General Chemistry Study Notes: Thermochemistry, Quantum Numbers, and Atomic Structure

Thermochemistry

Internal Energy and Heat Transfer

Thermochemistry studies the energy changes that occur during chemical reactions, particularly the transfer of heat and work.

• Internal Energy (ΔE): The total energy contained within a system. Changes in internal energy can be negative or positive depending on whether the system loses or gains energy.

• Heat (q) and Work (w): Energy can be transferred as heat or work. The sign convention is important: if the system gives off heat or does work, ΔE is negative.

• Equation:

$\Delta E = q + w$

• Example: If a system gives off heat and does work, both q and w are negative, making ΔE negative.

Enthalpy and Combustion Reactions

Enthalpy (ΔH) is a measure of the heat content of a system at constant pressure. It is commonly used to describe heat changes in chemical reactions, such as combustion.

• Combustion Reaction: The reaction of methane with oxygen is a classic example:

$\mathrm{CH_4(g) + 2O_2(g) \rightarrow 2H_2O(g) + CO_2(g)}$

• ΔH for the Reaction: ΔH is zero for the reactants before the reaction occurs.

• Example: For the combustion of methane, ΔH is zero for CH4(g) and O2(g).

Calculating Enthalpy Change

To calculate the enthalpy change for a reaction, use the enthalpy values of reactants and products.

• Example Reaction:

$2\mathrm{NaO_2(s) + 2H_2O(l) \rightarrow 4NaOH(s) + O_2(g)}$

• If ΔH for the reaction is -126 kJ, then 126 kJ are released per mole of reaction as written.

• To find the energy released for a specific amount, multiply the number of moles by the ΔH per mole.

Hess's Law and Reaction Enthalpy

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

• Example: For the reaction:

$\mathrm{IF_5(s) \rightarrow IF_3(g) + F_2(g)}$

• Given:

$\mathrm{IF_5(s) \rightarrow IF_3(g) + F_2(g)} \quad \Delta H = -390\ \mathrm{kJ}$ $\mathrm{IF_5(s) \rightarrow 2IF_3(g) + 2F_2(g)} \quad \Delta H = -745\ \mathrm{kJ}$

• Use algebraic manipulation to find ΔH for related reactions.

Electronic Structure of Atoms

Quantum Numbers

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

• Principal Quantum Number (n): Indicates the energy level.

• Angular Momentum Quantum Number (l): Indicates the shape of the orbital.

• Magnetic Quantum Number (ml): Indicates the orientation of the orbital.

• Spin Quantum Number (ms): Indicates the spin direction of the electron.

• Valid Sets: A valid set of quantum numbers must follow the rules: n > 0, 0 ≤ l < n, -l ≤ ml ≤ l, ms = ±1/2.

• Example Table:

n	l	ml	ms
2	1	0	+1/2
1	0	0	-1/2
3	2	2	+1/2

Principal Quantum Number

The principal quantum number (n) is the only quantum number that determines the energy level of an electron in a hydrogen atom.

• Example: n = 1, 2, 3, ...

Atomic Structure and Electron Configuration

Ground-State Electron Configuration

The ground-state electron configuration of an element shows the arrangement of electrons in its lowest energy state.

• Fluorine: Atomic number 9. The electron configuration is:

$\mathrm{[He]2s^2 2p^5}$

• Example: Fluorine: 1s2 2s2 2p5

Properties of Light and Electromagnetic Radiation

Wavelength and Frequency

Electromagnetic radiation has properties of both waves and particles. The energy of a photon is related to its frequency and wavelength.

• Energy and Frequency: Energy is directly proportional to frequency.

• Energy and Wavelength: Energy is inversely proportional to wavelength.

• Equation:

$E = h\nu = \dfrac{hc}{\lambda}$

• Shortest Wavelength: Ultraviolet radiation has a shorter wavelength than visible or infrared light.

Types of Electromagnetic Radiation

• X-ray: Very short wavelength, high energy.

• Microwave: Longer wavelength, lower energy.

• Ultraviolet: Shorter wavelength than visible light, higher energy.

• Infrared: Longer wavelength than visible light, lower energy.

Summary Table: Quantum Numbers

Quantum Number	Symbol	Possible Values	Physical Meaning
Principal	n	1, 2, 3, ...	Energy level
Angular Momentum	l	0 to n-1	Orbital shape
Magnetic	ml	-l to +l	Orbital orientation
Spin	ms	+1/2, -1/2	Electron spin direction

Additional info: Some explanations and tables were expanded for clarity and completeness based on standard General Chemistry curriculum.