Colligative Properties

Osmotic Pressure

Osmotic pressure is a colligative property that depends on the concentration of solute particles in a solution. It is important in biological and chemical systems for understanding processes such as osmosis and dialysis.

• Definition: Osmotic pressure (Π) is the pressure required to prevent the flow of solvent into a solution through a semipermeable membrane.

• Formula: The osmotic pressure is given by the equation: where M is the molarity, R is the gas constant ( L·atm/mol·K), and T is the temperature in Kelvin.

• Calculation Steps:

  1. Convert temperature from °C to K:

  2. Calculate moles of solute:

  3. Calculate molarity:

  4. Plug values into the osmotic pressure formula.

  5. Convert atm to torr if needed:

• Example: A solution is prepared by dissolving 35.8 mg of a compound (molar mass 598 g/mol) in 175 mL of water at 25°C. Calculate the osmotic pressure in torr.

  • Convert mass to moles:

  • Convert volume to liters:

  • Molarity:

  • Temperature:

  • Osmotic pressure:

  • Convert to torr:

Freezing Point Depression

Freezing point depression is another colligative property, describing the lowering of a solvent's freezing point when a solute is dissolved in it.

• Definition: The decrease in freezing point of a solvent upon addition of a non-volatile solute.

• Formula: where is the Van't Hoff factor (number of particles the solute dissociates into), is the molality, and is the freezing-point depression constant.

• Calculation Steps:

  1. Calculate molality:

  2. Determine Van't Hoff factor (): For KCl, (K+ and Cl-)

  3. Plug values into the formula to find

  4. Subtract from the pure solvent's freezing point to get the solution's freezing point.

• Example: 5.0 g KCl in 550.0 g water, C/m.

  • Moles KCl:

  • Molality:

  • C

  • Freezing point: C C C

Chemical Kinetics

Rate Laws and Reaction Order

Chemical kinetics studies the speed of chemical reactions and the factors affecting them. The rate law expresses the relationship between reaction rate and reactant concentrations.

• Rate Law:

  • is the rate constant

  • , are the reaction orders with respect to and

• Overall Order: Sum of exponents in the rate law ()

• Determining Order: Use experimental data to compare how changes in concentration affect the rate.

• Example Table:

  Experiment	[SO2]	[O2]	Initial Rate
  1	0.44	0.21	4.54
  2	0.44	0.66	6.65
  3	1.33	0.21	13.33

• Example: For the reaction , the rate law is determined by comparing rates and concentrations. Calculations show , , so .

Integrated Rate Laws

Integrated rate laws relate reactant concentration to time for different reaction orders.

• First Order:

  • Equation:

  • Half-life:

  • Plot: vs. time yields a straight line.

• Second Order:

  • Equation:

  • Plot: vs. time yields a straight line.

• Example: For the first-order decomposition of N2O5 with , half-life is .

Arrhenius Equation

The Arrhenius equation relates the rate constant to temperature and activation energy.

• Equation:

• Two-Point Form:

• Example: Given at and at , solve for :

Reaction Mechanisms

Elementary Steps and Rate Laws

Complex reactions often proceed via a series of elementary steps. The rate law for the overall reaction is determined by the slowest (rate-determining) step.

• Elementary Step: A single molecular event in a reaction mechanism.

• Rate-Determining Step: The slowest step controls the overall rate.

• Expressing Rate Law: The rate law is written in terms of reactants, not intermediates.

• Example Table:

  Step	Reaction	Type
  1	2A → 2B	Fast
  2	B + AB → 2AB	Slow

• Example: For the above mechanism, the rate law is . If is an intermediate, express in terms of using equilibrium from the fast step.

Overall Reaction Order

The overall order of a reaction is the sum of the exponents in the rate law.

• Example: For , overall order is .

Application of Integrated Rate Laws

Integrated rate laws are used to calculate concentrations at specific times and to determine rate constants from experimental data.

• Example: For a second-order reaction, if , , and :

Summary Table: Key Equations

Additional info: These notes expand on the original questions by providing definitions, formulas, and step-by-step examples for each concept, ensuring a self-contained study guide suitable for exam preparation in General Chemistry.