The Colligative Properties: Videos & Practice Problems

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 defined as the temperature at which a liquid's vapor pressure equals the external pressure, leading to a phase transition from liquid to gas. 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 liquid becomes a solid, occurring when the rates of melting and freezing are equal. The presence of solute lowers the freezing point, a phenomenon known as freezing point depression, as solute particles interfere with the formation of a solid structure.

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

Finally, 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 can be explored further.

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 the van't Hoff factor for ionic compounds 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 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.

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, which is crucial for understanding colligative properties such as boiling point elevation and freezing point depression.

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:

i = 4

Next, we consider a covalent compound, which consists solely of nonmetals. Such compounds do not dissociate into ions in solution, leading to a Van't Hoff factor of:

i = 1

For zinc oxide (ZnO), which is ionic, 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:

i = 2

Ammonia (NH₃) is also a covalent compound and does not dissociate into ions, resulting in:

i = 1

Lastly, phosphorus pentasulfide (P₂S₅) is another covalent compound, which similarly does not dissociate, yielding:

i = 1

Comparing all the calculated Van't Hoff factors, aluminum chloride has the highest value at:

i = 4

Thus, the compound with the largest Van't Hoff factor is aluminum chloride (option A).

Colligative properties are essential concepts in chemistry that describe how the addition of solute affects the physical properties of a solvent. When more solute is added, properties such as boiling point and osmotic pressure increase, while freezing point and vapor pressure decrease. The extent of these changes is influenced by the number of particles (ions) that the solute dissociates into, which is quantified by the van't Hoff factor (I).

The relationship between the amount of solute and its effect on colligative properties can be expressed through two key formulas: osmolarity and osmolality. Osmolarity refers to the concentration of solute particles in a solution and is defined as:

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

Here, I represents the number of ions produced by the solute, and molarity is the concentration of the solute in moles per liter. Similarly, osmolality, which is the concentration of solute particles in a solvent, is given by:

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

In this case, molality refers to the concentration of the solute in moles per kilogram of solvent. Understanding these concepts allows for the determination of how different solutes will affect boiling and freezing points, enabling predictions about which solutions will exhibit higher or lower colligative property values.

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 (PO₄^3-). This means that for every formula unit of potassium phosphate, there are a total of four ions produced: three potassium ions and one phosphate ion.

The ionic molality can be calculated using the formula:

Ionic Molality = Number of Ions × Molality of the Compound

In this case, the number of potassium ions is 3, and the molality of the potassium phosphate solution is 1.18 molal. Therefore, we can calculate the ionic molality of potassium ions as follows:

Ionic Molality = 3 × 1.18 molal = 3.54 molal

Thus, the ionic molality of potassium ions in the solution is 3.54 moles per kilogram of solvent.