The Colligative Properties: Videos & Practice Problems

As solutes are introduced into a pure solvent, transforming it into a solution, the colligative properties—boiling point, freezing point, vapor pressure, and osmotic pressure—are impacted. Boiling point and osmotic pressure increase with the addition of solute, while freezing point and vapor pressure decrease. The Van't Hoff factor (I) is crucial in quantifying these changes, representing the number of particles into which a solute dissociates in solution. Ionic compounds dissociate into multiple ions, thus having a Van't Hoff factor greater than one, whereas covalent compounds, being non-electrolytes, do not dissociate and have an I value of one. The colligative properties are further calculated using osmolarity and osmolality, which incorporate the Van't Hoff factor and the molarity or molality of the solution, respectively. These concepts are essential for predicting how a solution will behave compared to its pure solvent and for calculating the extent of colligative property changes.

Colligative Properties

Colligative properties describe how the addition of a solute to a pure solvent affects the solution's characteristics. When a solute is introduced, certain properties of the solvent change: boiling point and osmotic pressure increase, while freezing point and vapor pressure decrease. Understanding these changes is crucial for grasping the behavior of solutions.

The boiling point is the temperature at which a liquid's vapor pressure equals the atmospheric pressure, leading to a state of equilibrium between the liquid and gas phases. As solute is added, the boiling point elevates due to the disruption of the solvent's ability to vaporize, requiring a higher temperature to reach equilibrium.

In contrast, the freezing point is the temperature at which a solid and liquid coexist in equilibrium. When solute is added, the freezing point decreases, meaning the solution remains liquid at lower temperatures than the pure solvent. This phenomenon is known as freezing point depression.

Vapor pressure refers to the pressure exerted by a vapor in equilibrium with its liquid. The addition of solute lowers the vapor pressure of the solvent, as solute particles occupy space at the surface, reducing the number of solvent molecules that can escape into the vapor phase.

Lastly, osmotic pressure is the pressure required to stop the flow of solvent into a solution through a semipermeable membrane, driven by the movement of water from an area of low solute concentration to an area of high solute concentration. This process is essential in biological systems and various industrial applications.

In summary, the transition from a pure solvent to a solution through solute addition results in increased boiling point and osmotic pressure, while freezing point and vapor pressure decrease. These changes are fundamental to understanding solution behavior and are quantitatively described by specific mathematical relationships that will be explored further.

Boiling Point Elevation Example

Benzene, with the chemical formula \( C_6H_6 \), has a boiling point of 80.1 degrees Celsius. When a solute, such as glucose, is added to a pure solvent like benzene, the boiling point of the solution increases. This phenomenon is known as boiling point elevation, which occurs because the presence of solute particles disrupts the ability of solvent molecules to escape into the vapor phase.The relationship governing boiling point elevation can be expressed using the formula:\[\Delta T_b = i \cdot K_b \cdot m\]where:- \( \Delta T_b \) is the change in boiling point,- \( i \) is the van 't Hoff factor (which is 1 for glucose since it does not dissociate in solution),- \( K_b \) is the ebullioscopic constant of the solvent (for benzene, \( K_b \) is approximately 2.53 °C kg/mol),- \( m \) is the molality of the solute.Given that the boiling point of benzene is 80.1 °C, we can conclude that the boiling point of the solution will be higher than this value. Among the options provided, the only reasonable new boiling point after adding glucose is 89.6 °C. This aligns with the principle that adding solute increases the boiling point, while the other options either suggest no change or a decrease, which contradicts the established behavior of solutions. Thus, the expected boiling point after the addition of glucose is 89.6 °C.

Van't Hoff Factor

The van't Hoff factor, represented by the variable \( i \), quantifies the number of ions produced when a soluble solute dissolves in a solvent. Solutes are categorized as either ionic or covalent. Ionic compounds consist of positive and negative ions, where the positive ion can be a metal or an ammonium ion, and the negative ion is typically a nonmetal. For example, sodium hydroxide (NaOH) dissociates into two ions: \( \text{Na}^+ \) and \( \text{OH}^- \), resulting in a van't Hoff factor of \( i = 2 \).

Ammonium carbonate (NH₄)₂CO₃ breaks down into two ammonium ions and one carbonate ion, yielding a total of three ions, thus \( i = 3 \). Aluminum sulfate (Al₂(SO₄)₃) dissociates into two aluminum ions and three sulfate ions, giving a total of five ions, so \( i = 5 \). This illustrates that for ionic compounds, the van't Hoff factor is determined by the total number of ions produced upon dissolution.

In contrast, covalent compounds, which consist solely of nonmetals, do not dissociate into ions when dissolved. These compounds are characterized as non-volatile and non-electrolytes. Examples include glucose, chlorine, methanol, and urea. Since covalent solutes do not produce ions, their van't Hoff factor is always \( i = 1 \). This means that even though they do not break into ions, they are still counted as one entity in solution.

In summary, understanding the distinction between ionic and covalent solutes is crucial for accurately determining the van't Hoff factor. Ionic compounds yield multiple ions, while covalent compounds remain intact, leading to a consistent van't Hoff factor of one for the latter.

