Consider the following six beakers. All have \(100 \mathrm{~mL}\) of aqueous \(0.1 \mathrm{M}\) solutions of the following compounds: beaker A has HI beaker B has \(\mathrm{HNO}_{2}\) beaker \(\mathrm{C}\) has \(\mathrm{NaOH}\) beaker \(\mathrm{D}\) has \(\mathrm{Ba}(\mathrm{OH})_{2}\) beaker \(\mathrm{E}\) has \(\mathrm{NH}_{4} \mathrm{Cl}\) beaker \(\mathrm{F}\) has \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{NH}_{2}\)

First, let's identify each compound as either an acid, base, or neutral. - Beaker A (HI): HI is a strong acid, so it donates protons (H+) to the solution. - Beaker B (HNO2): HNO2 is a weak acid, so it partially donates protons (H+) to the solution. - Beaker C (NaOH): NaOH is a strong base, so it donates hydroxide ions (OH-) to the solution. - Beaker D (Ba(OH)2): Ba(OH)2 is also a strong base, and it donates two hydroxide ions per mole (2 OH-) to the solution. - Beaker E (NH4Cl): NH4Cl is the salt of a weak base (NH3) and a strong acid (HCl), so it primarily acts as a weak acid in solution and donates protons. - Beaker F (C2H5NH2): C2H5NH2 is a weak base (amine) that accepts protons in solution.

For strong acids and bases, we can directly calculate the pH from their concentrations. For weak acids and bases, we will use approximations, as they do not fully dissociate. - Beaker A: HI is a strong acid, so the pH = -log([H+]) = -log(0.1) = 1 - Beaker B: HNO2 is a weak acid, so we can approximate the pH to be between 1 and 7 - Beaker C: NaOH is a strong base, so the pOH = -log([OH-]) = -log(0.1) = 1, then pH = 14 - pOH = 14 - 1 = 13 - Beaker D: Ba(OH)2 is a strong base, so the pOH = -log([2*0.1]) = -log(0.2), then pH = 14 - pOH ≈ 12.3 - Beaker E: NH4Cl acts as a weak acid, so we can approximate the pH to be between 1 and 7 - Beaker F: C2H5NH2 is a weak base, so we can approximate the pH to be between 7 and 13

Now that we have an estimate for the pH of each solution, let's rank them from lowest to highest pH: 1. Beaker A: pH 1 2. Beaker B: Approximately between 1 and 7 3. Beaker E: Approximately between 1 and 7 4. Beaker F: Approximately between 7 and 13 5. Beaker D: pH 12.3 6. Beaker C: pH 13 This ranking gives us a general idea of the relative acidity and basicity of each solution, with A being the most acidic and C being the most basic.