General Chemistry 101: Final Exam Study Guide

Thermochemistry and Thermodynamic Functions

Enthalpy and Its Properties

Enthalpy (H) is a thermodynamic quantity equivalent to the total heat content of a system. It is used to quantify the heat flow into or out of a system at constant pressure.

• Definition: Enthalpy is defined as $H = E + PV$, where E is the internal energy, P is pressure, and V is volume.

• Properties of Enthalpy:

  • State function (depends only on initial and final states)

  • Extensive property (depends on the amount of substance)

  • Change in enthalpy ($\Delta H$) equals heat at constant pressure

  • Units: Joules (J) or kilojoules (kJ)

  • For exothermic reactions, $\Delta H < 0$; for endothermic, $\Delta H > 0$

  • Can be used to calculate heat of reaction, formation, fusion, vaporization, etc.

  • Hess's Law applies: $\Delta H$ for a reaction is the sum of $\Delta H$ for individual steps

  • Standard enthalpy change ($\Delta H^\circ$) refers to reactions under standard conditions (1 atm, 298 K)

  • Enthalpy changes are tabulated for many reactions

  • Used in calorimetry to measure heat flow

• Example: The enthalpy change for the combustion of methane: $CH_4(g) + 2O_2(g) \rightarrow CO_2(g) + 2H_2O(l)$, $\Delta H = -890.4$ kJ/mol.

Chemical Equilibrium and Le Châtelier’s Principle

Le Châtelier’s Principle

Le Châtelier’s Principle states that if a dynamic equilibrium is disturbed by changing the conditions, the position of equilibrium moves to counteract the change.

• Temperature: Increasing temperature favors the endothermic direction; decreasing favors exothermic.

• Concentration: Adding or removing reactants/products shifts equilibrium to oppose the change.

• Pressure: Increasing pressure favors the side with fewer moles of gas.

• Example: For $N_2(g) + 3H_2(g) \rightleftharpoons 2NH_3(g)$, increasing temperature shifts equilibrium left (since reaction is exothermic).

Atoms, Ions, and Isotopes

Atomic Structure and Isotopic Notation

Atoms consist of protons, neutrons, and electrons. Isotopes are atoms of the same element with different numbers of neutrons.

• Protons: Positively charged particles in the nucleus; atomic number (Z)

• Neutrons: Neutral particles in the nucleus; mass number (A) = protons + neutrons

• Electrons: Negatively charged particles in orbitals around the nucleus

• Isotopic Notation: $^{A}_{Z}X$ (e.g., $^{16}_{8}O$)

• Ions: Atoms or molecules with a net charge due to loss or gain of electrons

Symbol	Protons	Neutrons	Electrons	Net Charge
$^{56}_{26}Fe^{2+}$	26	30	24	2+
$^{118}_{50}Sn^{4+}$	50	68	46	4+
$^{35}_{17}Cl^-$	17	18	18	1-

Chemical Reactions and Stoichiometry

Limiting Reactant and Yield Calculations

Stoichiometry involves the calculation of reactants and products in chemical reactions. The limiting reactant is the substance that is completely consumed first, limiting the amount of product formed.

• Steps:

  1. Write the balanced chemical equation.

  2. Convert all given quantities to moles.

  3. Determine the limiting reactant by comparing mole ratios.

  4. Calculate the amount of product formed from the limiting reactant.

  5. Calculate excess reactant remaining, if required.

• Example: For $4NH_3 + 5O_2 \rightarrow 4NO + 6H_2O$, if 1.50 g NH3 reacts with 4.50 g O2, determine the limiting reactant and the amount of NO formed.

Gases and Gas Laws

Ideal Gas Law and Applications

The behavior of gases can be described by the ideal gas law, which relates pressure, volume, temperature, and amount of gas.

• Ideal Gas Law: $PV = nRT$ where P = pressure (atm), V = volume (L), n = moles, R = 0.08206 L·atm·mol-1·K-1, T = temperature (K)

• Applications: Calculating molar mass, density, and gas stoichiometry.

