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?

When a salt is dissolved in water, it dissociates into its ions. For each salt, we can write: 1. KBr: \(\mathrm{K^+}\) and \(\mathrm{Br^-}\) 2. NH\(_4\)Cl: \(\mathrm{NH_4^+}\) and \(\mathrm{Cl^-}\) 3. KCN: \(\mathrm{K^+}\) and \(\mathrm{CN^-}\) 4. K\(_2\)CO\(_3\): \(\mathrm{2K^+}\) and \(\mathrm{CO_3^{2-}}\)

For each of the ions in the solution, we will determine whether it will increase, decrease, or not affect the pH: 1. \(\mathrm{K^+}\): This is a Group 1 (alkali metal) cation and will not affect the pH of the solution. 2. \(\mathrm{Br^-}\): As the conjugate base of a strong acid (HBr), it will not affect the pH of the solution. 3. \(\mathrm{NH_4^+}\): This is the ammonium ion, which is the conjugate acid of a weak base (NH\(_3\)). It will slightly decrease the pH of the solution. 4. \(\mathrm{Cl^-}\): Like Br\(^-\), as the conjugate base of a strong acid (HCl), it will not affect the pH of the solution. 5. \(\mathrm{CN^-}\): This is the cyanide ion, which is the conjugate base of a weak acid (HCN). It will slightly increase the pH of the solution. 6. \(\mathrm{CO_3^{2-}}\): This is the carbonate ion, which is the conjugate base of a weak acid (H\(_2\)CO\(_3\)). It will increase the pH of the solution.

Now we must identify which combination of cations and anions will produce a neutral solution: 1. KBr: \(\mathrm{K^+}\) does not affect the pH and \(\mathrm{Br^-}\) does not affect the pH. 2. NH\(_4\)Cl: \(\mathrm{NH_4^+}\) decreases the pH and \(\mathrm{Cl^-}\) does not affect the pH. 3. KCN: \(\mathrm{K^+}\) does not affect the pH and \(\mathrm{CN^-}\) increases the pH. 4. K\(_2\)CO\(_3\): \(\mathrm{2K^+}\) does not affect the pH and \(\mathrm{CO_3^{2-}}\) increases the pH. From our analysis, only the KBr salt has both ions that do not affect the pH, which means it will produce a neutral solution when dissolved in water.

The identity of the unknown salt that forms a neutral 0.100 M solution is KBr (potassium bromide), as both ions do not affect the pH of the solution.