General Chemistry: Thermochemistry, Atomic Structure, and Periodic Trends Study Guide

Thermochemistry

Internal Energy and Work

The internal energy (ΔE) of a system is a fundamental concept in thermodynamics, representing the total energy contained within the system. Changes in internal energy occur when heat is absorbed or released and when work is done by or on the system.

• Formula: $\Delta E = q + w$ where q is heat and w is work.

• Example: If a system absorbs 220 J of heat and does 100 J of work on the surroundings, $\Delta E = 220\,\text{J} + (-100\,\text{J}) = 120\,\text{J}$.

Endothermic and Exothermic Processes

Endothermic processes absorb heat from the surroundings, while exothermic processes release heat.

• Endothermic Example: Melting of a solid (e.g., ice melting to water).

• Exothermic Process: ΔH is negative for exothermic reactions, indicating heat is released.

Standard Enthalpy of Formation (ΔHfo)

The standard enthalpy of formation of an element in its most stable form is zero.

• Elements with ΔHfo = 0: O2(g), N2(g), F2(g), S8(s), Br2(l), Ca(s)

Calculating Heat Consumed in a Reaction

To determine the heat consumed or released, use stoichiometry and the enthalpy change for the reaction.

• Example: For the decomposition of CH3OH(l), if ΔHrxn = +128.1 kJ and 50.0 g of CH3OH(l) decomposes, calculate the moles and multiply by ΔHrxn per mole.

• Calculation: $\text{Moles CH}_3\text{OH} = \frac{50.0\,\text{g}}{32.04\,\text{g/mol}} \approx 1.56\,\text{mol}$; $\text{Heat} = 1.56\,\text{mol} \times 128.1\,\text{kJ/mol} \approx 200.2\,\text{kJ}$

Specific Heat and Calorimetry

Specific heat capacity is the amount of heat required to raise the temperature of one gram of a substance by one degree Celsius.

• Formula: $q = m c \Delta T$

• Example: To heat 50.0 g of lead from 25°C to 45°C, $q = 50.0\,\text{g} \times 0.128\,\text{J/g}^\circ\text{C} \times 20^\circ\text{C} = 130\,\text{J}$

Hess's Law

Hess's Law states that the total enthalpy change for a reaction is the sum of the enthalpy changes for individual steps.

• Example: Given reactions:

  • 2S(s) + 3O2(g) → 2SO3(g), ΔH = -790 kJ

  • S(s) + O2(g) → SO2(g), ΔH = -297 kJ

  Find: ΔH for 2SO2(g) + O2(g) → 2SO3(g): $\Delta H = -790\,\text{kJ} - 2(-297\,\text{kJ}) = -196\,\text{kJ}$

Enthalpy of Reaction from Standard Enthalpies of Formation

The enthalpy change for a reaction can be calculated using standard enthalpies of formation:

• Formula: $\Delta H_{rxn} = \sum \Delta H_f^\circ(\text{products}) - \sum \Delta H_f^\circ(\text{reactants})$

• Example Table:

Substance	ΔHfo (kJ/mol)
CO (g)	-110.5
O2 (g)	0
CO2 (g)	-393.5
CaCO3 (s)	-1207.0

• Calculation for 2CO(g) + O2(g) → 2CO2(g): $\Delta H_{rxn} = [2 \times (-393.5)] - [2 \times (-110.5) + 0] = -566.4\,\text{kJ}$

Atomic Structure and Electron Configuration

Electron Configuration

Electron configuration describes the arrangement of electrons in an atom's orbitals.

• Full and Condensed Configuration for Se: 1s22s22p63s23p64s23d104p4

• For Ti2+: 1s22s22p63s23p63d2

Quantum Numbers and Orbitals

Quantum numbers describe the properties of atomic orbitals and the electrons in them.

• Number of s and p orbitals in n=2 shell: One s orbital, three p orbitals; total electrons = 8

Electron Subshells

• Order of filling: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 4d, 4f

Light and Electromagnetic Radiation

Frequency, Wavelength, and Energy

Light exhibits both wave and particle properties. The relationship between frequency (ν), wavelength (λ), and the speed of light (c) is:

• Formula: $c = \lambda \nu$

• Example: For ν = 1.20 × 1013 s-1, $\lambda = \frac{c}{\nu} = \frac{3.00 \times 10^8\,\text{m/s}}{1.20 \times 10^{13}\,\text{s}^{-1}} = 2.5 \times 10^{-5}\,\text{m}$

Photon Energy

• Formula: $E = \frac{hc}{\lambda}$

• Example: For λ = 8.0 m, $E = \frac{6.626 \times 10^{-34}\,\text{J·s} \times 3.00 \times 10^8\,\text{m/s}}{8.0\,\text{m}} = 2.48 \times 10^{-26}\,\text{J}$

Spectra

Atoms and molecules emit or absorb light at specific wavelengths, producing spectra.

• Line Spectrum: Contains only specific wavelengths; characteristic of elements.

Periodic Trends

Trends in the Periodic Table

Periodic trends describe how properties of elements change across periods and down groups.

• Atomic Radius: Increases down a group, decreases across a period.

• Ionization Energy: Increases across a period, decreases down a group.

Isoelectronic Series

Isoelectronic species have the same number of electrons but different nuclear charges.

• Example: B5+, S2-, As3-, Te2-

Ionization of Aluminum

Ionization energy is the energy required to remove an electron from an atom or ion.

• Second Ionization of Aluminum: $\text{Al}^+(g) \rightarrow \text{Al}^{2+}(g) + e^-$

Summary Table: Key Thermochemistry Data

Substance	ΔHfo (kJ/mol)
CO (g)	-110.5
O2 (g)	0
CO2 (g)	-393.5
CaCO3 (s)	-1207.0

Additional info: These notes expand on the original test questions and answers, providing academic context, definitions, and worked examples for key concepts in general chemistry.