Gases, Solutions, and Acid-Base Chemistry: Core Concepts and Calculations

Gases and the Kinetic Molecular Theory

Kinetic Molecular Theory of Gases

The Kinetic Molecular Theory (KMT) explains the behavior of ideal gases based on the motion of their particles. The theory is summarized by four main statements:

• Gas particles are in constant, random motion. They move in straight lines until they collide with each other or the walls of their container.

• The volume of individual gas particles is negligible compared to the total volume of the gas; most of the volume is empty space.

• There are no attractive or repulsive forces between gas particles; collisions are perfectly elastic.

• The average kinetic energy of gas particles is proportional to the absolute temperature (Kelvin).

Example: The behavior of air molecules in a room can be explained using KMT, predicting properties such as pressure and temperature changes.

Pressure and Pressure Units

Pressure is defined as the force exerted per unit area by gas particles colliding with the walls of their container.

• Common units of pressure: atmosphere (atm), pascal (Pa), torr, millimeters of mercury (mmHg).

• 1 atm = 101,325 Pa = 760 mmHg = 760 torr

Example: Atmospheric pressure at sea level is 1 atm.

Temperature Conversion: Celsius to Kelvin

Gas law calculations require temperature in Kelvin (K). To convert Celsius (°C) to Kelvin:

• Formula:

$K = ^\circ C + 273.15$

Example: 25°C = 25 + 273.15 = 298.15 K

Gas Laws

Gas laws describe the relationships between pressure, volume, temperature, and amount of gas.

• Boyle's Law: At constant temperature, the pressure and volume of a gas are inversely related.

$P_1V_1 = P_2V_2$

• Charles' Law: At constant pressure, the volume of a gas is directly proportional to its temperature (in Kelvin).

$\frac{V_1}{T_1} = \frac{V_2}{T_2}$

• Ideal Gas Law: Relates pressure, volume, temperature, and amount (in moles) of a gas.

$PV = nRT$

• Law of Partial Pressures (Dalton's Law): The total pressure of a mixture of gases equals the sum of the partial pressures of each component gas.

$P_{total} = P_1 + P_2 + P_3 + \ldots$

Example: Calculating the pressure of a gas collected over water using Dalton's Law.

Standard Temperature and Pressure (STP)

STP is a reference point for gas measurements:

• Standard Temperature: 0°C (273.15 K)

• Standard Pressure: 1 atm

• At STP, 1 mole of an ideal gas occupies 22.4 L

Application: Used in stoichiometry problems involving gases to relate moles and volume.

Solutions and Their Properties

Solute, Solvent, and Solubility

Solution: A homogeneous mixture of two or more substances.

• Solute: The substance dissolved in a solution (present in lesser amount).

• Solvent: The substance that dissolves the solute (present in greater amount).

• Solubility: The maximum amount of solute that can dissolve in a given amount of solvent at a specific temperature.

Example: In saltwater, salt is the solute and water is the solvent.

Concentration Calculations

Concentration expresses the amount of solute in a given quantity of solution.

• Mass/Volume Percent: $\text{Mass/Volume \%} = \frac{\text{mass of solute (g)}}{\text{volume of solution (mL)}} \times 100$

• Mass/Mass Percent: $\text{Mass/Mass \%} = \frac{\text{mass of solute (g)}}{\text{mass of solution (g)}} \times 100$

• Molarity (M): $M = \frac{\text{moles of solute}}{\text{liters of solution}}$

Example: A solution with 5 g NaCl in 100 mL water has a mass/volume percent of 5%.

Dilution Equation

Used to calculate the new concentration or volume when a solution is diluted:

$M_1V_1 = M_2V_2$

Where $M_1$ and $V_1$ are the initial molarity and volume, and $M_2$ and $V_2$ are the final molarity and volume.

Example: Diluting 50 mL of 2 M HCl to 100 mL results in a final concentration of 1 M.

Stoichiometry with Gases and Solutions

Stoichiometry involves using balanced chemical equations to calculate quantities of reactants and products.

• For gases at STP: 1 mole = 22.4 L

• For solutions: Use molarity and volume to find moles ($n = M \times V$)

Example: Calculating the volume of hydrogen gas produced from a reaction at STP.

Colligative Properties

Colligative properties depend on the number of solute particles, not their identity.

• Freezing Point Depression: Adding solute lowers the freezing point of a solvent.

• Boiling Point Elevation: Adding solute raises the boiling point of a solvent.

Example: Salt added to ice lowers its freezing point, helping to melt ice on roads.

Acids, Bases, and Solution Chemistry

Properties of Acids and Bases

• Acids: Taste sour, turn blue litmus red, react with metals to produce hydrogen gas.

• Bases: Taste bitter, feel slippery, turn red litmus blue.

Definitions of Acids and Bases

• Arrhenius Definition:

  • Acid: Produces H+ ions in aqueous solution.

  • Base: Produces OH- ions in aqueous solution.

• Brønsted-Lowry Definition:

  • Acid: Proton (H+) donor.

  • Base: Proton (H+) acceptor.

Example: HCl is an acid (donates H+), NH3 is a base (accepts H+).

Conjugate Acid-Base Pairs

In a chemical equation, acids and bases form conjugate pairs:

• Acid: Donates H+ to become its conjugate base.

• Base: Accepts H+ to become its conjugate acid.

Example: In the reaction $\mathrm{NH_3 + H_2O \rightarrow NH_4^+ + OH^-}$:

• NH3: base

• H2O: acid

• NH4+: conjugate acid

• OH-: conjugate base

Acid-Base Titration Stoichiometry

Titration involves reacting a solution of known concentration with one of unknown concentration to determine the latter.

• Use the balanced equation to relate moles of acid and base.

• Calculate unknown concentration or volume using stoichiometry.

Example: Determining the concentration of acetic acid in vinegar by titration with NaOH.

Water Ionization Constant (Kw) and pH Calculations

The ion-product constant for water ($K_w$) at 25°C is:

$K_w = [H_3O^+][OH^-] = 1.0 \times 10^{-14}$

• Given $[H_3O^+]$, calculate $[OH^-]$ and vice versa.

pH and pOH:

• $pH = -\log[H_3O^+]$

• $pOH = -\log[OH^-]$

• $pH + pOH = 14$ (at 25°C)

Example: If $[H_3O^+] = 1.0 \times 10^{-3}$ M, then $pH = 3$.

Acidic and Basic Solutions

• Acidic solution: $pH < 7$

• Neutral solution: $pH = 7$

• Basic solution: $pH > 7$

Buffered Solutions

A buffered solution resists changes in pH when small amounts of acid or base are added. Buffers typically consist of a weak acid and its conjugate base, or a weak base and its conjugate acid.

Example: A mixture of acetic acid and sodium acetate forms a buffer solution.