Chapter 12: Solutions – Factors Affecting Solubility and Concentration Expressions

Chapter 12: Solutions

Introduction

This chapter explores the factors that affect the solubility of substances and the various ways to express the concentration of solutions. Understanding these concepts is fundamental in general chemistry, as they are widely applicable in laboratory and real-world contexts.

Factors That Affect Solubility

Pressure Effects

The solubility of gases in liquids is significantly influenced by pressure. When a gas is dissolved in a solvent and the system is at equilibrium, the rate at which gas molecules enter the solution equals the rate at which they leave.

• Increasing the pressure of the gas above the solution increases the solubility of the gas in the liquid.

• At equilibrium, a higher pressure results in a higher concentration of dissolved gas.

Example: Carbonated beverages are bottled under high pressure to increase the solubility of CO2 in the liquid.

Henry's Law

Henry's Law quantitatively relates the solubility of a gas in a liquid to the pressure of the gas above the solution.

• The law is expressed as:

$S_{gas} = k_H P_{gas}$

• $S_{gas}$: Solubility of the gas (mol L-1 or g L-1)

• $k_H$: Henry's law constant (varies with gas, solvent, and temperature)

• $P_{gas}$: Partial pressure of the gas (bar or atm)

Note: Henry's law constants are different for each solute-solvent pair and change with temperature.

Example: The solubility of CO2 in soda is calculated using Henry's Law, given the pressure and the constant for CO2.

Gas	kH (mol L-1 bar-1)
CO2	3.3 × 10-2
O2	1.3 × 10-3
N2	6.1 × 10-4
NH3	6.1
SO2	1.2

Additional info: NH3 and SO2 have much higher solubility due to their ability to react with water.

Temperature Effects

Temperature has a significant effect on the solubility of solids and gases in water.

• The solubility of solid solutes in water generally increases with increasing temperature.

• The solubility of gases in water decreases with increasing temperature.

Example: Thermal pollution can reduce oxygen levels in lakes and rivers, affecting aquatic life.

Solubility Curves

Solubility curves graphically represent how the solubility of various substances changes with temperature.

• Each curve shows the maximum amount of solute that can dissolve in 100 g of water at various temperatures.

Example: The solubility of KNO3 increases sharply with temperature, while NaCl shows only a slight increase.

Concentration Expressions

Introduction

Concentration describes the amount of solute present in a given quantity of solvent or solution. There are several ways to express concentration, each useful in different contexts.

• Mass percentage

• Mole fraction

• Molality

Mass Percentage

Mass percentage is the ratio of the mass of a solution component to the total mass of the solution, multiplied by 100.

$\text{percent by mass} = \frac{\text{mass of solution component}}{\text{total mass of solution}} \times 100$

Example: A solution that is 28% NaOH by mass contains 28 g NaOH per 100 g of solution.

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

These units are used for very dilute solutions.

• $\text{ppm} = \frac{\text{mass of solute}}{\text{total mass of solution}} \times 10^6$

• $\text{ppb} = \frac{\text{mass of solute}}{\text{total mass of solution}} \times 10^9$

• $\text{ppt} = \frac{\text{mass of solute}}{\text{total mass of solution}} \times 10^{12}$

Example: If a 2.5 g sample of groundwater contains 5.4 μg of Zn2+:

$\text{ppm Zn}^{2+} = \frac{5.4 \times 10^{-6} \text{ g}}{2.5 \text{ g}} \times 10^6 = 2.2 \text{ ppm}$

Mole Fraction

The mole fraction is the ratio of the number of moles of a component to the total number of moles of all components in the solution.

$X = \frac{\text{moles of component}}{\text{total moles of all components}}$

• The sum of the mole fractions of all components in a solution must equal 1.

Example: Calculate the mole fraction of phenol (C6H5OH) in a solution containing 45.0 g phenol in 855 g H2O.

$n_{\text{phenol}} = \frac{45.0 \text{ g}}{94.11 \text{ g mol}^{-1}} = 0.478 \text{ mol}$ $n_{\text{H}_2\text{O}} = \frac{855 \text{ g}}{18.02 \text{ g mol}^{-1}} = 47.4 \text{ mol}$ $X_{\text{phenol}} = \frac{0.478}{47.4 + 0.478} = 9.98 \times 10^{-3}$ $X_{\text{H}_2\text{O}} = 1 - 9.98 \times 10^{-3} = 0.990$

Molality

Molality (m) is defined as the number of moles of solute per kilogram of solvent.

$\text{molality} = \frac{\text{moles of solute}}{\text{mass of solvent (kg)}}$

• Molality is temperature independent because it is based on mass, not volume.

• Molality is useful for colligative property calculations.

Example: If 1.09 mol of glycerol is dissolved in 0.100 kg of water, the molality is:

$m = \frac{1.09 \text{ mol}}{0.100 \text{ kg}} = 10.9 \text{ mol kg}^{-1}$

Molarity vs. Molality

Molarity (M) is defined as moles of solute per liter of solution, while molality (m) is moles of solute per kilogram of solvent.

• Molarity depends on the volume of solution, which can change with temperature.

• Molality depends on the mass of solvent, which does not change with temperature.

• To convert between molarity and molality, the density of the solution is required.

Unit Name	Definition	Units
Molarity (M)	Amount solute (mol) / Volume solution (L)	mol L-1
Molality (m)	Amount solute (mol) / Mass solvent (kg)	mol kg-1
Mass %	Mass solute / Mass solution × 100	%
ppm	Mass solute / Mass solution × 106	ppm
ppb	Mass solute / Mass solution × 109	ppb
Mole fraction (X)	Moles component / Total moles all components	None

Preparation of Solutions

To prepare a solution of a given concentration, calculate the required mass of solute and solvent based on the desired total mass or volume and the concentration expression used.

Example: To prepare 1.20 L of a 20.0% (by mass) Pb(NO3)2 solution (density = 1.20 g mL-1):

• Calculate total mass: $1.20 \text{ L} \times 1200 \text{ g L}^{-1} = 1440 \text{ g}$

• Calculate mass of Pb(NO3)2: $1440 \text{ g} \times 0.200 = 288 \text{ g}$

• Calculate mass of water: $1440 \text{ g} - 288 \text{ g} = 1152 \text{ g}$

Summary Table: Solution Concentration Units

Unit	Definition	Temperature Dependent?	Notes
Molarity (M)	mol solute / L solution	Yes	Common in labs
Molality (m)	mol solute / kg solvent	No	Used for colligative properties
Mass %	mass solute / mass solution × 100	No	Simple for mixtures
ppm	mass solute / mass solution × 106	No	Trace analysis
ppb	mass solute / mass solution × 109	No	Ultra-trace analysis
Mole fraction (X)	mol component / total mol	No	Used in gas mixtures