Unit 11

Class Learning Objectives

• Solubility, Dissolution, and Solubility Curves

• Molality and Concentration Units

• Calculating Concentrations

• Henry ’s Law

• Raoult ’s Law

• Practice Problems

• Colligative Properties - Vapor Pressure Lowering

  • Freezing Point Depression

  • Boiling Point Elevation

  • Osmotic Pressure

Solutions

• Definition: Solutions are homogeneous mixtures composed of two or more different chemical substances.

• A solution may consist of different phases of substances, including:- A solid and a liquid

  • A gas and a liquid

  • A gas with another gas

• Components of a Solution:- Majority Component: Solvent

  • Minority Component: Solute

• Solubility: When one substance (solute) dissolves in another (solvent), it is said to be soluble.

• Formation of Solutions: Solutions form due to intermolecular forces, where solute particles interact with solvent particles through these forces.

Concentration Measurements

• Concentration Definition: A solution is defined as a homogeneous mixture composed of a solute dissolved in a solvent.

• Concentration Measurements:- Mass Percent:
  $ext{Mass percent} = ext{mass of solute} imes 100$

  • Parts Per Million (ppm):
    
    $ext{ppm} = ext{mass percent} imes 10^6$

  • Parts Per Billion (ppb):
    
    $ext{ppb} = ext{mass percent} imes 10^9$

  • Molarity:
    
    $M = rac{ ext{moles of solute}}{ ext{liters of solution}}$

  • Mole Fraction:
    
    $ext{X}_A = rac{ ext{moles of A}}{ ext{total moles}}$

  • Mass Ratio:
    
    $ext{mass ratio} = rac{ ext{mass of solute}}{ ext{mass of solution}}$

  • Molality (m):
    
    $m = rac{ ext{moles of solute}}{ ext{kg of solvent}}$

Concentration Units

• Molarity (M): Amount of solute (in mol) per volume of solution (in L).

• Molality (m): Moles of solute per mass of solvent (in kg).

• Mole Fraction (X): Amount of solute (in mol) over the total moles of solute and solvent.

• Percent by Mass (%): Ratio of mass of solute to the total mass of the solution, expressed as a percentage.

• Parts Per Million by Mass (ppm): Mass of solute per total mass of solution scaled by $10^6$.

• Parts Per Billion by Mass (ppb): Mass of solute per total mass of solution scaled by $10^9$.

• Parts by Volume: Similar to mass but in terms of volume, using similar scaling factors for ppm and ppb.

Molarity, Molality, Mass Ratio, & Mole Fraction Calculation

• Example for Acetaminophen (C₈H₉NO₂):- Given: 3.77 g is diluted to 100 mL of solution with assumed density of 1.00 g/mL.

  • Calculations:

  • Mass Percent: rac{3.77 ext{ g}}{100 ext{ g}} imes 100 = 3.77 ext{ %}

  • PPM: $3.77 imes 10^4$ ppm

  • PPB: $3.77 imes 10^7$ ppb

  • Molarity:
    
    $M = rac{0.0249 ext{ mol Acetaminophen}}{0.1 ext{ L}} = 0.249 ext{ M}$

  • Mole Fraction:
    
    $X = rac{0.0249}{0.0249 + 5.3461} = 0.00464$

  • Mass Ratio:
    
    $rac{3.77 ext{ g Acetaminophen}}{100 ext{ g solution}} = 0.0377$

  • Molality:
    
    $m = rac{0.0249 ext{ mol}}{0.09623 ext{ kg H₂O}} <br><br>ightarrow 0.259 ext{ m}$

Effect of Intermolecular Forces on Solution Formation

• Energy Changes: Involves differences in attractive forces between particles.- To mix, must overcome:

  • All solute-solute attractive forces

  • Some solvent-solvent attractive forces

  • Both processes are endothermic.

Solubility

• Definition: Maximum amount (in grams or moles) that can be dissolved in a given solvent at a specific temperature.

