Colligative Properties and Chemical Kinetics: Study Notes

Colligative Properties of Solutions

Ion Pairing and Its Effects

Ion pairing refers to the association of oppositely charged ions in solution, which can affect the number of particles present and thus influence colligative properties.

• Ion Pairing: Occurs when cations and anions in solution associate, reducing the effective number of free ions.

• Effect on Colligative Properties: Fewer free ions mean a lower van 't Hoff factor (i), which decreases the magnitude of colligative effects such as freezing point depression and boiling point elevation.

• Example: Compounds with highly charged ions (e.g., CaSO4, MgSO4) exhibit more ion pairing than those with singly charged ions (e.g., NaF).

Freezing Point Depression

Freezing point depression is a colligative property that describes the lowering of a solvent's freezing point when a solute is added.

• Formula: $\Delta T_f = i m K_f$ where $\Delta T_f$ is the freezing point depression, i is the van 't Hoff factor (number of particles per formula unit), m is the molality, and $K_f$ is the cryoscopic constant of the solvent.

• Key Points:

  • Greater i and m lead to a larger decrease in freezing point.

  • Ion pairing reduces i, thus reducing the effect.

• Example Calculation:

  • Given: 2.05 g KBr (MW = 119 g/mol) and 4.82 g glucose (MW = 180 g/mol) in 186 g H2O, $K_f = 1.86$ °C/m.

  • Calculate moles: $\text{KBr: } 2.05\,\text{g} / 119\,\text{g/mol} = 0.0172\,\text{mol}$ $\text{Glucose: } 4.82\,\text{g} / 180\,\text{g/mol} = 0.02678\,\text{mol}$

  • Total particles: $2 \times 0.0172 + 0.02678 = 0.0612$ mol particles

  • Molality: $0.0612\,\text{mol} / 0.186\,\text{kg} = 0.329\,\text{m}$

  • Freezing point depression: $\Delta T_f = 0.329 \times 1.86 = 0.61$ °C

  • New freezing point: $0 - 0.61 = -0.61$ °C

Vapor Pressure Lowering (Raoult's Law)

The addition of a non-volatile solute to a solvent lowers the vapor pressure of the solvent.

• Raoult's Law: $P_A = X_A P_A^0$ where $P_A$ is the vapor pressure of the solvent above the solution, $X_A$ is the mole fraction of the solvent, and $P_A^0$ is the vapor pressure of the pure solvent.

• Calculation Example:

  • Given: 17.4 torr (pure water at 20°C), $X_{H_2O} = 0.994$

  • Vapor pressure: $P_{H_2O} = 0.994 \times 17.4 = 17.3$ torr

• Multiple Volatile Components: $P_{\text{total}} = X_{H_2O} P_{H_2O}^0 + X_{EtOH} P_{EtOH}^0$

Osmotic Pressure

Osmotic pressure is the pressure required to prevent the net flow of solvent through a semipermeable membrane separating two solutions of different concentrations.

• Formula: $\pi = \left( \frac{n}{V} \right) RT = MRT$ where $\pi$ is osmotic pressure, $n$ is moles of solute, $V$ is volume, $M$ is molarity, $R$ is the gas constant, and $T$ is temperature in Kelvin.

• Units: $R = 0.0821$ L·atm/(mol·K) or $8.314$ J/(mol·K)

• Application: Used to determine molar mass of unknown solutes.

• Sample Problem:

  • Given: 2.610 g of a compound in 250 mL solution, $\pi = 0.566$ atm at 25°C.

  • Calculate moles: $n = \frac{\pi V}{RT} = \frac{0.566 \times 0.250}{0.0821 \times 298} = 0.00578$ mol

  • Molar mass: $2.610\,\text{g} / 0.00578\,\text{mol} = 451\,\text{g/mol}$

Chemical Kinetics

Introduction to Kinetics

Chemical kinetics is the study of the rates at which chemical processes occur and the factors that affect these rates.

• Key Factors Affecting Reaction Rates:

  • Physical State: Reactants must be in contact; homogeneous mixtures react faster.

  • Concentration: Higher concentration increases the likelihood of collisions.

  • Temperature: Higher temperature increases kinetic energy and collision frequency.

  • Catalysts: Speed up reactions by providing alternative pathways; not consumed in the reaction.

Defining Reaction Rates

The rate of a reaction is the change in concentration of reactants or products per unit time.

• General Expression: For a reaction $aA + bB \rightarrow cC + dD$:

$\text{Rate} = -\frac{1}{a} \frac{d[A]}{dt} = -\frac{1}{b} \frac{d[B]}{dt} = \frac{1}{c} \frac{d[C]}{dt} = \frac{1}{d} \frac{d[D]}{dt}$

• Average Rate: Change in concentration over a time interval.

• Instantaneous Rate: Slope of the concentration vs. time curve at a specific time.

• Initial Rate: Rate at the very start of the reaction.

Rate Laws and Reaction Order

Rate laws express the relationship between the rate of a chemical reaction and the concentration of its reactants.

• General Form: $\text{Rate} = k [A]^x [B]^y$ where $k$ is the rate constant, $x$ and $y$ are the orders with respect to A and B.

• Overall Reaction Order: Sum of the exponents $x + y$.

• Units of $k$: Depend on overall order (e.g., for second order, $k$ has units of M-1s-1).

• Determining Order: Experimentally, by observing how rate changes with concentration.

• Example: If doubling [A] increases rate by a factor of 4, the reaction is second order in A.

Using Initial Rates to Determine Rate Laws

Initial rates are measured for different starting concentrations to deduce the rate law.

• Method: Compare how the rate changes as the concentration of one reactant is varied while others are held constant.

• Example Table:

Exp.	[NO] (M)	[Br2] (M)	Initial Rate (M/s)
1	0.10	0.20	24
2	0.25	0.20	150
3	0.10	0.50	60
4	0.35	0.50	735

• By comparing experiments, deduce the order with respect to each reactant.

Summary Table: Colligative Properties and Kinetics

Property	Formula	Key Variables	Example Application
Freezing Point Depression	$\Delta T_f = i m K_f$	i = van 't Hoff factor, m = molality, $K_f$ = constant	Salt in water lowers freezing point
Vapor Pressure Lowering	$P_A = X_A P_A^0$	$X_A$ = mole fraction, $P_A^0$ = pure vapor pressure	Sugar in water lowers vapor pressure
Osmotic Pressure	$\pi = MRT$	M = molarity, R = gas constant, T = temperature	Determining molar mass of a polymer
Reaction Rate	$\text{Rate} = k [A]^x [B]^y$	k = rate constant, x/y = order	Decomposition of H2O2

Additional info: These notes integrate both colligative properties (freezing point depression, vapor pressure lowering, osmotic pressure) and introductory chemical kinetics, as covered in a typical General Chemistry II course.