General Chemistry: Equilibrium, Acid-Base, Lewis Structures, and Solution Calculations – Study Guide

Equilibrium and Reaction Quotients

Reaction Quotient (Q) and Equilibrium Constant (K)

The reaction quotient (Q) and the equilibrium constant (K) are used to predict the direction of a chemical reaction and to determine if a system is at equilibrium. Both are calculated using the concentrations or partial pressures of reactants and products, but Q uses current (not necessarily equilibrium) values, while K uses equilibrium values.

• For a general reaction: $aA + bB \rightleftharpoons cC + dD$

• Equilibrium constant (K): $K = \frac{[C]^c[D]^d}{[A]^a[B]^b}$

• Reaction quotient (Q): $Q = \frac{[C]^c[D]^d}{[A]^a[B]^b}$ (using current concentrations or partial pressures)

• If $Q < K$, the reaction proceeds to the right (toward products).

• If $Q > K$, the reaction proceeds to the left (toward reactants).

• If $Q = K$, the system is at equilibrium.

Example: For the reaction $2SO_2(g) + O_2(g) \rightleftharpoons 2SO_3(g)$, the equilibrium expression in terms of partial pressures is:

$K_p = \frac{P_{SO_3}^2}{P_{SO_2}^2 P_{O_2}}$

Acid-Base Chemistry

Acid-Base Pairs and Reactions

Acid-base reactions involve the transfer of protons (H+) between species. The Brønsted-Lowry acid donates a proton, while the Brønsted-Lowry base accepts a proton. Each acid has a conjugate base, and each base has a conjugate acid.

• Conjugate acid-base pair: Two species that differ by one proton.

• Example: $HA + H_2O \rightleftharpoons A^- + H_3O^+$

• Here, HA is the acid, A- is its conjugate base; H2O is the base, H3O+ is its conjugate acid.

pH, pOH, and Solution Calculations

The pH of a solution measures its acidity or basicity. It is related to the concentration of hydrogen ions:

• $pH = -\log[H^+]$

• $pOH = -\log[OH^-]$

• $pH + pOH = 14$ (at 25°C)

• To find [OH-] from pH: $[OH^-] = 10^{-pOH}$

Example: If pH = 12.479, then $pOH = 14 - 12.479 = 1.521$, so $[OH^-] = 10^{-1.521}$ M.

Acid Dissociation and Ka

The acid dissociation constant ($K_a$) quantifies the strength of a weak acid:

• For $HA \rightleftharpoons H^+ + A^-$, $K_a = \frac{[H^+][A^-]}{[HA]}$

• Stronger acids have higher $K_a$ values.

• pKa is related: $pK_a = -\log K_a$

Example: For glycolyic acid, $K_a = 3.5 \times 10^{-4}$, calculate pH using ICE tables and the quadratic formula if necessary.

Lewis Structures and Resonance

Drawing Lewis Structures

Lewis structures represent the arrangement of electrons in molecules. They show bonds and lone pairs.

• Count total valence electrons.

• Arrange atoms, connect with single bonds.

• Distribute remaining electrons to complete octets.

• Check for formal charges: $\text{Formal charge} = \text{valence electrons} - \text{nonbonding electrons} - \frac{1}{2}(\text{bonding electrons})$

Resonance Structures

Resonance structures are different Lewis structures for the same molecule, showing delocalization of electrons. The actual structure is a hybrid of all resonance forms.

• Resonance structures must have the same arrangement of atoms but different placement of electrons.

• Equivalent resonance structures contribute equally to the hybrid.

Solution Dilution and Concentration Calculations

Dilution Formula

To dilute a solution, use the formula:

$M_1V_1 = M_2V_2$

• $M_1$ = initial molarity, $V_1$ = initial volume

• $M_2$ = final molarity, $V_2$ = final volume

Example: If 5.0 mL of 0.050 M HI is diluted to 125.0 mL, the new concentration is $M_2 = \frac{M_1V_1}{V_2}$.

Stoichiometry and Limiting Reactant

Stoichiometric Calculations

Stoichiometry involves using balanced chemical equations to calculate the amounts of reactants and products.

• Identify the limiting reactant (the reactant that is completely consumed first).

• Use mole ratios from the balanced equation to relate quantities.

Example: If $25.0$ mL of $0.036$ M $Cr(ClO_4)_3$ is mixed with $75.0$ mL of $0.045$ M $KOH$, calculate moles of $K_3[Cr(OH)_6]$ formed.

Acid-Base Strength and Conjugate Pairs

Relative Strengths

The strength of acids and bases can be compared using $K_a$ and $K_b$ values. The stronger the acid, the weaker its conjugate base.

• For a series of acids, the one with the largest $K_a$ (or smallest $pK_a$) is the strongest.

• For bases, the one with the largest $K_b$ is the strongest.

Tables: Acid-Base Properties at Different pH

The following table summarizes the acid-base properties of solutions at different pH values:

pH	[H3O+]	pOH	Solution Type
7.0	$1.0 \times 10^{-7}$ M	7.0	neutral
< 7.0	> $1.0 \times 10^{-7}$ M	> 7.0	acidic
> 7.0	< $1.0 \times 10^{-7}$ M	< 7.0	basic

Organic and Inorganic Nomenclature

Shorthand Notation and Empirical Formulas

Organic compounds are often represented in shorthand notation, showing only the carbon skeleton and functional groups. Empirical formulas give the simplest whole-number ratio of atoms in a compound.

• Example: Lactone, C6H10O4

Formal Charge and Lewis Structures for Polyatomic Ions

Formal Charge Calculation

Formal charge helps determine the most reasonable Lewis structure for a molecule or ion.

• Calculate for each atom: $\text{Formal charge} = \text{valence electrons} - \text{nonbonding electrons} - \frac{1}{2}(\text{bonding electrons})$

• The sum of formal charges should equal the overall charge of the molecule or ion.

Summary Table: Key Equilibrium and Acid-Base Formulas

Concept	Formula	Description
Equilibrium Constant (K)	$K = \frac{[\text{products}]}{[\text{reactants}]}$	Ratio of product to reactant concentrations at equilibrium
Reaction Quotient (Q)	$Q = \frac{[\text{products}]}{[\text{reactants}]}$	Same as K, but for any point in the reaction
pH	$pH = -\log[H^+]$	Measure of acidity
pOH	$pOH = -\log[OH^-]$	Measure of basicity
pH and pOH relationship	$pH + pOH = 14$	At 25°C
Dilution	$M_1V_1 = M_2V_2$	Relates concentrations and volumes before and after dilution

Additional info: Some questions involve interpreting molecular structures, resonance, and 3D representations, which are foundational for understanding chemical bonding and molecular geometry in General Chemistry.