General Chemistry III: Thermochemistry, Kinetics, Equilibrium, and Acid-Base Chemistry – Study Notes

Thermochemistry

Standard Enthalpy of Formation and Thermochemical Equations

Thermochemistry deals with the heat changes that accompany chemical reactions. The standard enthalpy of formation (ΔHf°) is the enthalpy change when one mole of a compound is formed from its elements in their standard states.

• Formation Reaction: A reaction where one mole of a compound forms from its elements in their standard states.

• Thermochemical Equation: A balanced chemical equation that includes the enthalpy change (ΔH).

• Example: The formation of sodium chromate: $2Na(s) + Cr(s) + 2O_2(g) \rightarrow Na_2CrO_4(s)$

• Calculating Enthalpy Change: Use the equation: $\Delta H_{rxn} = \sum n\Delta H_f^{\circ} (\text{products}) - \sum n\Delta H_f^{\circ} (\text{reactants})$

Hess's Law and Enthalpy Calculations

Hess's Law states that the total enthalpy change for a reaction is the same, no matter how many steps the reaction is carried out in. This allows calculation of enthalpy changes using known values from other reactions.

• Application: If given enthalpies of formation, you can calculate the enthalpy change for a reaction.

• Significance of Sign: A negative ΔH indicates an exothermic reaction; a positive ΔH indicates an endothermic reaction.

Gas Laws and Mixtures

Partial Pressure and Dalton's Law

Dalton's Law of Partial Pressures states that the total pressure of a mixture of gases equals the sum of the partial pressures of each individual gas.

• Partial Pressure: The pressure exerted by a single gas in a mixture.

• Dalton's Law: $P_{total} = P_1 + P_2 + P_3 + \ldots$

• Calculating Mass of a Gaseous Mixture: Use the ideal gas law: $PV = nRT$

• Example: Given the partial pressure of one gas and the volume, calculate the total mass of the mixture.

Chemical Kinetics

Rate Laws and Reaction Order

Chemical kinetics studies the speed of chemical reactions and the factors affecting them. The rate law expresses the relationship between the rate of a reaction and the concentration of reactants.

• General Rate Law: $\text{Rate} = k[A]^m[B]^n$ where k is the rate constant, and m and n are the reaction orders with respect to each reactant.

• Determining Rate Law: Use experimental data or information about the reaction mechanism.

• Effect of Concentration Changes: If the concentration of a reactant is multiplied by a factor, the rate increases by that factor raised to the power of the reaction order for that reactant.

• Example: For a reaction first order in [A] and second order in [B], doubling [A] and tripling [B] increases the rate by $2^1 \times 3^2 = 18$ times.

Reaction Mechanisms and Rate-Determining Step

• Reaction Mechanism: The sequence of elementary steps by which a chemical reaction occurs.

• Rate-Determining Step: The slowest step in a reaction mechanism, which controls the overall rate.

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

• Arrhenius Equation: $k = A e^{-E_a/RT}$

• Energy Profile Diagram: Shows the energy changes during a reaction, including activation energies for each step.

Chemical Equilibrium

Equilibrium Expressions and Le Châtelier's Principle

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

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

• Le Châtelier's Principle: If a system at equilibrium is disturbed, it will shift to counteract the disturbance.

• Effects of Changes:

  • Increasing concentration of a reactant shifts equilibrium to the right (toward products).

  • Increasing concentration of a product shifts equilibrium to the left (toward reactants).

  • Increasing temperature (for endothermic reactions) shifts equilibrium to the right; for exothermic, to the left.

Acids, Bases, and Aqueous Equilibria

Acid-Base Reactions and Conjugate Pairs

Acids donate protons (H+), and bases accept protons. In aqueous solutions, acid-base reactions involve the transfer of protons between conjugate acid-base pairs.

• Conjugate Acid-Base Pair: Two species that differ by one proton.

• Example: In the reaction $HSO_4^-(aq) + HCO_3^-(aq) \rightarrow SO_4^{2-}(aq) + H_2CO_3(aq)$, $HSO_4^-$ is the acid and $SO_4^{2-}$ is its conjugate base.

• Writing Balanced Equations: Ensure mass and charge are balanced.

pH and pOH Calculations

The pH of a solution measures its acidity or basicity. It is calculated as the negative logarithm of the hydrogen ion concentration.

• pH Formula: $pH = -\log[H^+]$

• pOH Formula: $pOH = -\log[OH^-]$

• Relationship: $pH + pOH = 14.00$ (at 25°C)

• For Weak Acids: Use the acid dissociation constant ($K_a$) to find [H+]: $K_a = \frac{[H^+][A^-]}{[HA]}$

Relative Strengths and Trends

• Acid/Base Strength: Strong acids/bases dissociate completely; weak acids/bases only partially dissociate.

• Trends:

  • For binary acids (HX), acid strength increases down a group and across a period (to the right).

  • For oxoacids (H-O-X), acid strength increases with increasing electronegativity of X and number of oxygens.

Reference Tables

Physical Constants and Standard Enthalpies of Formation

Constant	Value
Avogadro's Number, NA	6.0221415 × 1023 particles/mole
Gas Constant, R	0.0821 L·atm/(mol·K) or 8.314 J/(mol·K)
Standard Temperature	273.15 K (0°C)

Substance	ΔHf° (kJ/mol)
CO2(g)	-393.5
H2O(l)	-285.8
Na2CrO4(s)	-813.4
Cr(s)	0
Na(s)	0

Rate Law	Integrated Rate Law	Half-life
Zero Order	$[A]_t = [A]_0 - kt$	$t_{1/2} = \frac{[A]_0}{2k}$
First Order	$\ln[A]_t = \ln[A]_0 - kt$	$t_{1/2} = \frac{0.693}{k}$
Second Order	$\frac{1}{[A]_t} = \frac{1}{[A]_0} + kt$	$t_{1/2} = \frac{1}{k[A]_0}$

Periodic Table of the Elements

The periodic table organizes elements by increasing atomic number and groups elements with similar chemical properties into columns. It is a fundamental reference for predicting element behavior, valence, and trends in properties such as electronegativity, atomic radius, and ionization energy.

Additional info: These notes are based on exam questions and reference tables provided in the file. Where necessary, standard academic context and definitions have been added for completeness.