Solutions and Mixtures Overview

Solutions: Mixing It Up

• Matter encountered in daily life are mixtures
• Mixtures can be solid (e.g., a porch chair), liquid (e.g., coffee) or gaseous (e.g., air)
• Air is a mixture of N₂, O₂, CO₂, and other elements
• Coffee is a mixture containing cellulose, sugars, and water

Solutions: Homogeneous Mixtures

• Solutions are homogeneous mixtures of two or more pure substances
• Each substance in a solution is a component
• The solvent is the component present in the greatest amount
• All other components are solutes, uniformly dispersed throughout the solvent
• Aqueous solutions have water as the solvent, with either gas, liquid or solid as the solute

Saturated Solutions and Solubility

• A saturated solution holds the maximum amount of solute possible at a given temperature
• Additional solute will not dissolve in a saturated solution
• Solubility is the maximum amount of solute that can dissolve in a given amount of solvent at a specific temperature
• Example: the solubility of NaCl in H₂O at 0°C is 35.7 g per 100 mL of water

Types of Solutions

Unsaturated

• An unsaturated solution contains less solute than the solvent can dissolve at that temperature
• A solution containing 10g of NaCl per 100mL of water at 0°C is unsaturated, meaning more solute can be dissolved.

Supersaturated

• In a supersaturated solution, the solvent holds more solute than is normally possible at that temperature
• These solutions are unstable and crystallization can be stimulated by adding a "seed crystal" or scratching the sides of the container
• Rock candy grows when a string is suspended in a supersaturated sugar solution

Ways of Expressing Solution Concentrations

Mass Percentage

• Mass % of A = (mass of A in solution/total mass of solution) * 100
• Example: vinegar is a 5% by mass solution of acetic acid in water.

Parts per Million (ppm) and Parts per Billion (ppb)

• ppm = (Mass of A in solution/Total mass of solution) * 10⁶
• ppb = (Mass of A in solution /Total mass of solution) * 10⁹

Mole Fraction (X)

• Xₐ = (moles of A/total moles of all components)
• Mole fractions have no units
• The sum of the mole fractions of all components equals 1
• Example: 1 mole of HCl and 8 moles of H₂O in a solution has a mole fraction of X_HCl = 0.111 and X_H₂O = 0.889.

Molarity (M)

• M = (moles of solute/liters of solution)
• Molarity is temperature-dependent

Molality (m)

• m = (moles of solute/kilograms of solvent)
• Molality is not temperature-dependent

The Solution Process

• The ability of substances to form solutions depends on two factors

1. The natural tendency of substances to mix and spread into larger volumes
2. The types of intermolecular interactions involved in solution processes

Entropy of Solutions

• Entropy, is related to the number of ways a system can disperse its energy, related to the freedom of motion of the particles.
• In solids, particles are fixed, little freedom of motion
• In liquids, particles move around each other, greater freedom of motion
• In gases, particles have little restriction, much more freedom of motion
• The more freedom of motion, the more ways they can distribute their energy; thus S_gas > S_liquid > S_solid.
• Solution formation involves a change in entropy; usually a solution has higher entropy than the pure solute and pure solvent.
• There are more interactions when solute and solvent mix than when they are pure.

Intermolecular Forces on Solution Formation

• Gases spontaneously mix, but liquid and solid solvents and solutes involve intermolecular forces that determine whether a solution forms.
• Miscibility implies that liquids mix in all proportions, while immiscibility means that they do not mix.
• Factors affecting solubility of solutes in solvents are:
  1. Solute-solute interactions
  2. Solvent-solvent interactions
  3. Solvent-solute interactions (solvation)

Energetics of Solution Formation

• Solution formation involves changes in enthalpy (heat)
• Solutions can be exothermic (release heat) or endothermic (absorb heat)
• Three factors affecting enthalpy changes are: separation of solute, separation of solvent, and new interactions between solute and solvent

Hot/Cold Packs

• Hot packs utilize exothermic solution processes (releasing heat)
• Cold packs utilize endothermic solution processes (absorbing heat)

Colligative Properties

• Physical properties of solutions that depend on the number of solute particles, not their identity
• Examples: vapor-pressure lowering, boiling-point elevation, freezing-point depression, osmotic pressure

Vapor-Pressure Lowering

• When a non-volatile solute is added to a solvent, the vapor pressure of the solvent decreases
• Fewer solvent molecules have enough energy to escape into the gaseous phase because of solute-solvent interactions

Raoult's Law

• The vapor pressure of a solution is proportional to the mole fraction of the solvent and the vapor pressure of the pure solvent
• P_solution = X_A * P_A

Boiling-Point Elevation

• The presence of a non-volatile solute in a solvent raises the boiling point of the solution above that of the pure solvent. This occurs because higher solute concentrations in the solution make it more difficult for the solvent to escape into the gaseous phase

Freezing-Point Depression

• The presence of a non-volatile solute in a solvent lowers the freezing point of the solution below that of the pure solvent, as solute particles interfere with solvent molecules' ability to form a crystal structure
• The change in freezing point is calculated using the equation ΔTf = - i * Kf * m

Osmosis

• Osmosis is the movement of solvent molecules across a semipermeable membrane from an area of higher solvent concentration (lower solute concentration) to an area of lower solvent concentration (higher solute concentration to equalize the solute concentrations on both sides of the membrane)
• Osmotic pressure is the pressure required to stop osmosis.