Colligative Properties of Solutions | General Chemistry 2

Solution and solute:

• A solution is a homogeneous mixture where one or more substances (solutes) are uniformly dispersed in another substance (solvent). The solvent typically dictates the phase of the solution, and the particles in a solution are very small, typically less than 1 nanometer in size.
• A solute is the substance that is dissolved in the solvent. The amount of solute relative to the solvent determines the concentration of the solution.
   

In a saltwater solution:

• Salt (sodium chloride, NaCl) is the solute,
• Water (H₂O) is the solvent.

The salt dissolves completely in the water, creating a homogeneous mixture where the salt particles are uniformly distributed at the molecular level.

Saturated, unsaturated, and supersaturated solutions:

• Saturated solution: A solution that contains the maximum amount of solute that can dissolve at a given temperature. Any additional solute added will not dissolve and will remain undissolved in the solution.
• Unsaturated solution: A solution that contains less solute than the maximum amount that can be dissolved at a given temperature. More solute can still be dissolved in the solvent.
• Supersaturated solution: A solution that contains more solute than the solvent can theoretically dissolve at a given temperature. This is an unstable state, and the excess solute can precipitate out of the solution if disturbed.

Colloids:

A colloid is a mixture of a solvent and suspended particles that are larger than those in a true solution but smaller than those in a suspension. The particles in a colloid range in size from 1 to 100 nanometers, making them larger than simple molecules but small enough to remain in suspension and not settle out.

• Hydrophilic colloids: Colloids in which the dispersed particles have an affinity for water. They are usually stable in aqueous solutions.
• Hydrophobic colloids: Colloids in which the dispersed particles do not have an affinity for water. They tend to aggregate and separate from the dispersion medium unless stabilized by surfactants.
   

Hydrophilic colloids: gelatin, starch.

Hydrophobic colloids: oil droplets in water.

Tyndall effect: This is the scattering of light by colloidal particles. It is a characteristic feature of colloids, where a beam of light passing through the colloid becomes visible due to the scattering by the dispersed particles.

Steps in the solution process:

• Step 1 - Solute separation: The first step in the solution process involves breaking the intermolecular forces or ionic bonds within the solute. This step requires energy, known as the lattice energy in ionic compounds or the cohesive energy in molecular solutes. The energy required to separate the solute particles is always endothermic.
• Step 2 - Solvent separation: The solvent molecules must also be separated to create space for the solute particles. This step also requires energy and is endothermic. The solvent molecules must overcome their intermolecular forces, such as hydrogen bonding in water, to make room for the solute.
• Step 3 - Solvation (or hydration in water): The final step involves the interaction between solute particles and solvent molecules. Solvent molecules surround the solute particles, stabilizing them in the solution. This step releases energy, making it an exothermic process.

Enthalpy of solution:

The overall enthalpy change of the solution process (ΔH_solution​) depends on the balance of energy changes in the three steps:
 

• If ΔH_solution < 0: the dissolution process is exothermic, and the solution will release heat.
• If ΔH_solution > 0: the dissolution process is endothermic, and the solution will absorb heat.

Entropy (S) of the solution process:

The dissolution process often leads to an increase in entropy because the solute particles become more dispersed in the solvent. This increase in disorder usually drives the solution process forward, even if the enthalpy change is positive (endothermic).

Molarity (M):

Molarity is defined as the number of moles of solute dissolved in one liter of solution:
 

Mass percent (w/w%):

Mass percent is the mass of the solute divided by the total mass of the solution, multiplied by 100:
 

Volume percent (v/v%):

Volume percent is the volume of the solute divided by the total volume of the solution, multiplied by 100:
 

Mole fraction (χ):

Mole fraction is the ratio of the number of moles of a component to the total number of moles of all components in the solution:
 

Parts per million (ppm) and parts per billion (ppb):

These units are used to express very dilute concentrations of substances. Ppm is the number of parts of solute per million parts of the solution, and ppb is the number of parts of solute per billion parts of the solution.
 

Effect of temperature:

• For most solid solutes, solubility increases as the temperature rises. The increased kinetic energy of the molecules at higher temperatures allows more solute particles to overcome the forces holding them in the solid state, thus dissolving in the solvent.
   

The solubility of sugar in water increases as the temperature is increased. This is why sugar dissolves more quickly in hot water compared to cold water.

• The solubility of gases in liquids typically decreases with an increase in temperature. Higher temperatures provide gas molecules with more energy, allowing them to escape from the solvent into the gas phase more easily.
   

Carbonated beverages, such as soda, lose carbonation more rapidly when they are warm because the solubility of carbon dioxide decreases as the temperature increases.