• Factors Affecting Solubility:- Solute type

  • Solvent type

  • Temperature

  • Pressure (for gases)

• Example Solubility Values by Polarity: - MgSO₄: 71g / 100g H₂O at 20°C

  • CS₂: 0.22g / 100g H₂O at 20°C

• Temperature Dependence:- Solids typically more soluble at higher temperatures (with exceptions).

  • Gases generally more soluble at lower temperatures and higher pressures (e.g., soda).

  • "Like Dissolves Like" principle.

Temperature Dependence of Solubility of Solids in Water

• Saturation Concentration: Depends on temperature and pressure.

• Trends:- Generally, solubility increases with temperature for solids.

  • Solubility curves can represent saturated (on the line), unsaturated (below the line), and supersaturated (above the line) solutions.

Enthalpy of Solution

• ΔHsoln: Could be endothermic or exothermic.- Usually exothermic for gases and endothermic for solids.

• Three energy components in dissolving solids:1. Disruption of solute particle interactions.

  2. Disruption of solvent particle interactions.

  3. Favorable creation of solute-solvent interactions.

• The enthalpy of solution can be calculated as:
  
  $ΔHsoln = ΔHsolute + ΔHsolvent - ΔHsolute-solvent$

Solution Process

1. Separating the solute into constituent particles.

2. Separating the solvent particles to make room for the solute.

3. Mixing solute with solvent.

• The overall enthalpy change can be represented as:
  
  $ΔHsolution = ΔHsolute + ΔHsolvent + ΔHmix$

Henry

                    ’s Law

• Law Statement: The concentration (solubility) of a dissolved gas in a liquid is directly proportional to the partial pressure of the gas.

• Formula:
  
  $C = kP$
  
  where k = specific constant for gas/liquid interaction.

• Concept Question: If a closed bottle of soda has a pressure of 1.5 atm of CO₂ and is increased to 2.0 atm with N₂, will CO₂ concentration increase?

• Example Calculation: What is [CO₂] in water under 5.00 atm with k for CO₂ = 0.031 mol/L·atm at 25°C?

Practical Examples of Henry

                    ’s Law

• Example: Calculate the grams of CO₂ dissolved in a 1.00 L bottle under 2.40 atm at 25°C:- Calculation:
  
  $M = rac{2.40 ext{ atm}}{29.76 ext{ atm/M}} = 0.08064 ext{ M}$
  
  resulting in 3.55 g of CO₂.

Raoult

                    ’s Law and Vapor Pressure

• Concept: Vapor pressure is a colligative property, meaning it depends on the concentration of solute, not its identity.

• Formula:
  
  $P<em>{solution} = χ</em>{solvent} P_{solvent}^0$

• The identity of particles does not matter, but the number of particles present is critical.

• Example Calculation: - Calculate the vapor pressure of a glucose solution prepared with 250 g of glucose in 500 g of H₂O at 25°C.

  • Use $P_{H₂O}^0 = 23.8 ext{ torr}$.

Boiling Point Elevation and Freezing Point Depression

• Impacts on Phase Diagrams:- The addition of solute lowers vapor pressure, raising boiling point and lowering freezing point, expanding the liquid region in the phase diagram.

Osmosis and Osmotic Pressure

• Definition of Osmosis: The flow of solvent from a lower concentration solution to a higher concentration solution through a semipermeable membrane.

• Importance of Semipermeable Membranes: Allow solvent passage while restricting solute flow.

• Osmotic Pressure: Measured pressure needed to prevent flow and is proportional to solute concentration.

• Formula:
  
  $ext{π} = iMRT$ where R = 0.08206 (atm·L)/(mol·K).

Osmotic Pressure Calculation Example

• Given: 0.133 g protein in 2.2 mL solution and osmotic pressure = 23.5 torr at 25°C.

• Use the equation to find molar mass of the protein:
  
  $ext{π} = rac{n}{V}RT$
  
  where volume V is expressed in liters.

Unit 11 Review – Key Concepts

• Mastering calculations for molarity, molality, mass percent, ppm, ppb, and mole fractions.

• Understanding temperature and pressure effects on solubility of solids and gases.

• Grasping Henry
  ’s Law concepts and calculations.

• Applying Raoult
  ’