Problem 49 Describe four colligative proper... [FREE SOLUTION]

Chapter 14: Problem 49

Describe four colligative properties of solutions.

Short Answer

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The four colligative properties of solutions are: 1. Vapor Pressure Lowering: The vapor pressure of a solution is lower than that of the pure solvent due to the presence of solute particles. This can be described by Raoult's Law: \(P_{solution} = P^{\circ}_{solvent} \cdot x_{solvent}\). 2. Freezing Point Depression: The freezing point of a solution is lower than that of the pure solvent because solute particles interfere with the crystallization process. The freezing point depression can be calculated as \(\Delta T_f = K_f \cdot m\). 3. Boiling Point Elevation: The boiling point of a solution is higher than that of the pure solvent due to the presence of solute particles, which increases the energy required for phase transition. The boiling point elevation can be calculated as \(\Delta T_b = K_b \cdot m\). 4. Osmotic Pressure: The pressure required to prevent the flow of solvent across a semipermeable membrane. Osmotic pressure can be calculated using the equation \(\pi = nRT \cdot \frac{N_{solute}}{V}\).

Step by step solution

1. Vapor Pressure Lowering

Vapor pressure lowering occurs when a non-volatile solute is dissolved in a volatile solvent. Because the solute particles occupy space on the surface of the solvent, there are fewer solvent molecules available to escape into the vapor phase, resulting in a lower vapor pressure. The effect can be described using Raoult's Law, which states that the vapor pressure of a solution is directly proportional to the mole fraction of the solvent: \[ P_{solution} = P^{\circ}_{solvent} \cdot x_{solvent} \] where \(P_{solution}\) is the vapor pressure of the solution, \( P^{\circ}_{solvent}\) is the vapor pressure of the pure solvent, and \(x_{solvent}\) is the mole fraction of the solvent in the solution.

2. Freezing Point Depression

Freezing point depression occurs when a solute is dissolved in a solvent, leading to a lower freezing point compared to the pure solvent. The solute particles interfere with the crystallization process of the solvent, reducing the temperature at which the solution freezes. The freezing point depression can be calculated using the following equation: \[ \Delta T_f = K_f \cdot m \] where \(\Delta T_f\) is the freezing point depression, \(K_f\) is the cryoscopic constant of the solvent, and \(m\) is the molality of the solute.

3. Boiling Point Elevation

Boiling point elevation occurs when a solute is dissolved in a solvent, leading to a higher boiling point compared to the pure solvent. The presence of solute particles in the solution increases the amount of energy required for the solvent molecules to transition from the liquid to vapor phase. The boiling point elevation can be calculated using the following equation: \[ \Delta T_b = K_b \cdot m \] where \(\Delta T_b\) is the boiling point elevation, \(K_b\) is the ebullioscopic constant of the solvent, and \(m\) is the molality of the solute.

4. Osmotic Pressure

Osmotic pressure refers to the pressure that must be applied to a solution to prevent the flow of solvent across a semipermeable membrane. This property is important in many biological systems, where fluid balance and transport are regulated by osmotic pressure. The osmotic pressure of a solution can be described by the following equation: \[ \pi = nRT \cdot \frac{N_{solute}}{V} \] where \(\pi\) is the osmotic pressure, \(n\) is the number of particles produced by each solute molecule (e.g., ions or molecules), \(R\) is the ideal gas constant, \(T\) is the temperature in Kelvin, \(N_{solute}\) is the amount of solute in moles, and \(V\) is the volume of the solution.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Vapor Pressure Lowering

When a non-volatile solute dissolves into a volatile solvent, the ability of solvent molecules to escape into the vapor phase is reduced. This phenomenon is known as vapor pressure lowering. Essentially, solute particles take up space at the surface of the solution, decreasing the number of solvent molecules that can vaporize. This results in a decrease in the vapor pressure of the solution compared to that of the pure solvent.

Vapor pressure lowering can be explained using Raoult's Law, which relates the vapor pressure of a solution to the mole fraction of the solvent:

It shows that the vapor pressure of the solution (\[P_{solution}\]) is directly proportional to the vapor pressure of the pure solvent (\[P^{\circ}_{solvent}\]) and the mole fraction of the solvent (\[x_{solvent}\]).

Raoult's Law captures how less solvent vaporizes in the presence of solute, which is especially crucial when studying colligative properties in chemistry.

Freezing Point Depression

Freezing point depression is the process by which the freezing point of a solvent is lowered when a solute is dissolved in it. This occurs because solute particles disrupt the formation of a solid lattice structure necessary for freezing. As a result, a lower temperature is needed to achieve the freezing point.

The extent to which the freezing point is lowered can be calculated using the equation:

The freezing point depression (\[\Delta T_f\]) is equal to the cryoscopic constant (\[K_f\]) of the solvent multiplied by the molality (\[m\]) of the solute.

This principle is widely applied in real life, such as when salt is spread on icy roads to melt ice by lowering the freezing point of water.

Boiling Point Elevation

Boiling point elevation happens when a solute is added to a solvent, leading to an increase in the boiling point of the solution compared to the pure solvent. Basically, solute particles require additional energy for the solvent molecules to overcome atmospheric pressure and turn into a gas, hence the increase in boiling point.

The boiling point elevation can be calculated using:

The boiling point elevation (\[\Delta T_b\]) is determined by the product of the ebullioscopic constant (\[K_b\]) and the molality (\[m\]) of the solute.

This concept is used in kitchen activities like adding salt to water when cooking pasta, as it helps increase the water's boiling point leading to a more efficient cooking process.

Osmotic Pressure

Osmotic pressure is a critical colligative property that represents the pressure required to stop the flow of solvent through a semipermeable membrane. It tends to occur naturally when lower concentration solutions move towards higher concentration solutions to equalize concentrations on either side of the membrane.

Osmotic pressure is calculated using:

The equation \[\pi = nRT \cdot \frac{N_{solute}}{V}\], where \[\pi\] is the osmotic pressure, \[n\] is the number of particles each solute molecule forms, \[R\] is the ideal gas constant, \[T\] is the temperature in Kelvin, \[N_{solute}\] is the amount of solute in moles, and \[V\] is the volume of the solution.

This property is crucial in biological systems, affecting cell liquid balance and nutrient transport, making osmotic pressure essential in life sciences.

91影视

Describe four colligative properties of solutions.

Short Answer

Step by step solution

1. Vapor Pressure Lowering

2. Freezing Point Depression

3. Boiling Point Elevation

4. Osmotic Pressure

Key Concepts

Vapor Pressure Lowering

Freezing Point Depression

Boiling Point Elevation

Osmotic Pressure

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