Problem 88 - Chemistry: The Central Science

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?

Step-by-Step Solution

Answer

The identity of the unknown salt that forms a neutral \(0.100 \mathrm{M}\) solution is \(\mathrm{KBr}\), as neither \(\mathrm{K^{+}}\) nor \(\mathrm{Br^{-}}\) influence the pH of the solution.

Step 1: Write the ionization of all salts in water

For each salt, write the equation for its ionization or dissolution in water. The possible salts are \(\mathrm{KBr}, \mathrm{NH}_{4} \mathrm{Cl}, \mathrm{KCN} \text{, and } \mathrm{K}_{2} \mathrm{CO}_{3}\) 1. \(\mathrm{KBr \rightarrow K^{+} + Br^{-}}\) 2. \(\mathrm{NH_{4}Cl \rightarrow NH_{4}^{+} + Cl^{-}}\) 3. \(\mathrm{KCN \rightarrow K^{+} + CN^{-}}\) 4. \(\mathrm{K_{2}CO_{3} \rightarrow 2K^{+} + CO_{3}^{2-}}\)

Step 2: Determine the acidity or basicity of each ion

Now, determine the acidity or basicity of each ion formed by examining their reactivity with water. Strong acids completely dissociate, while weak acids and weak bases will partially dissociate. 1. \(\mathrm{K^{+}}:(\text{Group 1 cations do not affect pH})\) 2. \(\mathrm{Br^{-}}:(\text{Conjugate of a strong acid, no effect on pH})\) 3. \(\mathrm{NH_{4}^{+}}: (\text{Weak acid, NH_{4}^{+} + H_{2}O \rightleftharpoons NH_{3} + H_{3}O^{+}})\) 4. \(\mathrm{Cl^{-}}: (\text{Conjugate of a strong acid, no effect on pH})\) 5. \(\mathrm{CN^{-}}: (\text{Weak base, HCN + H_{2}O \rightleftharpoons CN^{-} + H_{3}O^{+}})\) 6. \(\mathrm{CO_{3}^{2-}}: (\text{Weak base, H_{2}CO_{3} + H_{2}O \rightleftharpoons CO_{3}^{2-} + H_{3}O^{+}})\)

Step 3: Identify the salt that forms a neutral solution

Now that we know the acidity or basicity of each ion, identify the salt that would result in a neutral solution when dissolved in water. A neutral solution has a pH of 7, which occurs when the acidic effects of the cations balance out with the basic effects of the anions. 1. \(\mathrm{KBr}: \text{Neutral} (\text{Neither K}^{+} \text{nor Br}^{-} \text{influence the pH})\) 2. \(\mathrm{NH_{4}Cl}: \text{Acidic} (\text{NH}_{4}^{+} \text{is acidic and Cl}^{-} \text{does not influence the pH})\) 3. \(\mathrm{KCN}: \text{Basic} (\text{K}^{+} \text{does not influence the pH, and CN}^{-} \text{is } \text{basic})\) 4. \(\mathrm{K_{2}CO_{3}}: \text{Basic} (\text{K}^{+} \text{does not influence the pH, and CO}_{3}^{2-} \text{is } \text{basic})\)

Step 4: Determine the identity of the unknown salt

Based on our analysis, the unknown salt must be the one that forms a neutral solution in water - \(\mathrm{KBr}\).

Key Concepts

Ionization in Water

When salts dissolve in water, they undergo a process called ionization. This means that the salt separates into its ions. For example, when potassium bromide ( KBr ) dissolves, it separates into potassium ions ( K^+ ) and bromide ions ( Br^- ). This process is crucial because it sets the stage for various interactions with water and helps determine the salt's overall effect on the solution environment.

• Salts Dissolve: The ions separate and interact with water molecules.
• Ion Interaction: These ions can affect the acidity or basicity of a solution.

Understanding ionization helps identify the properties of a solution. Whether a solution becomes acidic, basic, or remains neutral can often be predicted by looking at the ionization of the salts involved.

Acid-Base Reactions

In a solution, acid-base reactions determine whether the solution is acidic or basic. This happens because some ions formed from the dissolved salts can react with water. Consider the ammonium ion ( NH_4^+ ). It's a weak acid that can donate a hydrogen ion (proton) to water, forming hydronium ions ( H_3O^+ ) which increase acidity. Similarly, a weak base like the cyanide ion ( CN^- ) in solutions tends to accept a proton, forming hydroxide ions ( OH^- ) which make the solution basic.

• Weak Acids: Partially donate protons to water, making it acidic.
• Weak Bases: Accept protons from water, causing basicity.

Recognizing these properties helps us predict the pH effect of salts in solutions. If the cation or anion from a salt is known to be acidic or basic, these properties contribute directly to the solution's pH.

Neutral Solutions

A neutral solution occurs when the concentrations of hydrogen ions ( H^+ ) and hydroxide ions ( OH^- ) in water are equal, which gives it a pH of 7. To achieve neutrality, the salt dissolved in water should not affect the pH. For example, potassium bromide ( KBr ) results in a neutral solution because both ions ( K^+ and Br^- ) do not react further with water to affect the pH.

• Neutral Salts: Do not affect the water's pH, balanced charges of ions.
• pH Balance: Occurs when neither acidic nor basic ions predominate.

Hence, recognizing neutral salts is crucial to understanding how different salts affect solution properties and can help identify the correct salt based on the solution's pH behavior.