GOB Chemistry: Mole, Mass Relationships, Thermodynamics, and Chemical Equilibrium

Chemical RXNs: Mole and Mass Relationships

The Mole and Avogadro's Number

The mole is a fundamental unit in chemistry that represents a specific number of objects, typically atoms, molecules, or ions. Avogadro's number defines the number of objects in one mole.

• Definition: The mole is the amount of substance containing $6.022 \times 10^{23}$ objects.

• Avogadro's Number: $6.022 \times 10^{23}$ units per mole.

• Units: Objects/mole (can be atoms, molecules, ions, etc.)

• Analogy: Like a dozen (12 objects), but much larger.

• Applications: Used to count atoms, molecules, ions in chemical reactions.

Example: 1 mole of copper contains $6.022 \times 10^{23}$ copper atoms.

Atomic Mass and Molar Mass

Atomic mass is the mass of a single atom, while molar mass (MM) is the mass of one mole of a substance, expressed in grams per mole.

• Atomic Mass: Not used in calculations; always use molar mass (MM).

• Molar Mass (MM): The mass of 1 mole of a substance, in grams/mole.

• Formula: $\text{MM} = \frac{\text{grams}}{\text{mole}}$

Example: Molar mass of sodium bicarbonate (NaHCO3) is the sum of atomic masses of Na, H, C, and O.

Stoichiometry and Unit Analysis

Stoichiometry in Chemical Reactions

Stoichiometry involves using balanced chemical equations to relate quantities of reactants and products.

• Unit Analysis: Use units to track conversions between grams, moles, and molecules.

• Balanced Equations: Essential for correct stoichiometric calculations.

• Example: How many grams of CO2 are made if 1.176 grams of butane (C4H10) are burned with excess oxygen?

Empirical and Molecular Formulas

Empirical formulas show the simplest whole-number ratio of elements in a compound. Molecular formulas show the actual number of atoms of each element in a molecule.

• Calculating Empirical Formula:

  1. Convert % composition to grams.

  2. Convert grams to moles using MM.

  3. Divide all mole values by the smallest to get the ratio.

  4. If ratios are fractions, multiply to get whole numbers.

• Example: Phosphorus burns in air, forming a white solid. Analysis: 43.64% P, 56.36% O. Find empirical formula.

• Molecular Formula: Determined by comparing empirical formula mass to molar mass from experiment.

Limiting Reagent and Percent Yield

The limiting reagent is the reactant that is completely consumed first, limiting the amount of product formed. Percent yield measures the efficiency of a reaction.

• Limiting Reagent: Calculate moles of each reactant; the one producing the least product is limiting.

• Percent Yield Formula: $\% = \left(\frac{\text{part}}{\text{whole}}\right) \times 100$

Example: How much ammonia can be made from 5.00 g H2 and 20.0 g N2?

Chemical Potential Energy and Thermodynamics

Enthalpy and Energy Changes

Enthalpy (H) is the heat given off or absorbed at constant pressure. Chemical reactions involve changes in energy, often measured as enthalpy change ($\Delta H$).

• Standard Heat of Formation: $\Delta H^\circ_{rxn} = \Sigma \Delta H^\circ_{products} - \Sigma \Delta H^\circ_{reactants}$

• Work and Heat: $\Delta E = q + w$ (First Law of Thermodynamics)

• Bond Dissociation Energy: Energy required to break a bond; energy released when bonds form.

Example: $\mathrm{N} \equiv \mathrm{N}$ bond: $\Delta H = +226$ kcal/mole to break; $\Delta H = -226$ kcal/mole to form.

Exothermic and Endothermic Reactions

Exothermic reactions release heat ($q$ is negative, $\Delta H$ is negative), while endothermic reactions absorb heat ($q$ is positive, $\Delta H$ is positive).

• Exothermic: Heat is a product; feels hot.

• Endothermic: Heat is a reactant; feels cold.

Example: Combustion reactions are typically exothermic.

Spontaneity, Entropy, and Gibbs Free Energy

Spontaneous processes occur without external influence. Entropy ($S$) measures disorder; Gibbs Free Energy ($\Delta G$) determines spontaneity.

• Gibbs Free Energy Formula: $\Delta G = \Delta H - T\Delta S$

• Spontaneous: $\Delta G < 0$

• Non-spontaneous: $\Delta G > 0$

• Entropy: Increases in spontaneous processes.

$\Delta H$	$\Delta S$	$\Delta G$	Spontaneity
-	+	-	Spontaneous at all T
+	-	+	Non-spontaneous at all T
-	-	Depends	Spontaneous at low T
+	+	Depends	Spontaneous at high T

Chemical Kinetics and Reaction Rates

Reaction Rate

Reaction rate measures how fast a chemical reaction occurs. It depends on concentration, temperature, and orientation of molecules.

• Rate Formula: $\text{Rate} = \frac{\Delta [A]}{\Delta t}$

• Activation Energy ($E_a$): Minimum energy required for a reaction to proceed.

• Catalysts: Lower $E_a$, increase rate, do not change reaction composition.

Example: Enzymes are biological catalysts.

Chemical Equilibrium

Dynamic Equilibrium

At equilibrium, the rate of the forward reaction equals the rate of the reverse reaction. Concentrations of reactants and products remain constant.

• Law of Mass Action: $K_{eq} = \frac{[C]^c[D]^d}{[A]^a[B]^b}$

• Equilibrium Constant ($K_{eq}$): Indicates whether products or reactants are favored.

• Manipulating $K$: Reversing a reaction inverts $K$; multiplying coefficients changes $K$ exponent.

Reaction	Equilibrium Constant
A → B	K1
B → A	1/K1
2A → 2B	K12

Le Châtelier's Principle

If a system at equilibrium is disturbed, it will shift to counteract the disturbance.

• Increase in Pressure: Shifts equilibrium to side with fewer moles of gas.

• Increase in Reactants: Shifts equilibrium toward products.

• Increase in Products: Shifts equilibrium toward reactants.

• Exothermic Reaction: Heat can be considered a product.

Example: Adding more reactant shifts equilibrium toward product formation.

Periodic Table and Chemical Formulas

Periodic Table of the Elements

The periodic table organizes elements by atomic number and properties. It is essential for determining atomic masses and chemical behavior.

• Groups: Columns with similar chemical properties.

• Periods: Rows indicating energy levels.

• Applications: Used to find atomic masses for molar mass calculations.

Example: Calculating molar mass of sodium bicarbonate (NaHCO3) using atomic masses from the periodic table.

Additional info: Some context and examples were expanded for clarity and completeness, including stepwise explanations for empirical formula calculation and Le Châtelier's Principle.