• Example: A 4.0 L tube contains 4.0 g of neon at 1.78 atm and 30°C. What is the volume of the gas at STP?

Solutions and Concentrations

Molarity and Solution Calculations

Molarity (M) is the number of moles of solute per liter of solution. It is commonly used to express concentration in chemistry.

• Formula: $M = \frac{\text{moles of solute}}{\text{volume of solution (L)}}$

• Example: One cup of orange juice contains 124 mg of ascorbic acid (vitamin C, C6H8O6). Given that one cup = 236.6 mL, calculate the molarity of vitamin C in the juice.

Acids, Bases, and Buffers

pH, pOH, and Buffer Calculations

The pH scale measures the acidity or basicity of a solution. Buffers are solutions that resist changes in pH upon addition of small amounts of acid or base.

• pH and pOH: $\text{pH} = -\log[H^+]$ $\text{pOH} = -\log[OH^-]$ $\text{pH} + \text{pOH} = 14$

• Buffer Solutions: Consist of a weak acid and its conjugate base (or weak base and conjugate acid). The Henderson-Hasselbalch equation is used to calculate pH: $\text{pH} = \text{p}K_a + \log\left(\frac{[A^-]}{[HA]}\right)$

• Example: Calculate the pH of a buffer solution after addition of a small amount of NaOH.

Chemical Kinetics and Equilibrium

Equilibrium Constant and Reaction Quotient

The equilibrium constant (K) expresses the ratio of product and reactant concentrations at equilibrium. The reaction quotient (Q) is calculated the same way but for non-equilibrium conditions.

• Equilibrium Constant Expression: $K = \frac{[\text{products}]}{[\text{reactants}]}$

• Relationship to Free Energy: $\Delta G^\circ = -RT \ln K$

• Example: Given $\Delta G^\circ$ for a reaction, calculate $K$ at 298 K.

Redox Reactions and Balancing Equations

Oxidation-Reduction and Identifying Agents

Redox reactions involve the transfer of electrons between species. The substance that loses electrons is oxidized (reducing agent), and the one that gains electrons is reduced (oxidizing agent).

• Steps to Balance Redox Equations:

  1. Assign oxidation numbers to all elements.

  2. Identify what is oxidized and what is reduced.

  3. Balance atoms and charges, often using the half-reaction method.

  4. In basic solution, add OH- as needed to balance H+.

• Example: Balance $MnO_4^- + ClO^- \rightarrow MnO_2 + Cl^-$ in basic solution and identify oxidizing/reducing agents.

Acid-Base Equilibria and Hydrolysis

Weak Bases and Hydrolysis

Weak bases partially ionize in water. The base dissociation constant ($K_b$) quantifies this equilibrium.

• Base Hydrolysis: $B + H_2O \rightleftharpoons BH^+ + OH^-$

• Calculating $K_b$: Use pH to find [OH-], then set up an ICE table to solve for $K_b$.

• Percent Hydrolysis: $\% \text{hydrolysis} = \frac{[OH^-]}{[B]_0} \times 100$

• Example: For a 5.13 × 10-3 M solution of codeine with pH 9.95, calculate $K_b$ and percent hydrolysis.

Constants and Useful Equations

Reference Values and Formulas

• Gas constant: $R = 0.08206$ L·atm·mol-1·K-1

• Avogadro’s number: $6.022 \times 10^{23}$ mol-1

• Atomic mass unit: $1.6605 \times 10^{-24}$ g

• STP: 1 atm and 0°C

• 1 Calorie = 4.184 kJ

• Quadratic formula: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

• Ideal gas law: $PV = nRT$

• pH: $-\log[H^+]$

• pOH: $-\log[OH^-]$

• $K_a \times K_b = K_w$

• Gibbs free energy: $\Delta G = \Delta H - T\Delta S$

• Relationship between $\Delta G$ and $K$: $\Delta G^\circ = -RT \ln K$

Additional info: The above guide covers the main topics and equations referenced in the exam, including thermochemistry, equilibrium, atomic structure, stoichiometry, gas laws, solutions, acids and bases, redox reactions, and key constants and formulas.