Chemistry Unit 10

1. Acids and Bases

1.1. Definitions

• Arrhenius:

  • Acid: Produces $H^+$ ions in water.

  • Base: Produces $OH^-$ ions in water.

• Brønsted-Lowry:

  • Acid: Donates a proton ($H^+$).

  • Base: Accepts a proton ($H^+$).

• Lewis:

  • Acid: Accepts an electron pair.

  • Base: Donates an electron pair.

1.2. pH and pOH

• $pH = -log[H^+]$

• $pOH = -log[OH^-]$

• $pH + pOH = 14$

1.3. Acid-Base Reactions

• Neutralization: Acid + Base → Salt + Water

• Titration: A process to determine the concentration of an acid or base.

1.4. Strong vs. Weak Acids and Bases

• Strong Acids: Completely dissociate in water (e.g., HCl, $H<em>2SO</em>4$, $HNO_3$).

• Strong Bases: Completely dissociate in water (e.g., NaOH, KOH).

• Weak Acids/Bases: Partially dissociate in water; use $K<em>a$ and $K</em>b$ to quantify.

1.5. Equations to Memorize

• $pH = -log[H^+]$

• $pOH = -log[OH^-]$

• $pH + pOH = 14$

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

• $K_a = \frac{[H^+][A^-]}{[HA]}$ (Acid dissociation constant)

• $K_b = \frac{[BH^+][OH^-]}{[B]}$ (Base dissociation constant)

2. Reaction Rates

2.1. Factors Affecting Reaction Rates

• Concentration: Higher concentration, faster rate.

• Temperature: Higher temperature, faster rate.

• Surface Area: Greater surface area, faster rate (for heterogeneous reactions).

• Catalysts: Speed up reactions without being consumed.

2.2. Rate Laws

• Rate = $k[A]^m[B]^n$, where:

  • k is the rate constant

  • [A] and [B] are reactant concentrations

  • m and n are reaction orders

2.3. Reaction Order

• Zero Order: Rate is independent of reactant concentration. Rate = k

• First Order: Rate is directly proportional to reactant concentration. Rate = $k[A]$

• Second Order: Rate is proportional to the square of reactant concentration. Rate = $k[A]^2$

2.4. Arrhenius Equation

• $k = Ae^{-\frac{E_a}{RT}}$, where:

  • k is the rate constant

  • A is the pre-exponential factor

  • $E_a$ is the activation energy

  • R is the gas constant (8.314 J/mol·K)

  • T is the temperature in Kelvin

2.5. Equations to Memorize

• Rate = $k[A]^m[B]^n$

• $k = Ae^{-\frac{E_a}{RT}}$

3. Equilibrium

3.1. Equilibrium Constant (K)

• For a reaction $aA + bB \rightleftharpoons cC + dD$

• $K = \frac{[C]^c[D]^d}{[A]^a[B]^b}$

3.2. Le Chatelier's Principle

• If a system at equilibrium is subjected to a change (e.g., concentration, temperature, pressure), the system will adjust itself to counteract the change and restore a new equilibrium.

3.3. Factors Affecting Equilibrium

• Concentration: Adding reactants shifts equilibrium to products, and vice versa.

• Temperature:

  • For endothermic reactions, increasing temperature shifts equilibrium to products.

  • For exothermic reactions, increasing temperature shifts equilibrium to reactants.

• Pressure: Affects gaseous systems; increasing pressure shifts equilibrium to the side with fewer moles of gas.

3.4. Equations to Memorize

• $K = \frac{[C]^c[D]^d}{[A]^a[B]^b}$

• $\Delta G = -RT \ln{K}$, where $\Delta G$ is the Gibbs free energy change

4. Gas Laws

4.1. Basic Gas Laws

• Boyle's Law: $P<em>1V</em>1 = P<em>2V</em>2$ (at constant temperature and moles)

• Charles's Law: $\frac{V<em>1}{T</em>1} = \frac{V<em>2}{T</em>2}$ (at constant pressure and moles)

• Avogadro's Law: $\frac{V<em>1}{n</em>1} = \frac{V<em>2}{n</em>2}$ (at constant temperature and pressure)

• Combined Gas Law: $\frac{P<em>1V</em>1}{T<em>1} = \frac{P</em>2V<em>2}{T</em>2}$

4.2. Ideal Gas Law

• $PV = nRT$, where:

  • P is pressure

  • V is volume

  • n is the number of moles

  • R is the ideal gas constant (0.0821 L·atm/mol·K or 8.314 J/mol·K)

  • T is temperature in Kelvin

4.3. Dalton's Law of Partial Pressures

• The total pressure of a gas mixture is the sum of the partial pressures of each gas.

• $P<em>{total} = P</em>1 + P<em>2 + P</em>3 + …$

4.4. Equations to Memorize

• $PV = nRT$

• $\frac{P<em>1V</em>1}{T<em>1} = \frac{P</em>2V<em>2}{T</em>2}$

• $P<em>{total} = P</em>1 + P<em>2 + P</em>3 + …$

5. Heat Energy (Thermochemistry)

5.1. Basic Concepts

• Enthalpy (H): A measure of the total heat content of a system.

• Endothermic: Absorbs heat from the surroundings (\Delta H > 0).

• Exothermic: Releases heat to the surroundings (\Delta H < 0).

5.2. Calorimetry

• $q = mc\Delta T$, where:

  • q is heat energy

  • m is mass

  • c is specific heat capacity

  • $\Delta T$ is the change in temperature

5.3. Hess's Law

• The enthalpy change for a reaction is the same whether it occurs in one step or in multiple steps.

5.4. Equations to Memorize

• $q = mc\Delta T$

• $\Delta H<em>{reaction} = \sum \Delta H</em>{f(products)} - \sum \Delta H_{f(reactants)}$