Thermochemistry and Chemical Kinetics: Study Guide

Thermochemistry and Chemical Kinetics

Conversions & Constants

Understanding key constants and conversion factors is essential for solving problems in thermochemistry and kinetics.

• Temperature: $^\circ C = 5/9 (F - 32)$; $K = ^\circ C + 273.15$

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

• Pressure: $101.3$ kPa = $1$ atm

• Energy: $1$W = $1$ J/s; $1$J = $1$ kg·m$^2$/s$^2$

Key Thermochemistry Formulas

These formulas are fundamental for calculating heat, work, and enthalpy changes in chemical reactions.

• Heat (q): $q = C_s \times m \times \Delta T$ Where $C_s$ is specific heat, $m$ is mass, and $\Delta T$ is the temperature change.

• Change in Internal Energy: $\Delta E = q + w$ Where $w$ is work done by or on the system.

• Work (at constant pressure): $w = -P \Delta V$

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

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

Thermochemistry: Concepts and Applications

Thermochemistry deals with the heat changes that accompany chemical reactions.

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

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

• Example: $H_2O(l) \rightarrow H_2O(g)$ is endothermic because energy is required to convert liquid water to vapor.

• Enthalpy Calculations: Use standard enthalpy of formation ($\Delta H_f^\circ$) values to determine $\Delta H_{rxn}$ for reactions.

Sample Table: Selected $\Delta H_f^\circ$ Values

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

Example: To find $\Delta H_{rxn}$ for the reaction: $\mathrm{Ca(s) + 2H_2O(l) \rightarrow Ca^{2+}(aq) + 2OH^-(aq) + H_2(g)}$ Apply the formula for $\Delta H_{rxn}$ using the table above.

Calorimetry

Calorimetry is used to measure the heat absorbed or released during a chemical or physical process.

• Coffee Cup Calorimeter: Used for reactions at constant pressure (e.g., solution reactions).

• Formula: $q = m \times C_s \times \Delta T$

• Example: If a reaction absorbs 13.7 kJ in 60.0 g of water ($C_s = 4.184$ J/g$^\circ$C), calculate the final temperature using the above formula.

Chemical Kinetics: Rate Laws and Reaction Order

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

• Rate Law: $\text{Rate} = k[A]^m[B]^n$ Where $k$ is the rate constant, $[A]$ and $[B]$ are concentrations, and $m$, $n$ are the reaction orders.

• First-Order Reaction: $\text{Rate} = k[A]$

• Second-Order Reaction: $\text{Rate} = k[A]^2$ or $k[A][B]$

• Zero-Order Reaction: $\text{Rate} = k$

Integrated Rate Laws

• First-Order: $\ln\left(\frac{[A]_t}{[A]_0}\right) = -kt$

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

• Half-Life (First-Order): $t_{1/2} = \frac{0.693}{k}$

Arrhenius Equation

• Temperature Dependence of Rate Constant: $k = A e^{-E_a/(RT)}$

• Linear Form: $\ln\left(\frac{k_2}{k_1}\right) = -\frac{E_a}{R}\left(\frac{1}{T_2} - \frac{1}{T_1}\right)$

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

Factors Affecting Reaction Rate

• Concentration: Increasing reactant concentration generally increases the rate.

• Temperature: Higher temperature increases the rate constant $k$ (and thus the rate).

• Surface Area: Greater surface area increases reaction rate for solids.

• Catalysts: Lower activation energy, increasing the rate.

Reaction Mechanisms

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

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

• Elementary Step: A single step in a reaction mechanism, each with its own rate law.

• Example: For a two-step mechanism, if the first step is slow, it controls the rate.

Using Experimental Data to Determine Rate Laws

Experimental data (initial rates and concentrations) can be used to deduce the order of reaction with respect to each reactant.

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

Example: If doubling [NO] triples the rate, the reaction is first order in NO. If changing [O2] does not affect the rate, the reaction is zero order in O2.

Graphical Analysis 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.

Periodic Table Reference

The periodic table is a fundamental tool for identifying elements, their atomic numbers, and properties relevant to chemical reactions.

Summary Table: Reaction Order and Integrated Rate Laws

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

Additional info:

• Some questions and data tables are based on standard General Chemistry exam formats, focusing on thermochemistry and kinetics.

• Students should be familiar with interpreting experimental data, using the periodic table, and applying formulas to solve quantitative problems.