An unknown salt is either \(\mathrm{KBr}, \mathrm{NH}_{4} \mathrm{Cl}, \mathrm{KCN},\) or \(\mathrm{K}_{2} \mathrm{CO}_{3} .\) If a \(0.100 \mathrm{M}\) solution of the salt is neutral, what is the identity of the salt?

First, let's list the given salts and their respective ions: 1. KBr: K⁺ (potassium ion), Br⁻ (bromide ion) 2. NH₄Cl: NH4⁺ (ammonium ion), Cl⁻ (chloride ion) 3. KCN: K⁺ (potassium ion), CN⁻ (cyanide ion) 4. K₂CO₃: 2 K⁺ (potassium ions), CO₃²⁻ (carbonate ion)

Now we will analyze the acidic or basic properties of each ion: - K⁺: Since potassium belongs to Group 1 of the periodic table, it forms neutral solutions as cations of this group do not hydrolyze. - NH4⁺: The ammonium ion behaves as a weak acid, releasing a H⁺ ion in solution: \(\mathrm{NH_4^+} \rightleftharpoons \mathrm{NH_3} + \mathrm{H^+}\) - Br⁻, Cl⁻: Both bromide and chloride are conjugate bases of strong acids (HBr and HCl). Therefore, they are weak bases and will cause a negligible change to the pH of the solution. - CN⁻: The cyanide ion is the conjugate base of the weak acid, HCN. So, it behaves as a weak base by accepting a H⁺ ion from water: \(\mathrm{CN^-} + \mathrm{H_2O} \rightleftharpoons \mathrm{HCN} + \mathrm{OH^-}\) - CO₃²⁻: The carbonate ion is a weak base. It accepts a H⁺ ion from water, yielding bicarbonate: \(\mathrm{CO_3^{2-}} + \mathrm{H_2O} \rightleftharpoons \mathrm{HCO_3^-} + \mathrm{OH^-}\)

Based on our analysis in Step 2, let us examine each salt to see which one would produce a neutral solution: 1. KBr: K⁺ does not impact pH, and Br⁻ does not significantly change the pH. So, a KBr solution would be neutral. 2. NH₄Cl: NH4⁺ acts as a weak acid and Cl⁻ does not significantly change the pH. This combination would result in a slightly acidic solution. 3. KCN: K⁺ does not affect the pH, but CN⁻ acts as a weak base. The solution of KCN would be slightly basic. 4. K₂CO₃: K⁺ does not affect the pH, but CO₃²⁻ acts as a weak base. The solution of K₂CO₃ would be slightly basic. Since we are looking for a salt that forms a neutral solution, the only suitable candidate is KBr (potassium bromide). So, the identity of the unknown salt is KBr.