pH ≈ 7.
• D. Sodium hydrogentrioxocarbonate(IV) (NaHCO₃): a salt of a weak acid and a strong base, so it is slightly alkaline with pH ≈ 8.3.

Order of pH: HCl (0) < ethanoic acid (about 2.4) < NaCl (7) < NaHCO₃ (about 8.3).

Answer: The solution with the lowest pH is hydrochloric acid, option B.

Tip: For equal concentrations, ask first whether the substance is a strong acid, weak acid, neutral salt, or base. The order of pH is strong acid < weak acid < neutral < weak base < strong base. Strong acids always win on "lowest pH" questions.