Rank the following 0.10\(M\) solutions in order of increasing \(\mathrm{pH.}\) a. \(\mathrm{NH}_{3}\) b. KOH c. \(\mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}\) d. \(\mathrm{KCl}\) e. HCl

We have five compounds: \(\mathrm{NH}_{3}\), KOH, \(\mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}\), \(\mathrm{KCl}\), and HCl. Let's identify their nature: a. \(\mathrm{NH}_{3}\) is a weak base b. KOH is a strong base c. \(\mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}\) is a weak acid d. \(\mathrm{KCl}\) is a salt of a strong acid and strong base, thus neutral e. HCl is a strong acid

Now we will calculate the pH for each solution, considering their nature and concentration. a. Ammonia (\(\mathrm{NH}_{3}\)): As a weak base, we need to use a simplified version of the Henderson-Hasselbalch equation: \(\mathrm{pOH} = \mathrm{pK}_{b} - \log{\frac{[\mathrm{NH}_{3}]}{[\mathrm{OH}^-]}}\). However, for ranking purpose, we don't need the exact pH value. b. Potassium hydroxide (KOH): As a strong base, it fully dissociates in water: \(\mathrm{KOH} \rightarrow \mathrm{K}^+ + \mathrm{OH}^-\). Hence, \([\mathrm{OH}^-]\) will be \(0.10\,\mathrm{M}\). We can calculate the pOH as \(\mathrm{pOH} = -\log{[\mathrm{OH}^-]}\), and then find the pH using \(\mathrm{pH} = 14 - \mathrm{pOH}\). c. Acetic acid (\(\mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}\)): As a weak acid, we can also use the simplified version of the Henderson-Hasselbalch equation: \(\mathrm{pH} = \mathrm{pK}_{a} - \log{\frac{[\mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}]}{[\mathrm{H}^+]}}\). Again, we don't need the exact pH value for ranking purposes. d. Potassium chloride (\(\mathrm{KCl}\)): As a neutral salt, the pH will be 7. e. Hydrochloric acid (HCl): As a strong acid, it fully dissociates in water: \(\mathrm{HCl} \rightarrow \mathrm{H}^+ + \mathrm{Cl}^-\). Hence, \([\mathrm{H}^+]\) will be \(0.10\,\mathrm{M}\). We can calculate the pH as \(\mathrm{pH} = -\log{[\mathrm{H}^+]}\).

Based on the pH calculations and the nature of each compound, we can rank the solutions as follows: 1. Hydrochloric acid (HCl): strong acid 2. Acetic acid (\(\mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}\)): weak acid 3. Potassium chloride (\(\mathrm{KCl}\)): neutral 4. Ammonia (\(\mathrm{NH}_{3}\)): weak base 5. Potassium hydroxide (KOH): strong base