Van't Hoff Factor Example

To determine which compound has the largest Van't Hoff factor (i), we need to analyze how each compound dissociates in solution. The Van't Hoff factor represents the number of particles into which a compound dissociates in solution.

Starting with aluminum chloride (AlCl₃), this ionic compound dissociates into one aluminum ion (Al³⁺) and three chloride ions (Cl^-), resulting in a total of four ions. Therefore, the Van't Hoff factor (i) for aluminum chloride is 4.

Next, we consider a covalent compound, which consists solely of nonmetals. Such compounds do not dissociate into ions, so their Van't Hoff factor is 1.

For zinc oxide (ZnO), which is an ionic compound, it dissociates into one zinc ion (Zn²⁺) and one oxide ion (O^2-), giving a total of two ions. Thus, the Van't Hoff factor for zinc oxide is 2.

Ammonia (NH₃) is also a covalent compound and does not dissociate into ions, resulting in a Van't Hoff factor of 1. Similarly, phosphorus pentasulfide (P₂S₅) is a covalent compound with a Van't Hoff factor of 1.

In summary, the compound with the highest Van't Hoff factor is aluminum chloride (AlCl₃), with a value of 4, indicating it produces the most particles in solution compared to the other compounds analyzed.

Colligative Properties

Colligative properties are essential concepts in chemistry that describe how the properties of a solvent change when a solute is added. As more solute is introduced, the boiling point and osmotic pressure of the solution increase, while the freezing point and vapor pressure decrease. This relationship highlights the importance of the amount of solute, which is quantified by the van't Hoff factor (I). The van't Hoff factor represents the number of particles (ions) that a solute dissociates into when dissolved.

To calculate the effects of solute on colligative properties, we can use the formulas for osmolarity and osmolality. Osmolarity (Osm) is defined as:

$$\text{Osmolarity} = I \times \text{Molarity}$$

where I is the van't Hoff factor and Molarity is the concentration of the solute in moles per liter. Similarly, osmolality (Osm) is given by:

$$\text{Osmolality} = I \times \text{Molality}$$

where Molality is the concentration of the solute in moles per kilogram of solvent. Both osmolarity and osmolality are crucial for determining the total concentration of solute particles in a solution, which in turn influences the boiling point elevation and freezing point depression.

Understanding these concepts allows for the prediction of which solutions will exhibit higher boiling points or lower freezing points based on the amount and type of solute present. This knowledge is particularly useful in various applications, including biological systems and industrial processes.

Ionic Molality Example

To determine the ionic molality of potassium ions in a 1.18 molal solution of potassium phosphate, we first need to understand the dissociation of potassium phosphate in solution. Potassium phosphate dissociates into three potassium ions (K⁺) and one phosphate ion (PO₄³⁻). The formula for calculating ionic molality is given by:\[\text{Ionic Molality} = \text{Number of ions} \times \text{Molality of the compound}\]In this case, potassium phosphate produces a total of four ions (3 K⁺ and 1 PO₄³⁻). However, since we are specifically interested in the potassium ions, we focus on the three potassium ions.Given that the molality of the potassium phosphate solution is 1.18 molal, we can calculate the ionic molality of potassium ions as follows:\[\text{Ionic Molality of K⁺} = 3 \times 1.18 \, \text{molal} = 3.54 \, \text{molal}\]Thus, the ionic molality of potassium ions in the solution is 3.54 molal. This calculation highlights the importance of understanding ionic dissociation in solutions and how it affects the concentration of individual ions.

Which of the following compounds will have the highest boiling point?

• A. 0.10 M sucrose
• B. 0.10 M AgCl
• C. 0.25 M NH₄NO₃
• D. 0.45 M pure water

Answer: (C)

Which of the following compound will have the highest vapor pressure?

• A. 0.45 m dinitrogen pentoxide
• B. 0.10 m aluminum chloride
• C. 0.50 m iron (III) perchlorate
• D. 0.15 m calcium phosphate
• E. 0.30 m Potassium sulfide

Answer: (B)

Here’s what students ask on this topic:

What are the colligative properties?

Colligative properties are characteristics of solutions that depend on the number of dissolved particles in the solution, rather than the identity of the solute molecules. These properties arise because the presence of solute particles affects the properties of the solvent. There are four main colligative properties:

1. Vapor Pressure Lowering: The presence of a non-volatile solute reduces the vapor pressure of the solvent. This happens because solute particles occupy space at the surface of the liquid, making it harder for solvent molecules to escape into the gas phase.
2. Boiling Point Elevation: The boiling point of a solvent will be higher when a solute is dissolved in it. This occurs because the lower vapor pressure requires more heat to reach the boiling point.
3. Freezing Point Depression: The freezing point of a solvent is lowered when a solute is dissolved in it. This is because the solute particles disrupt the formation of the solid structure of the solvent, requiring a lower temperature to solidify.
4. Osmotic Pressure: This is the pressure required to stop the flow of the solvent into the solution through a semipermeable membrane. It is directly proportional to the concentration of the solute particles in the solution.

Understanding these properties is important in fields like chemistry, biology, and engineering, as they influence various processes and applications.