Question

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?

Short answer

The salt that forms a 0.100 M neutral solution is \(\mathrm{KBr}\). This is because when dissolved in water, both the \(\mathrm{K^+}\) and \(\mathrm{Br^-}\) ions do not undergo any reaction or hydrolysis, resulting in a neutral solution.

Step-by-step solution

Write the dissociation reactions of each salt

Write the dissociation of each salt in water: 1. \(\mathrm{KBr}: \mathrm{KBr} \rightarrow \mathrm{K^+} + \mathrm{Br^-}\) 2. \(\mathrm{NH}_{4} \mathrm{Cl}: \mathrm{NH}_{4} \mathrm{Cl} \rightarrow \mathrm{NH_{4}^+} + \mathrm{Cl^-}\) 3. \(\mathrm{KCN}: \mathrm{KCN} \rightarrow \mathrm{K^+} + \mathrm{CN^-}\) 4. \(\mathrm{K}_{2} \mathrm{CO}_{3}: \mathrm{K}_{2} \mathrm{CO}_{3} \rightarrow 2\mathrm{K^+} + \mathrm{CO_{3}^{2-}}\)

Determine the acidity/basicity of the resulting ions

Investigate the behavior of the resulting ions in water: 1. \(\mathrm{K^+}\) and \(\mathrm{Br^-}\): K+ ions are derived from a strong base, KOH and Br- ions are derived from a strong acid, HBr. Neither of them undergoes any reaction or hydrolysis in water. Hence, the resulting solution will be neutral. 2. \(\mathrm{NH_{4}^+}\) and \(\mathrm{Cl^-}\): NH4+ ions are derived from a weak base, NH3 and Cl- ions are derived from a strong acid, HCl. Although Cl- ions do not affect the pH, NH4+ ions undergo hydrolysis in water forming hydronium ions, which make the solution acidic. 3. \(\mathrm{K^+}\) and \(\mathrm{CN^-}\): K+ ions are derived from a strong base, KOH, and CN- ions are derived from a weak acid, HCN. CN- undergoes hydrolysis in water absorbing a proton from water and forming OH- ions, making the solution basic. 4. \(\mathrm{K^+}\) and \(\mathrm{CO_{3}^{2-}}\): K+ ions are derived from strong base, and CO3^2- ions are derived from a weak acid, H2CO3. CO3^2- ions undergo hydrolysis in water forming OH- ions, making the solution basic.

Identify the neutral salt

Based on the acidity or basicity of the resulting ions of each salt, we can identify which salt will form a neutral solution: 1. \(\mathrm{KBr}\): Neutral solution 2. \(\mathrm{NH}_{4} \mathrm{Cl}\): Acidic solution 3. \(\mathrm{KCN}\): Basic solution 4. \(\mathrm{K}_{2} \mathrm{CO}_{3}\): Basic solution Therefore, the identity of the salt that forms a 0.100 M neutral solution is \(\boxed{\mathrm{KBr}}\).

Key concepts

Neutral Solution

In the realm of chemistry, a neutral solution is one where the concentration of hydrogen ions ( ce{H+} ) is equal to the concentration of hydroxide ions ( ce{OH-} ), resulting in a pH of 7. When a salt, such as ce{KBr} , disassociates in water, it produces ce{K+} and ce{Br-} ions. These ions are derived from strong acids and bases: potassium bromide comes from potassium hydroxide (a strong base) and hydrobromic acid (a strong acid).
Because both components are strong, neither undergoes any significant hydrolysis in water, meaning they do not react further to change the pH. As a result, the solution remains neutral. This characteristic is central to identifying the salt ce{KBr} as producing a neutral solution among the given options, as the other salts result in either acidic or basic solutions.

Acidic Solution

An acidic solution forms when there is an excess of hydrogen ions ( ce{H+} ) in the solution, leading to a pH less than 7. This typically happens when a salt derived from a weak base and a strong acid dissolves in water. Take ce{NH4Cl} , for example. When it dissociates, it forms ce{NH4+} and ce{Cl-} ions.
The ce{Cl-} ions, coming from strong hydrochloric acid, do not undergo hydrolysis and remain inert concerning the pH. However, the ce{NH4+} ions, originating from the weak base ce{NH3} , do react with water, releasing hydrogen ions. This increase in ce{H+} ions causes the solution to become acidic. Consequently, solutions of ce{NH4Cl} are consistently acidic, demonstrating their source from a weak base and a strong acid.

Basic Solution

A basic solution is characterized by a surplus of hydroxide ions ( ce{OH-} ) and a pH greater than 7. Salts that lead to basic solutions are generally derived from strong bases and weak acids. For instance, when either ce{KCN} or ce{K2CO3} salts dissociate, they form the following ions:

• For ce{KCN} : ce{K+} and ce{CN-}
• For ce{K2CO3} : ce{K+} and ce{CO3^2-}

Both ce{K+} ions come from a strong base, potassium hydroxide, and they don't hydrolyze in water. However, both ce{CN-} and ce{CO3^2-} ions, derived from weak acids (hydrocyanic acid and carbonic acid respectively), do undergo hydrolysis.
They absorb hydrogen ions from water and release hydroxide ions in their place. This process increases the ce{OH-} concentration in the solution, making it basic. Thus, in the presence of such salt ions, the solution becomes basic, as seen in the cases of ce{KCN} and ce{K2CO3} solutions.