Thermochemistry and Chemical Kinetics: Study Guide

Thermochemistry and Chemical Kinetics

Conversions, Constants, and Formulas

This section provides essential constants, unit conversions, and formulas commonly used in general chemistry, particularly in thermochemistry and kinetics.

• Temperature Conversions:

  • °C to °F: $C = 5/9 (F - 32)$

  • K = °C + 273.15

• Gas Constant: $R = 0.08206$ L·atm/(K·mol) or $8.314$ J/(K·mol)

• Pressure Conversion: $101.3$ J = $1$ L·atm

• Energy Units: $1$J = $1$ kg·m2/s2

Key Thermochemistry Formulas

• Heat (q): $q = c_s \times m \times \Delta T$

• Change in Internal Energy: $\Delta E = q + w$

• Work (w): $w = -P\Delta V$

• Enthalpy Change per Mole: $\Delta H = \frac{q_{system}}{mol}$

• Standard Enthalpy of Reaction: $\Delta H_{rxn} = \sum_{products} n_p \Delta H_f^{\circ} (products) - \sum_{reactants} n_r \Delta H_f^{\circ} (reactants)$

Key Kinetics Formulas

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

• Integrated Rate Laws:

  • First Order: $[A]_t = [A]_0 e^{-kt}$ or $\ln [A]_t = -kt + \ln [A]_0$

  • Second Order: $\frac{1}{[A]_t} = kt + \frac{1}{[A]_0}$

• Arrhenius Plot: $\ln k = \ln A - \frac{E_a}{RT}$

• Two-Point Arrhenius Equation: $\ln \frac{k_2}{k_1} = -\frac{E_a}{R} \left( \frac{1}{T_2} - \frac{1}{T_1} \right)$

Periodic Table Reference

The periodic table is a fundamental tool for identifying elements, their atomic numbers, and their properties. It is essential for solving stoichiometry, thermochemistry, and kinetics problems.

Thermochemistry

Endothermic and Exothermic Processes

Thermochemistry studies the heat changes that accompany chemical reactions and physical changes.

• Endothermic Process: Absorbs heat from the surroundings (e.g., evaporation of water).

• Exothermic Process: Releases heat to the surroundings (e.g., combustion reactions).

• Example: $H_2O(l) \rightarrow H_2O(g)$ (evaporation) is endothermic because energy is absorbed to convert liquid to gas.

Enthalpy Change ($\Delta H$) Calculations

Enthalpy change for a reaction can be determined using standard enthalpies of formation or by combining known reactions (Hess's Law).

• Standard Enthalpy of Formation ($\Delta H_f^{\circ}$): The enthalpy change when one mole of a compound is formed from its elements in their standard states.

• Hess's Law: The total enthalpy change for a reaction is the sum of the enthalpy changes for individual steps.

• Example Table:

Species	$\Delta H_f^{\circ}$ (kJ/mol)
Ca2+ (aq)	-226.7
OH- (aq)	-230.0
H2O (l)	-285.83
H2 (g)	0

• Application: Use the above values to calculate $\Delta H$ for reactions involving these species.

Sample Enthalpy Calculations

• Combustion of $H_2$: $2H_2(g) + O_2(g) \rightarrow 2H_2O(g)$, $\Delta H = -483.6$ kJ (exothermic).

• Sign of $q_{sys}$: If a substance melts in your hand, $q_{sys}$ is positive (system absorbs heat).

Calorimetry

Calorimetry measures the heat exchanged in a chemical or physical process.

• q = cs × m × ΔT: Used to calculate heat absorbed or released.

• Example: Dissolving NH4NO3 in water is endothermic; the solution cools as heat is absorbed.

Chemical Kinetics

Reaction Rates and Rate Laws

Chemical kinetics studies the speed of chemical reactions and the factors affecting them.

• Rate Law: Expresses the rate as a function of reactant concentrations.

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

• Order of Reaction: The sum of the exponents in the rate law.

• Example Table:

Exp.	[NO] (M)	[O2] (M)	Initial Rate (M/s)
1	0.090	0.050	0.440
2	0.090	0.100	0.440
3	0.270	0.050	1.32

• Application: Use changes in concentration and rate to determine reaction order with respect to each reactant.

Factors Affecting Reaction Rate

• Concentration: Increasing reactant concentration generally increases rate.

• Temperature: Higher temperature increases rate (more molecules have sufficient energy to react).

• Surface Area: Greater surface area increases rate for heterogeneous reactions.

• Catalysts: Lower activation energy, increasing rate.

Half-Life and Integrated Rate Laws

• Half-Life ($t_{1/2}$): Time required for half the reactant to be consumed.

• First Order: $t_{1/2} = \frac{0.693}{k}$

• Second Order: $t_{1/2} = \frac{1}{k[A]_0}$

Arrhenius Equation and Activation Energy

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

• Effect of $E_a$: As activation energy increases, the rate constant $k$ decreases.

• Temperature Dependence: Increasing temperature increases $k$.

Reaction Mechanisms

Reaction mechanisms describe the stepwise sequence of elementary reactions by which overall chemical change occurs.

• Rate-Determining Step: The slowest step controls the overall rate.

• Elementary Steps: Each step has its own rate law.

• Example: For a two-step mechanism, the slow step determines the observed rate law.

Graphical Representation of Rate Laws

• First Order: Plot of $\ln [A]$ vs. time is linear.

• Second Order: Plot of $1/[A]$ vs. time is linear.

• Zero Order: Plot of $[A]$ vs. time is linear.

Summary Table: Key Equations and Concepts

Concept	Equation	Notes
Heat (q)	$q = c_s m \Delta T$	cs: specific heat, m: mass, ΔT: temperature change
Work (w)	$w = -P\Delta V$	Pressure-volume work
Enthalpy Change	$\Delta H = \sum n_p \Delta H_f^{\circ} (products) - \sum n_r \Delta H_f^{\circ} (reactants)$	Standard enthalpy of formation
First Order Rate Law	$\ln [A]_t = -kt + \ln [A]_0$	Straight line: $\ln [A]$ vs. time
Second Order Rate Law	$\frac{1}{[A]_t} = kt + \frac{1}{[A]_0}$	Straight line: $1/[A]$ vs. time
Arrhenius Equation	$k = A e^{-E_a/(RT)}$	Temperature dependence of rate constant
Half-Life (First Order)	$t_{1/2} = \frac{0.693}{k}$	Independent of initial concentration

Additional info: The above notes synthesize the key concepts, equations, and applications from the provided exam practice questions and formula sheet, with added academic context for clarity and completeness.