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 Ammonium chloride (NH4Cl). This is because, upon dissociation, it forms a weak acid (NH₄⁺) and a weak base (Cl⁻) that, when combined in equal amounts, neutralize each other, resulting in a neutral solution (pH ≈ 7).

Step-by-step solution

List all the possible combinations of ions in water for each salt given

For each salt, we will write their dissociation reaction with water: 1. KBr: K⁺(aq) + Br⁻(aq) 2. NH4Cl: NH₄⁺(aq) + Cl⁻(aq) 3. KCN: K⁺(aq) + CN⁻(aq) 4. K2CO3: 2K⁺(aq) + CO₃²⁻(aq) Now we have the dissociation reactions for each salt.

Analyze the pH effect of the dissociation products for each salt

Let's analyze the pH effect of each dissociation product: 1. KBr: Potassium ion (K⁺) does not affect the pH. Bromide ion (Br⁻) is a weak base, which means the resultant solution will be basic (pH > 7). 2. NH4Cl: Ammonium ion (NH₄⁺) is a weak acid. Chloride ion (Cl⁻) is a weak base. When a weak acid and a weak base are combined in equal amounts, the solution is neutral (pH ≈ 7). 3. KCN: Potassium ion (K⁺) does not affect the pH. Cyanide ion (CN⁻) is a weak base, which means the resultant solution will be basic (pH > 7). 4. K2CO3: Potassium ion (K⁺) does not affect the pH. Carbonate ion (CO₃²⁻) is a weak acid, which means the resultant solution will be acidic (pH < 7).

Identify the neutral salt

Based on our analysis in Step 2, we can determine that the only salt that produces a neutral solution (pH ≈ 7) when dissolved in water is NH4Cl (Ammonium chloride). Thus, the identity of the unknown neutral salt is Ammonium chloride (NH4Cl).

Key concepts

pH determination

Understanding the pH of a solution is crucial in chemistry, especially when dealing with reactions where the acidity or basicity of the environment can affect the outcome. The pH scale is used to quantify the acidity or alkalinity of a solution. It ranges from 0 to 14, with 7 considered neutral, values lower than 7 acidic, and values higher than 7 basic.

The pH of a solution can be determined by analyzing the properties of the dissolved ions after dissociation. For salts, determining pH involves looking at the acid-base properties of the constituent ions. In the given exercise, the salt that results in a neutral pH (around 7) would not substantially contribute to the formation of hydrogen ions (H+) or hydroxide ions (OH-).

For instance, the ammonium ion (NH₄⁺) is known to slightly release H+ ions into the solution, while chloride ions (Cl⁻) don't significantly contribute to the pH in dilute solutions. As such, a solution containing these ions would be expected to have a pH close to 7. The NH4Cl, therefore, leads to a neutral solution, and its behavior in water is the key to identifying the salt in the given problem.

Salt dissociation reactions

Salts are ionic compounds that can dissociate into their respective positive and negative ions in water. The process of salt dissociation is essential for predicting the resulting pH of a solution. It's this very property of salts that can shift the balance of H+ and OH- ions in a solution, and hence, influence its pH.

Each salt has a unique dissociation reaction in water. For example, potassium bromide (KBr) dissociates into potassium ions (K⁺) and bromide ions (Br⁻). These ions may interact with water to various extents, but it's mainly the acid-base properties of these ions that determine the effect on pH. Some salts, like KBr, have ions that are relatively unreactive with water and therefore have a negligible effect on the pH.

The correct identification of the dissociation products is fundamental to predicting the resulting pH, as seen with KBr, which does not impact pH in contrast to NH4Cl, whose dissociation products lead to a neutral pH solution.

Acid-base properties of ions

Ions can exhibit acid-base properties when dissolved in water. These properties are informed by the Bronsted-Lowry theory of acids and bases, where acids are proton donors and bases are proton acceptors. The behavior of ions in water determines whether they will act as an acid or a base.

For example, the ammonium ion (NH₄⁺) is the conjugate acid of the weak base ammonia (NH₃) and can donate a proton to water, slightly reducing the pH. Conversely, a cyanide ion (CN⁻) is a base that can accept a proton, increasing the pH.

In solutions of salts, these interactions are crucial. If the ion is a weak acid or base, the solution's pH is affected in a way that reflects its dissociation and subsequent reactivity with water. The relationship between the ions and their acid-base properties is what makes pH determination possible, and this is a foundational concept in understanding chemical equilibrium in ionic solutions.