Solution Concentration and Colligative Properties

Solution Concentration and Colligative Properties

Introduction

This study guide covers the quantification of solution concentration and the physical properties of solutions that depend on their composition, focusing on colligative properties. These topics are central to understanding Chapter 13: Properties of Solutions in General Chemistry.

Quantifying Solution Concentration

Common Units of Concentration

There are several standard ways to express the concentration of a solution. Each unit provides different information and is useful in specific contexts.

• Mass Percent (%): The mass of a component divided by the total mass of the solution, multiplied by 100%. Formula: $\text{Mass \%} = \frac{\text{mass of component}}{\text{total mass of solution}} \times 100\%$

• Parts per Million (ppm), Billion (ppb), Trillion (ppt): Used for very dilute solutions. Formula: $\text{ppm} = \frac{\text{mass of component in solution}}{\text{total mass of solution}} \times 10^6$ Similarly, $\text{ppb} = \times 10^9$, $\text{ppt} = \times 10^{12}$

• Mole Fraction (x): The ratio of moles of a component to the total moles of all components in the solution. Formula: $x_i = \frac{\text{moles of component } i}{\text{total moles of all components}}$ Note: $\sum x_i = 1$

• Molarity (M): The number of moles of solute per liter of solution. Formula: $M = \frac{\text{moles of solute}}{\text{liters of solution}}$

• Molality (m): The number of moles of solute per kilogram of solvent. Formula: $m = \frac{\text{moles of solute}}{\text{kg of solvent}}$ Molality is useful because it does not change with temperature.

Worked Example: Calculating Concentrations in a Solution

Given a gin solution labeled as 44% alcohol by volume (ethanol, CH3CH2OH) and the remainder water (H2O), with known densities, the following steps are used to determine various concentration units:

1. Assume 1.000 L of solution.

2. Calculate the volume, mass, and moles of each component using density and molar mass.

3. Apply the formulas above to find mass percent, mole fraction, molarity, and molality.

Example Calculation (Mass Percent):

• Mass of ethanol: 347 g

• Mass of water: 559 g

• Mass percent ethanol: $\frac{347}{347+559} \times 100 = 38.3\%$

Practice Problem: Trace Contaminants

EPA standards require action if Pb2+ in water exceeds 15 ppb. For 1.00 L of water (density 1.00 g/cm3):

• Convert 1.00 L to 1000 g.

• Calculate mass of Pb: $\text{mass solute} = \frac{(15)(1000)}{10^9} = 1.5 \times 10^{-5} \text{g} = 0.015 \text{mg}$

Colligative Properties of Solutions

Definition and Importance

Colligative properties are physical properties of solutions that depend only on the concentration of solute particles, not their identity. These properties are crucial in many real-world and laboratory contexts, such as cooking, environmental science, and biology.

• Assume ideal solutions: solute-solvent and solvent-solvent interactions are of equal strength.

• The driving force is the stabilization of the solution by entropy.

The Four Key Colligative Properties

1. Vapor Pressure Lowering

   • Adding a nonvolatile solute lowers the vapor pressure of the solvent.

   • Raoult’s Law: $P_{\text{solution}} = X_{\text{solvent}} P^0_{\text{solvent}}$

   • Express concentration in terms of mole fraction ($X_{\text{solvent}}$).

2. Boiling Point Elevation

   • Boiling point increases when a solute is added.

   • Formula: $\Delta T_b = i K_b m$

   • Express concentration in terms of molality ($m$).

3. Freezing Point Depression

   • Freezing point decreases when a solute is added.

   • Formula: $\Delta T_f = -i K_f m$

   • Express concentration in terms of molality ($m$).

4. Osmotic Pressure

   • Pressure required to stop osmosis across a semipermeable membrane.

   • Formula: $\Pi = iMRT$

   • Express concentration in terms of molarity ($M$).

Why Colligative Properties Matter

• Vapor Pressure Lowering: Affects evaporation, boiling, and environmental fate of chemicals.

• Boiling Point Elevation/Freezing Point Depression: Important for cooking, safe handling of materials, and battery operation at various temperatures.

• Osmotic Pressure: Critical in biological systems (cells, blood), medicine (dialysis), and water treatment (desalination).

Raoult’s Law and Dalton’s Law of Partial Pressures

• Raoult’s Law: Used for solutions with nonvolatile solutes or ideal mixtures of volatile components.

• Dalton’s Law: In an ideal solution of two volatile components, total vapor pressure is the sum of the partial pressures: $P_{\text{total}} = X_A P_A^0 + X_B P_B^0$

• Non-ideal mixtures deviate due to strong or repulsive interactions.

Phase Diagrams and Solution Effects

• Adding a solute lowers the freezing point and raises the boiling point of a solvent.

• Phase diagrams shift accordingly, stabilizing the liquid phase over a wider temperature range.

Boiling Point Elevation and Freezing Point Depression Constants

Solvent	Normal Boiling Point (°C)	Kb (°C/m)	Normal Freezing Point (°C)	Kf (°C/m)
Water, H2O	100.0	0.51	0.0	1.86
Benzene, C6H6	80.1	2.53	5.5	5.12
Ethanol, C2H5OH	78.4	1.22	-114.6	1.99
Carbon tetrachloride, CCl4	76.8	5.02	-23.0	2.98
Chloroform, CHCl3	61.2	3.63	-63.5	4.68

The van’t Hoff Factor (i)

The van’t Hoff factor ($i$) accounts for the number of particles a solute produces in solution. For ionic compounds, $i$ is greater than 1 due to dissociation.

Compound	Expected $i$
Sucrose	1.00
NaCl	2.00
K2SO4	3.00
MgSO4	2.00

*Measured values may be slightly less than expected due to ion pairing in solution.

Summary

• Solution concentration can be quantified using mass percent, ppm/ppb, mole fraction, molarity, and molality.

• Colligative properties—vapor pressure lowering, boiling point elevation, freezing point depression, and osmotic pressure—depend on the number of solute particles, not their identity.

• These properties have significant practical and theoretical importance in chemistry and related fields.