General Chemistry II: Key Concepts, Equations, and Applications (Midterm Study Guide)

Chemical Kinetics and Reaction Mechanisms

First-Order Kinetics and Half-Life

Chemical kinetics studies the rates of chemical reactions and the factors affecting them. First-order reactions are those whose rate depends linearly on the concentration of one reactant.

• First-order rate law: $\text{Rate} = k[A]$

• Integrated first-order equation: $[A]_t = [A]_0 e^{-kt}$

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

• Application: The breakdown of DDT in soil is modeled as a first-order process, allowing calculation of concentration over time.

• Example: If the half-life of DDT is 55 days, after 55 days, half the initial concentration remains.

Reaction Rate and Mechanism Analysis

Understanding the mechanism of a reaction helps explain how reactants are converted to products and how the rate depends on reactant concentrations.

• Rate law determination: Experimentally, the rate is measured as a function of reactant concentrations.

• Example Table:

Rate	[Me2SO]	[DNA]
1	0.01	0.01
2	0.02	0.01
3	0.01	0.02
4	0.02	0.02

• Graphical analysis: Plotting rate vs. [Me2SO] or [DNA] can reveal the order with respect to each reactant.

• Mechanism: A reaction coordinate diagram shows the energy changes as reactants convert to products, indicating intermediates and transition states.

• Differential rate law: For a reaction with mechanism $A + B \rightarrow C$, the rate law may be $\text{Rate} = k[A][B]$ if both are involved in the rate-determining step.

Chemical Equilibrium

Equilibrium Constant and Reaction Quotient

Chemical equilibrium occurs when the rates of the forward and reverse reactions are equal, and concentrations of reactants and products remain constant.

• Equilibrium constant ($K$): For a general reaction $aA + bB \rightleftharpoons cC + dD$, $K = \frac{[C]^c[D]^d}{[A]^a[B]^b}$

• Reaction quotient ($Q$): Calculated using current concentrations; compared to $K$ to predict direction of shift.

• Application: The Mond process for nickel purification involves equilibrium between Ni, CO, and Ni(CO)4.

• Example: At equilibrium, mole fractions and partial pressures can be used to calculate $K$ and predict the composition of the system.

Thermodynamics and Entropy

Gibbs Free Energy and Entropy

Thermodynamics describes the energy changes in chemical reactions. The spontaneity of a reaction is determined by the Gibbs free energy change ($\Delta G$).

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

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

• Entropy ($S$): A measure of disorder; reactions that increase entropy are often favored at higher temperatures.

• Example: The synthesis of formaldehyde from methanol and oxygen involves changes in enthalpy and entropy, affecting $K$ at different temperatures.

Acid-Base Equilibria and Solubility

Solubility Product and pH Dependence

The solubility of ionic compounds can depend on pH, especially for salts of weak acids or bases.

• Solubility product ($K_{sp}$): For $CaC_2O_4 (s) \rightleftharpoons Ca^{2+} (aq) + C_2O_4^{2-} (aq)$, $K_{sp} = [Ca^{2+}][C_2O_4^{2-}]$

• pH effect: If the anion is a weak base, lowering pH increases its protonation, reducing its concentration and increasing solubility.

• Principal species: The dominant form of oxalic acid at a given pH can be determined using its $pK_a$ values.

• Example: At low pH, $C_2O_4^{2-}$ is protonated to $HC_2O_4^-$ or $H_2C_2O_4$, affecting the solubility of calcium oxalate.

Important Equations and Constants

Key Equations

• Energy of a photon: $E = h\nu = \frac{hc}{\lambda}$

• Ideal gas law: $PV = nRT$

• First law of thermodynamics: $\Delta E = q + w$

• Entropy change: $\Delta S = \frac{q_{rev}}{T}$

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

• Equilibrium constant: $K = e^{-\Delta G^\circ/RT}$

• Arrhenius equation: $k = Ae^{-E_a/RT}$

• Rate laws:

Order	Rate Law	Integrated Rate Law	Units of k
0	$\text{Rate} = k$	$[A]_t = [A]_0 - kt$	mol/L·s
1	$\text{Rate} = k[A]$	$\ln([A]_t/[A]_0) = -kt$	s-1
2	$\text{Rate} = k[A]^2$	$\frac{1}{[A]_t} - \frac{1}{[A]_0} = kt$	L/mol·s

Physical Constants

• Avogadro's number ($N_A$): $6.022 \times 10^{23}$ mol-1

• Planck's constant ($h$): $6.626 \times 10^{-34}$ J·s

• Gas constant ($R$): $0.0821$ L·atm/mol·K or $8.314$ J/mol·K

• Boltzmann constant ($k_B$): $1.38 \times 10^{-23}$ J/K

• Standard temperature: $0^\circ$C = 273 K

Periodic Table and VSEPR Theory

Periodic Table

The periodic table organizes elements by increasing atomic number and groups elements with similar chemical properties.

• Groups: Vertical columns; elements in the same group have similar valence electron configurations.

• Periods: Horizontal rows; properties change progressively across a period.

VSEPR Theory

Valence Shell Electron Pair Repulsion (VSEPR) theory predicts the shapes of molecules based on electron pair repulsion around a central atom.

• Common geometries: Linear, trigonal planar, tetrahedral, trigonal bipyramidal, octahedral.

• Example: $CO_2$ is linear; $CH_4$ is tetrahedral.

Additional info: These notes synthesize key concepts from a midterm exam covering chemical kinetics, equilibrium, thermodynamics, acid-base equilibria, solubility, and molecular structure, with reference tables and equations for General Chemistry II.