General Chemistry Exam 3 Study Guide: Thermochemistry, Chemical Kinetics, Equilibrium, and Acids/Bases

Thermochemistry

Standard Enthalpy of Formation and Thermochemical Equations

Thermochemistry deals with the energy changes that occur during chemical reactions, particularly the transfer of heat. The standard enthalpy of formation ($\Delta H_f^\circ$) is the enthalpy change when one mole of a compound is formed from its elements in their standard states.

• Balanced Thermochemical Equation: Represents the formation or reaction with all reactants and products, including their physical states.

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

• Example: For the reaction $2CrO_3(s) + 2NaCl(s) + H_2O(l) \rightarrow 2NaClO_3(s) + Cr_2O_3(s)$, calculate $\Delta H$ using standard enthalpies of formation.

Significant Figures: Always pay attention to significant figures in calculations.

Enthalpy Change from Tabulated Data

Enthalpy changes can be calculated using tabulated values for standard enthalpies of formation.

• Example: Calculate $\Delta H$ for $3Fe(s) + 4H_2O(g) \rightarrow Fe_3O_4(s) + 4H_2(g)$ using tabulated $\Delta H_f^\circ$ values.

Gas Mixtures and Partial Pressure

In a mixture of gases, each gas exerts a partial pressure proportional to its mole fraction.

• Partial Pressure Formula: $P_i = X_i P_{\text{total}}$ where $X_i$ is the mole fraction of gas $i$.

• Example: Calculate the mass of a mixture given partial pressures and volumes.

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, $m$ and $n$ are the reaction orders.

• Example: For the reaction $CH_3COCH_3(aq) + HOCl(aq) \rightarrow CH_3COCH_2Cl(aq) + H_2O(l)$, if first order in $CH_3COCH_3$ and $HOCl$, rate law is: $\text{Rate} = k[CH_3COCH_3][HOCl]$

• Effect of Concentration: If concentrations are increased, the rate increases by the product of the factors raised to their respective orders.

Reaction Time and Rate Constants

The time required for a reaction to reach a certain completion can be calculated using integrated rate laws.

• First Order Reaction: $t = \frac{1}{k} \ln\left(\frac{[A]_0}{[A]_t}\right)$

• Example: Calculate the time for $N_2O_5$ to decompose to 99% at a given rate constant.

Reaction Mechanisms and Energy Diagrams

Reaction mechanisms describe the stepwise sequence of elementary reactions. Energy diagrams illustrate the energy changes during a reaction.

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

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

• Frequency Factor ($A$): Related to the number of collisions and orientation of reactants.

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

Chemical Equilibrium

Equilibrium Expressions and Le Châtelier's Principle

Chemical equilibrium occurs when the rates of the forward and reverse reactions are equal. The equilibrium constant ($K$) expresses the ratio of product and reactant concentrations at equilibrium.

• Equilibrium Expression: $K = \frac{[\text{products}]}{[\text{reactants}]}$

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

• Example: For $ISO_3^-(aq) + H_2O(l) \rightleftharpoons SO_2^-(aq) + H_3O^+(aq)$, predict the direction of shift upon changes in concentration.

Acids and Bases

Acid-Base Reactions and Conjugate Pairs

Acids donate protons ($H^+$), while bases accept protons. Each acid-base reaction involves conjugate acid-base pairs.

• Conjugate Acid-Base Pair: The acid and base that differ by one proton.

• Example: For $NaHSO_4(aq) + NaH_2PO_4(aq) \rightarrow$ products, identify the conjugate pairs.

Calculating pH and pOH

The pH measures the acidity of a solution, while pOH measures its basicity.

• pH Formula: $pH = -\log[H^+]$

• pOH Formula: $pOH = -\log[OH^-]$

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

• Example: Calculate the pH of $0.050$ M $HBr$ and the pOH of $0.40$ M monoprotic acid.

Acid Strength and Trends

Acid strength depends on molecular structure and periodic trends.

• Binary Acids: Strength increases down a group and across a period.

• Oxoacids: Strength increases with more oxygen atoms and higher electronegativity of the central atom.

• Volatility: For $CH_3Cl$, $CH_3Br$, $CH_3I$, volatility decreases with increasing molar mass.

Reference Tables

Physical Constants

Constant	Value
Avogadro's Number	$6.0221415 \times 10^{23}$ particles/mol
Gas Constant ($R$)	$0.0821$ L·atm/(mol·K) or $8.314$ J/(mol·K)

Arrhenius Equation

• $k = A e^{-E_a/(RT)}$

• $\ln k = \ln A - \frac{E_a}{RT}$

Standard Enthalpies of Formation

Compound	$\Delta H_f^\circ$ (kJ/mol)
CO$_2$(g)	-393.5
H$_2$O(l)	-285.8
SO$_2$(g)	-296.8
SO$_3$(g)	-395.7

Periodic Table of the Elements

The periodic table organizes elements by increasing atomic number and groups elements with similar chemical properties. It is essential for referencing atomic masses, element symbols, and periodic trends.

Additional info:

• Some context and formulas were inferred from standard General Chemistry curriculum and the provided exam sheet.

• Physical constants and enthalpy values are standard and may be referenced in calculations.