Question

From the following: Pure water solution of \(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}(m=0.01)\) in water solution of \(\mathrm{NaCl}(m=0.01)\) in water solution of \(\mathrm{CaCl}_{2}(m=0.01)\) in water Choose the one with the a. highest freezing point. b. lowest freezing point. c. highest boiling point. d. lowest boiling point. e. highest osmotic pressure.

Short answer

a. Highest freezing point: pure water b. Lowest freezing point: \(\mathrm{CaCl}_{2}\) solution c. Highest boiling point: \(\mathrm{CaCl}_{2}\) solution d. Lowest boiling point: pure water e. Highest osmotic pressure: \(\mathrm{CaCl}_{2}\) solution

Step-by-step solution

Define the colligative properties

Colligative properties include freezing point depression, boiling point elevation, and osmotic pressure. These properties depend on the number of solute particles when considering a fixed amount of solvent.

Identify the number of solute particles in each solution

Determine the number of particles each solute dissociates into when dissolved in water. 1. Pure water does not have any solute particles. 2. \(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\) is a non-electrolyte, so it doesn't dissociate in water and hence contributes as 1 particle. 3. \(\mathrm{NaCl}\) is an electrolyte and dissociates into 2 ions: Na⁺ and Cl⁻, thus contributes as 2 particles. 4. \(\mathrm{CaCl}_{2}\) is an electrolyte and dissociates into 3 ions: Ca²⁺ and 2Cl⁻, thus contributes as 3 particles.

Highest and lowest freezing points

A higher number of solute particles results in a greater depression of the freezing point. a. Highest freezing point: pure water (0 solute particles) b. Lowest freezing point: \(\mathrm{CaCl}_{2}\) solution (3 solute particles)

Highest and lowest boiling points

A higher number of solute particles results in a greater elevation of the boiling point. c. Highest boiling point: \(\mathrm{CaCl}_{2}\) solution (3 solute particles) d. Lowest boiling point: pure water (0 solute particles)

Highest osmotic pressure

Osmotic pressure is greater when there are more solute particles in a solution. e. Highest osmotic pressure: \(\mathrm{CaCl}_{2}\) solution (3 solute particles) In summary: a. Highest freezing point: pure water b. Lowest freezing point: \(\mathrm{CaCl}_{2}\) solution c. Highest boiling point: \(\mathrm{CaCl}_{2}\) solution d. Lowest boiling point: pure water e. Highest osmotic pressure: \(\mathrm{CaCl}_{2}\) solution

Key concepts

Freezing Point Depression

Freezing point depression is a phenomenon that occurs when a solute is added to a solvent, resulting in the lowering of the freezing point of the solvent. This is a key colligative property, which means it depends on the number, not the type, of solute particles present. In the context of the exercise, freezing point depression is observed in solutions like

• Sucrose solution (\(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\)), which doesn't dissociate and counts as one solute particle.
• Sodium chloride (\(\mathrm{NaCl}\)) solution, which dissociates into two ions, Na⁺ and Cl⁻, thereby contributing two solute particles.
• Calcium chloride (\(\mathrm{CaCl}_{2}\)) solution, which dissociates into three ions, Ca²⁺ and two Cl⁻, contributing the most solute particles.

The greater the number of solute particles, the more the freezing point decreases. In the exercise, the pure water has the highest freezing point at 0 solute particles, and the calcium chloride solution has the lowest due to its dissociation into more particles. Understanding these interactions is essential in fields like chemistry and biology where solutions are frequently used.

Boiling Point Elevation

Boiling point elevation is the opposite of freezing point depression. When a solute is added to a solvent, the boiling point of the solution is increased, another colligative property. This happens because the presence of solute particles disrupts the boiling process, requiring more energy (heat) to achieve the boiling state.
For example, when considering solutions from the exercise:

• Pure water, with no solute particles, has the lowest boiling point.
• Sucrose (\(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\)) solution, with just one solute particle, raises the boiling point slightly.
• Salt (\(\mathrm{NaCl}\)) solution increases it further due to its two dissociating ions.
• Calcium chloride (\(\mathrm{CaCl}_{2}\)) solution has the highest boiling point elevation because it dissociates into three ions.

The more particles present, the more substantial the elevation in boiling point. Therefore, the calcium chloride solution shows the highest boiling point among the options provided in the exercise.

Osmotic Pressure

Osmotic pressure is another important colligative property that is influenced by the amount of solute particles in a solution. It is the pressure exerted by the solute particles when they are separated by a semipermeable membrane from pure solvent, striving to become evenly distributed.
Let's consider the solutions listed in the exercise:

• Sucrose (\(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\)), as a non-electrolyte, has a lower osmotic pressure than electrolytic solutions.
• Solutions like \(\mathrm{NaCl}\) increase the osmotic pressure with their two ions.
• The highest osmotic pressure is observed in the \(\mathrm{CaCl}_{2}\) solution because it dissociates into three ions, the most among the examples stated.

This property is crucial in biological processes such as cell function and water regulation, where concentrations within and outside cells need careful control to maintain health and function. The connection between solute concentration and osmotic pressure illustrates why the \(\mathrm{CaCl}_{2}\) solution exhibits the highest osmotic pressure in this exercise.