Problem 96 - Chemistry The Molecular Nature of Matter

Question

What is the expected van't Hoff factor for \(\mathrm{K}_{2} \mathrm{SO}_{4}\) in an aqueous solution, assuming \(100 \%\) dissociation?

Step-by-Step Solution

Answer

The expected van't Hoff factor (i) for \( \mathrm{K}_{2} \mathrm{SO}_{4} \) is 3.

Step 1: Understanding the van't Hoff factor

The van't Hoff factor (i) indicates the number of particles a compound splits into when it dissolves in solution. For complete dissociation, the factor equals the number of ions formed from one formula unit of the substance.

Step 2: Writing the dissociation equation

Write the chemical equation for the complete dissociation of \( \mathrm{K}_{2} \mathrm{SO}_{4} \) in water: \[ \mathrm{K}_{2} \mathrm{SO}_{4} \rightarrow 2\mathrm{K}^{+} + \mathrm{SO}_{4}^{2-} \].

Step 3: Calculating the van't Hoff factor

Count the total number of ions produced from the dissociation of one formula unit of \( \mathrm{K}_{2} \mathrm{SO}_{4} \). In this case, 2 potassium ions (\(2\mathrm{K}^{+}\)) and 1 sulfate ion (\(\mathrm{SO}_{4}^{2-}\)) give a total of 3 ions.

Key Concepts

Dissociation in Aqueous Solution

To comprehend the behavior of compounds like potassium sulfate (\( \text{K}_2\text{SO}_4 \) in water, we must first recognize the concept of dissociation in aqueous solution. When a substance dissolves in water, it may separate into its constituent ions—a process known as dissociation. This is fundamental to understanding solutions of electrolytes, which are substances that conduct electricity when dissolved in water.

Dissociation in aqueous solutions is influenced by the nature of the solute (substance being dissolved) and solvent (water in this case) interactions. For instance, certain ionic compounds, like table salt (\( \text{NaCl} \) dissolve in water and dissociate almost completely into (\( \text{Na}^\text{+} \) and (\( \text{Cl}^\text{-} \) ions. In contrast, molecular compounds may not dissociate at all since they form covalent bonds that do not typically produce ions in solutions.

For educational clarity, visualize a crystal of an ionic compound entering water and the ions gradually pulling apart and dispersing throughout the solution. This process is crucial for numerous biological and chemical processes, such as nerve function, where electrolytes must be present in the body for the transmission of electrical impulses.

Chemical Equation

A chemical equation provides a symbolic representation of a chemical reaction, where reactants are transformed into products. Understanding how to write a chemical equation is essential for grasping chemical processes like dissolution and reaction mechanisms.

In the given problem, we encounter the equation for the dissolution of potassium sulfate, where the chemical formula (\( \text{K}_2\text{SO}_4 \) represents the reactants, and the ions produced upon dissociation represent the products. Writing a balanced chemical equation involves ensuring that the number of atoms for each element is the same on both sides of the reaction arrow, following the law of conservation of mass.

Example of a Dissociation Equation

• \( \text{K}_2\text{SO}_4(s) \rightarrow 2\text{K}^\text{+}(aq) + \text{SO}_4^\text{2-}(aq) \)

This step is not only about balancing charges and atoms but also facilitates a visual understanding of the dissociation process and the ratio in which the ions are produced. Mastery of the skill to interpret and write chemical equations significantly improves the understanding of various concepts in chemistry.

Electrolyte Dissociation

Electrolytes are substances that, when dissolved in water, produce a solution that can conduct electricity. Electrolyte dissociation refers to the separation of an electrolyte into its constituent ions in an aqueous solution. Depending on the degree to which the substance dissociates, electrolytes can be classified as strong or weak.

Strong electrolytes, such as \(\text{K}_2\text{SO}_4\), dissociate completely into ions in solution, leading to a higher conductivity. This is because the movement of ions conducts electricity in the solution. In the provided example, each molecule of \(\text{K}_2\text{SO}_4\), a strong electrolyte, dissociates to form three ions which can each carry charge through the solution.

On the other hand, weak electrolytes do not dissociate completely and exist in the solution as a combination of ions and undissociated molecules. This results in fewer charged particles and hence, reduced conductivity. Acetic acid (\( \text{CH}_3\text{COOH} \) is a common example of a weak electrolyte.

Understanding the process of electrolyte dissociation is essential in fields such as medicine, physiology, and any scenario involving the chemistry of solutions. Assessing whether a substance will be a strong or weak electrolyte can impact decisions in manufacturing, the formulation of medications, and the treatment of electrolyte imbalances in the human body.