Problem 13 - Chemistry in 30 days

Question

Which of the following aqueous solutions has the highest boiling point ? (a) \(0.1 \mathrm{M} \mathrm{KNO}_{3}\) (b) \(0.1 \mathrm{M} \mathrm{Na}_{3} \mathrm{PO}_{4}\) (c) \(0.1 \mathrm{M} \mathrm{BaCl}_{2}\) (d) \(0.1 \mathrm{M} \mathrm{K}_{2} \mathrm{SO}_{4}\)

Step-by-Step Solution

Answer

The solution with the highest boiling point is \(0.1 \mathrm{M} \mathrm{Na}_3 \mathrm{PO}_4\).

Step 1: Understand the Concept

The boiling point of a solution is affected by the number of solute particles in the solution. This is explained by the colligative property known as boiling point elevation. The formula for the change in boiling point, 9T_b, is given by: \[9T_b = i b m\]where 9T_b is the boiling point elevation, \(K_b\) is the ebullioscopic constant, \(m\) is the molality of the solution, and \(i\) is the van't Hoff factor which represents the number of particles the compound dissociates into in solution.

Step 2: Identify Van't Hoff Factor

Determine the van't Hoff factor (\(i\)) for each compound, which represents the number of ions into which the compound dissociates:- \(\text{KNO}_3\) dissociates into 2 ions: \(\text{K}^+\) and \(\text{NO}_3^-\), so \(i = 2\).- \(\text{Na}_3\text{PO}_4\) dissociates into 4 ions: 3 \(\text{Na}^+\) and 1 \(\text{PO}_4^{3-}\), so \(i = 4\).- \(\text{BaCl}_2\) dissociates into 3 ions: 1 \(\text{Ba}^{2+}\) and 2 \(\text{Cl}^-\), so \(i = 3\).- \(\text{K}_2\text{SO}_4\) dissociates into 3 ions: 2 \(\text{K}^+\) and 1 \(\text{SO}_4^{2-}\), so \(i = 3\).

Step 3: Compare Boiling Point Elevations

Using the understanding that boiling point elevation is greater with a higher van't Hoff factor (since the ebullioscopic constant and concentration are the same for all solutions): - \(\text{Na}_3\text{PO}_4\) has the highest \(i\) (4), meaning its solution has the highest boiling point elevation. - The other solutions \(\text{KNO}_3, \text{BaCl}_2,\) and \(\text{K}_2\text{SO}_4\) have lower van't Hoff factors (2 and 3), resulting in lesser boiling point elevations.

Key Concepts

Colligative Properties

Colligative properties are foundational concepts in chemistry that help explain how the properties of solutions change when solutes are added. These properties are unique because they depend on the number of solute particles in a given amount of solvent, rather than the specific type of particles. This means that whether you're adding sodium chloride or glucose to water, the effect on the solution's boiling point or freezing point is determined by the quantity of dissolved particles, not their identity.

Key colligative properties include:

• Boiling Point Elevation: Solutions boil at higher temperatures than the pure solvent.
• Freezing Point Depression: Solutions freeze at lower temperatures than the pure solvent.
• Osmotic Pressure: Solutions exert pressure on a semipermeable membrane.
• Vapor Pressure Lowering: Solutions have a lower vapor pressure than the pure solvent.

Boiling point elevation, in particular, is a direct application of colligative properties. When you dissolve a solute in a solvent, such as salt in water, the solution's boiling point increases. The amount of increase is described by the equation \(\Delta T_b = iK_bm\), where \(\Delta T_b\) is the change in boiling point, \(i\) is the Van't Hoff factor, \(K_b\) is the ebullioscopic constant of the solvent, and \(m\) is the molality of the solution.

Van't Hoff Factor

The Van't Hoff factor, denoted as \(i\), plays a crucial role in determining the changes in colligative properties when a solute is dissolved in a solvent. This factor represents the number of particles a solute dissociates into in solution. For instance, sodium chloride (\(\text{NaCl}\)) dissociates completely into two ions: \(\text{Na}^+\) and \(\text{Cl}^-\), giving it a Van't Hoff factor of 2.

Understanding the Van't Hoff factor is essential for predicting how different substances will affect the boiling and freezing points of solutions. It directly influences how much a solution's properties, such as boiling point or freezing point, will change compared to the pure solvent.

Examples include:

• \(\text{KNO}_3\) with \(i = 2\), as it breaks into two ions.
• \(\text{Na}_3\text{PO}_4\) with \(i = 4\), as it dissociates into four ions.
• \(\text{BaCl}_2\) with \(i = 3\), providing three ions.
• \(\text{K}_2\text{SO}_4\) with \(i = 3\), splitting into three ions.

Higher values of \(i\) indicate a greater number of particles in solution, resulting in more pronounced colligative property changes. Therefore, substances with a higher Van't Hoff factor cause greater boiling point elevations.

Aqueous Solutions

Aqueous solutions are solutions where water acts as the solvent. They are ubiquitous in chemistry and everyday life, forming the basis for countless chemical reactions and processes. Water, being a solvent with unique polar properties, effectively dissolves various types of solutes, making it crucial for more effective chemical education and experimentation.

Important characteristics of aqueous solutions include:

• Solubility: Water can dissolve ionic compounds by separating the positive and negative ions, as well as polar covalent compounds.
• Concentration: The amount of solute dissolves in a given volume of water, measured in units like molarity (M), affecting how solutions behave.
• Electrical Conductivity: Ionic solutions can conduct electricity due to the presence of free-moving ions.
• Temperature Dependence: The solubility of gases and some solids in water varies with temperature.

In the study of boiling point elevation, aqueous solutions are often used to demonstrate the practical applications of colligative properties. Through simple solutions, students can observe how adding certain salts or compounds to water can affect its boiling point, providing a tangible way to grasp theoretical concepts.

Chemistry Education

Chemistry education covers a broad range of topics and requires effective methods to teach complex concepts, such as colligative properties and the Van’t Hoff factor. Educators employ various strategies to make these topics more understandable for students. These include practical experiments, visual aids, and real-life examples.

Effective chemistry education can involve:

• Hands-on Experiments: Like salt in water to observe boiling point elevation.
• Visual Aids: Diagrams showing molecular interactions and dissociation of solutes.
• Relating to Real Life: Connecting chemical principles to everyday phenomena, such as why salt is used on icy roads.
• Step-by-Step Problem Solving: Breaking down complex calculations into clear, manageable steps.

By incorporating these methods, students not only understand the concepts academically but also appreciate their practical applications. For instance, grasping why boiling point changes with solutes helps in culinary applications and in understanding natural processes such as ocean salinity's effect on weather patterns. This comprehensive educational approach ensures students gain a well-rounded understanding of chemistry and its significance in both science and everyday life.