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 unknown salt is KBr (potassium bromide), as it forms a neutral solution. This is because the K⁺ ion does not affect the pH, and the Br⁻ ion does not significantly change the pH either.

Step-by-step solution

List the possible salts and their ions

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)

Analyze the acidic or basic properties of the ions

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: \(\mathrm{CO_3^{2-}} + \mathrm{H_2O} \rightleftharpoons \mathrm{HCO_3^-} + \mathrm{OH^-}\)

Determine which salt would produce a neutral solution

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.

Key concepts

pH analysis

Understanding pH is crucial for distinguishing between acidic, basic, and neutral solutions. The pH scale ranges from 0 to 14, where 7 is neutral. Acidic solutions have a pH lower than 7, while basic solutions have a pH higher than 7.
A neutral solution indicates that the concentrations of hydrogen ions ( H⁺ ) and hydroxide ions ( OH⁻ ) are equal ( [ H⁺ ] = [ OH⁻ ] ). In pH analysis of salts, such as in this exercise, we must consider the potential of the salt's ions to alter the pH. This involves identifying whether the ions in the salt solution can participate in reactions that change hydrogen or hydroxide ion levels.

• For strong acids and bases: their ions will not react, leaving the solution neutral.
• For weak acids or bases: they can donate or accept hydrogen ions making the solution acidic or basic.

Recognizing the specific behavior of each ion helps in effectively predicting the neutrality of a solution.

acid-base properties

Acid-base properties of ions give insight into why certain salts affect the pH of a solution. These properties depend on whether the ions can donate or accept protons in an aqueous environment.
For example, a cation like NH₄⁺ (ammonium ion) acts as an acid. It can donate a proton to the solution, making it slightly acidic. Conversely, anions such as CN⁻ (cyanide ion) and CO₃^{2-} (carbonate ion) behave as bases. They accept protons from water and increase the concentration of hydroxide ions OH⁻, making the solution basic.
In the case of neutral ionic compounds:

• Cations like K⁺ (potassium ion) and Na⁺ (sodium ion) generally do not affect pH because they do not undergo hydrolysis.
• Similarly, anions like Br⁻ (bromide ion) and Cl⁻ (chloride ion) are very weak bases, causing negligible pH change.

This understanding is imperative for explaining why only certain salts can lead to neutral solutions while others make them acidic or basic.

ionic compounds

Ionic compounds are formed from the electrostatic attraction between cations and anions. They result in the formation of neutral compounds overall, even though individual ions may have an acid or base character.
An ionic compound like potassium bromide ( KBr ) is composed of a neutral cation (K⁺) and an anion (Br⁻) that does not significantly alter pH in solution. This makes the compound neutral in water.
Ionic compounds exhibit:

• Strong ionic bonds, making them usually stable and quite solid at room temperature.
• High melting and boiling points, attributed to the substantial energy required to break the ionic bonds.
• Good solubility in water, enabling them to dissociate into individual ions and participate in acid-base reactions.

By understanding ionic compounds and the behavior of their ions, students can better predict and explain the outcomes of neutralization reactions and pH analysis.