Effect of pressure:

Pressure significantly affects the solubility of gases in liquids. According to Henry's Law, the solubility of a gas in a liquid is directly proportional to the partial pressure of the gas above the liquid:
 

The Henry's Law constant varies depending on the gas and the solvent, and it typically decreases with increasing temperature. This constant quantifies how much gas will dissolve in the solvent under a given pressure.
 

Carbonated beverages are bottled under high pressure to increase the solubility of carbon dioxide in the liquid. When the bottle is opened, the pressure is released, reducing the solubility of CO₂, which escapes as bubbles, causing the beverage to go flat.

Raoult's law:

Raoult's law states that the vapor pressure of a solvent in an ideal solution is directly proportional to the mole fraction of the solvent in the solution. This law is applicable to solutions where the solute does not volatilize and does not react with the solvent.
 

Vapor-pressure lowering:

When a non-volatile solute is added to a solvent, the solute particles occupy space at the surface of the liquid, reducing the number of solvent molecules that can escape into the vapor phase. As a result, the vapor pressure of the solvent above the solution is lower than that of the pure solvent.

The vapor-pressure lowering (ΔP) can be calculated as:
 

Alternatively, since χ_solute + χ_solvent = 1, we can express the vapor-pressure lowering as:
 

Boiling-point elevation:

Boiling-point elevation (ΔT_b) is the increase in the boiling point of a solvent upon the addition of a non-volatile solute. It is defined as the difference between the boiling point of the solution and the boiling point of the pure solvent:
 

The change in boiling point is directly proportional to the molal concentration of the solute in the solution:
 

Mechanism:

• Lowered vapor pressure: The addition of a non-volatile solute decreases the solvent's vapor pressure because fewer solvent molecules can escape into the vapor phase. As a result, a higher temperature is required for the vapor pressure to equal atmospheric pressure, leading to a higher boiling point.
• Colligative property: Boiling-point elevation is a colligative property, meaning it depends on the number of solute particles in the solution, not the identity of the solute. This property is particularly useful for determining the molar mass of unknown solutes.

Freezing-point depression:

Freezing-point depression (ΔT_f) is the decrease in the freezing point of a solvent when a solute is dissolved in it. It is defined as the difference between the freezing point of the pure solvent and the freezing point of the solution:
 

This effect is proportional to the number of solute particles present in the solution, regardless of their identity:
 

Mechanism:

• Disruption of freezing: The presence of solute particles interferes with the ability of solvent molecules to arrange themselves into a solid crystalline structure. As a result, the temperature must be lowered further to reach the point where the solvent can solidify.
• Colligative property: Freezing-point depression is a colligative property, meaning it depends only on the number of solute particles in the solution and not on their chemical identity.

Semipermeable membrane:

A semipermeable membrane allows only certain molecules, such as solvent molecules, to pass through it while blocking solute particles. This differential permeability creates a natural movement of solvent from the region of lower solute concentration to the region of higher solute concentration.
 

Osmosis:

Osmosis is the process by which solvent molecules move across a semipermeable membrane from a dilute solution (or pure solvent) into a more concentrated solution. This movement continues until the concentrations on both sides of the membrane are equal, or until osmotic pressure is applied to stop the flow.

Osmotic pressure:

Osmotic pressure (Π) is the pressure that must be applied to a solution to prevent the inward flow of water (or another solvent) across a semipermeable membrane. It is directly proportional to the concentration of solute particles in the solution:
 

Osmotic pressure is a colligative property, meaning it depends on the number of solute particles in the solution, not their identity. The more solute particles present, the higher the osmotic pressure.

Electrolytes:

Electrolytes are substances that, when dissolved in water or other solvents, dissociate into ions. These ions are responsible for conducting electricity in the solution. There are 2 types of electrolytes:

• Strong electrolytes: Completely dissociate into ions in solution, resulting in high electrical conductivity.
• Weak electrolytes: Partially dissociate into ions in solution, resulting in lower electrical conductivity.
   

• Sodium chloride (NaCl), potassium hydroxide (KOH), hydrochloric acid (HCl) are strong electrolytes.
• Acetic acid (CH₃COOH), ammonia (NH₃), weak organic acids, and bases are weak electrolytes.

Van 't Hoff factor (i):

The van 't Hoff factor represents the number of particles into which a solute dissociates in solution. It can be expressed as:
 

Thus, i is 1 for all nonelectrolytes, and greater than 1 for strong electrolytes.
 

i (Sucrose): 1; i (NaCl): 2; i (KBr): 2; i (CaCl₂): 3; i (FeCl₃): 4.

Colligative properties of electrolyte solutions:

Electrolyte solutions exhibit colligative properties such as boiling-point elevation, freezing-point depression, and osmotic pressure. The presence of more ions (as in strong electrolytes) amplifies these effects compared to nonelectrolyte solutions. The equations for colligative properties are modified as follows: