ACS General Chemistry Second-Term Practice Items: Comprehensive Study Notes

Solutions and Aqueous Reactions

Concentration Calculations

Concentration is a measure of the amount of solute dissolved in a given quantity of solvent. The most common unit is molarity (M), defined as moles of solute per liter of solution.

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

• Example: To find the molarity of a solution made by dissolving 2.52 g of potassium nitrate (KNO3) in 250 mL of water, first calculate moles of KNO3 and then divide by volume in liters.

Solubility and Saturation

Solubility refers to the maximum amount of solute that can dissolve in a solvent at a given temperature. A solution is saturated when it contains the maximum amount of dissolved solute.

• Solubility Curve: Shows how solubility changes with temperature.

• Example: Only KNO3 is saturated at 60 g in 100 g water at 40°C, based on the solubility curve.

Chemical Kinetics

Rate Laws and Reaction Order

The rate law expresses the relationship between the rate of a chemical reaction and the concentration of its reactants.

• General Rate Law: $\text{rate} = k[A]^m[B]^n$

• Order of Reaction: Determined experimentally by observing how rate changes with concentration.

• Example: For the reaction $2A + B \rightarrow C$, use experimental data to determine the rate law.

First-Order Reactions

First-order reactions have rates proportional to the concentration of one reactant.

• Integrated Rate Law: $[A]_t = [A]_0 e^{-kt}$

• Half-life: $t_{1/2} = \frac{0.693}{k}$

• Example: If the half-life is 7.1 s, after 14.2 s, 1/4 of the sample remains.

Reaction Mechanisms and Energy Diagrams

Reaction mechanisms describe the stepwise sequence of elementary reactions by which overall chemical change occurs. Energy diagrams illustrate the energy changes during a reaction.

• Activation Energy: The minimum energy required for a reaction to occur.

• Example: The mechanism consistent with a multi-peaked energy diagram involves multiple steps, each with its own activation energy.

Chemical Equilibrium

Equilibrium Constant Expressions

At equilibrium, the rates of the forward and reverse reactions are equal. The equilibrium constant ($K$) quantifies the ratio of product to reactant concentrations.

• General Expression: $K = \frac{[\text{products}]}{[\text{reactants}]}$ (raised to their stoichiometric coefficients)

• Example: For $N_2O_4 \rightleftharpoons 2NO_2$, $K = \frac{[NO_2]^2}{[N_2O_4]}$

Le Châtelier's Principle

Le Châtelier's Principle states that if a system at equilibrium is disturbed, it will shift to counteract the disturbance.

• Example: Increasing the concentration of a reactant shifts equilibrium toward products.

Acids and Bases

Definitions and Strengths

Acids donate protons (H+), while bases accept protons. The strength of an acid or base is determined by its degree of ionization in water.

• Strong Acids/Bases: Completely ionize in solution.

• Weak Acids/Bases: Partially ionize.

• Example: HCl is a strong acid; CH3COOH is a weak acid.

pH Calculations

pH is a measure of the hydrogen ion concentration in solution.

• Formula: $\text{pH} = -\log[H^+]$

• Example: For 0.15 M CH3COOH, use $K_a$ to find [H+] and calculate pH.

Buffers

Buffers are solutions that resist changes in pH upon addition of small amounts of acid or base. They consist of a weak acid and its conjugate base.

• Henderson-Hasselbalch Equation: $\text{pH} = \text{p}K_a + \log\left(\frac{[A^-]}{[HA]}\right)$

• Example: A buffer made from CH3COOH and CH3COONa.

Solubility Equilibria

Solubility Product Constant ($K_{sp}$)

$K_{sp}$ is the equilibrium constant for the dissolution of a sparingly soluble ionic compound.

• Expression: $K_{sp} = [\text{cation}]^m[\text{anion}]^n$

• Example: For AgCl, $K_{sp} = [Ag^+][Cl^-]$

Thermodynamics

Enthalpy and Free Energy

Thermodynamics studies energy changes in chemical reactions. Enthalpy ($\Delta H$) and free energy ($\Delta G$) are key concepts.

• Standard Enthalpy Change: $\Delta H^\circ = \sum \Delta H^\circ_{\text{products}} - \sum \Delta H^\circ_{\text{reactants}}$

• Gibbs Free Energy: $\Delta G = \Delta H - T\Delta S$

• Example: Calculate $\Delta H$ for NO formation using standard enthalpies.

Spontaneity

A reaction is spontaneous if $\Delta G < 0$.

• Example: The decomposition of NO2 is exothermic and spontaneous at all temperatures.

Electrochemistry

Redox Reactions and Cell Potentials

Electrochemistry involves the study of redox reactions and the generation of electrical energy from chemical reactions.

• Cell Potential: $E^\circ_{cell} = E^\circ_{cathode} - E^\circ_{anode}$

• Nernst Equation: $E = E^\circ - \frac{0.0592}{n} \log Q$

• Example: Calculate cell potential for a given redox reaction.

Faraday's Laws

Faraday's laws relate the amount of substance produced at an electrode to the quantity of electricity passed through the cell.

• Formula: $m = \frac{Q}{F} \times \frac{M}{n}$

• Example: Calculate mass of Ag deposited using current and time.

Nuclear Chemistry

Radioactive Decay

Nuclear chemistry studies changes in atomic nuclei, including radioactive decay processes.

• Types of Decay: Alpha ($\alpha$), Beta ($\beta$), Gamma ($\gamma$)

• Example: Radon-226 decays to radon-222 by emitting an alpha particle.

Summary Table: Key Equations and Concepts

Topic	Key Equation	Example/Application
Concentration	$M = \frac{\text{mol}}{\text{L}}$	Calculate molarity of KNO3 solution
Kinetics	$\text{rate} = k[A]^m[B]^n$	Determine reaction order from data
Equilibrium	$K = \frac{[\text{products}]}{[\text{reactants}]}$	Write $K$ for $N_2O_4 \rightleftharpoons 2NO_2$
Acids/Bases	$\text{pH} = -\log[H^+]$	Find pH of acetic acid solution
Thermodynamics	$\Delta G = \Delta H - T\Delta S$	Predict spontaneity of reaction
Electrochemistry	$E^\circ_{cell} = E^\circ_{cathode} - E^\circ_{anode}$	Calculate cell potential
Nuclear Chemistry	Alpha decay: $^{A}_{Z}X \rightarrow ^{A-4}_{Z-2}Y + ^{4}_{2}\alpha$	Radon-226 to radon-222

Additional info: These notes expand upon the practice questions by providing definitions, formulas, and examples for each major topic covered in the ACS General Chemistry Second-Term Practice Items. The summary table consolidates key equations for quick reference.