General Chemistry 1050: Thermochemistry, Atomic Structure, and Quantum Theory Study Notes

Thermochemistry

Enthalpy Changes and Thermochemical Equations

Thermochemistry deals with the heat changes that accompany chemical reactions. The enthalpy change, ΔH, is a key concept, representing the heat absorbed or released at constant pressure.

• Thermochemical Equation: A balanced chemical equation that includes the enthalpy change.

• Standard Enthalpy of Reaction (ΔHorxn): The enthalpy change when reactants in their standard states are converted to products in their standard states.

• Hess's Law: The total enthalpy change for a reaction is the same, no matter how many steps the reaction is carried out in.

Example: Calculating ΔHorxn using a series of thermochemical equations or using standard enthalpies of formation:

• Given reactions and their ΔH values, manipulate and sum them to obtain the target reaction and its enthalpy change.

• Alternatively, use standard enthalpies of formation:

$\Delta H^\circ_{\text{rxn}} = \sum n_p \Delta H^\circ_f(\text{products}) - \sum n_r \Delta H^\circ_f(\text{reactants})$

• State Function: Enthalpy is a state function, meaning its change depends only on the initial and final states, not the path taken.

Calorimetry

Calorimetry is the measurement of heat flow. A bomb calorimeter is used to measure the change in internal energy (ΔU) at constant volume.

• Heat Capacity (C): The amount of heat required to raise the temperature of the calorimeter by 1 K.

• Calculation: The heat released or absorbed is calculated as:

$q = C \Delta T$

• For bomb calorimetry, the work term (w) is negligible because the volume is constant, so:

$\Delta U = q_v$

• To find the final temperature after combustion, rearrange the equation:

$\Delta T = \frac{q}{C}$

• Where q is the heat released (negative for exothermic reactions).

Atomic Structure and Quantum Theory

Atomic Orbitals and Electron Configuration

Electrons in atoms occupy orbitals, which are regions of space with a high probability of finding an electron. The arrangement of electrons is described by the electron configuration.

• Quantum Numbers: Each electron is described by four quantum numbers:

  • Principal quantum number (n): Indicates the energy level (shell).

  • Angular momentum quantum number (l): Indicates the subshell (s, p, d, f).

  • Magnetic quantum number (ml): Indicates the orientation of the orbital.

  • Spin quantum number (ms): Indicates the spin direction (+1/2 or -1/2).

• Orbital Filling Diagrams: Show the arrangement of electrons in orbitals, following the Aufbau principle, Pauli exclusion principle, and Hund's rule.

• Paramagnetism and Diamagnetism:

  • Paramagnetic: Atoms with unpaired electrons; attracted to a magnetic field.

  • Diamagnetic: Atoms with all electrons paired; weakly repelled by a magnetic field.

Example: Sulphur (S) electron configuration: 1s2 2s2 2p6 3s2 3p4

Radial Probability Distributions and Nodes

The probability of finding an electron at a certain distance from the nucleus is described by the radial probability distribution. Nodes are regions where the probability is zero.

• Radial Nodes: Spherical regions where the probability of finding an electron is zero; number of radial nodes = n - l - 1.

• Angular Nodes: Planar regions (for p, d, f orbitals) where the probability is zero; number of angular nodes = l.

Example Table:

Orbital	Radial Nodes	Angular Nodes
2s	1	0
2p	0	1
3p	1	1

Energy Levels and Spectroscopy

Electrons in atoms occupy discrete energy levels. When an electron transitions between levels, it absorbs or emits a photon of energy equal to the difference between the levels.

• Energy of a Photon:

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

• Rydberg Formula for Hydrogen-like Atoms:

$E_n = -2.179 \times 10^{-18} \left( \frac{Z^2}{n^2} \right) \text{J}$

• Where Z is the atomic number, n is the principal quantum number.

• Frequency of Emitted Photon:

$\nu = \frac{E}{h}$

• Wavelength and Visibility: Visible light has wavelengths between 400 and 750 nm. Transitions that emit photons outside this range are not visible to the human eye.

Significant Figures and Units

Reporting Results

All numerical answers in chemistry must be reported with the correct number of significant figures and appropriate units. Marks may be deducted for incorrect use.

• Significant Figures: Reflect the precision of measured or calculated values.

• Units: Always include units in your answers (e.g., kJ, mol, K).

Useful Constants and Formulas

Common Constants

Quantity	Symbol	Value
Avogadro's Number	NA	6.022 × 1023 mol−1
Gas Constant	R	8.314 J·mol−1·K−1
Planck's Constant	h	6.626 × 10−34 J·s
Speed of Light	c	2.998 × 108 m·s−1
Rydberg Constant	RH	1.097 × 107 m−1

Key Equations

• Ideal Gas Law:

$PV = nRT$

• Energy of an Electron in Hydrogen-like Atom:

$E_n = -2.179 \times 10^{-18} \left( \frac{Z^2}{n^2} \right) \text{J}$

• Change in Energy for Electron Transition:

$\Delta E = E_{n_f} - E_{n_i}$

• Relationship between Energy, Frequency, and Wavelength:

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

• Enthalpy of Reaction from Heats of Formation:

$\Delta H^\circ_{\text{rxn}} = \sum n_p \Delta H^\circ_f(\text{products}) - \sum n_r \Delta H^\circ_f(\text{reactants})$

• First Law of Thermodynamics:

$\Delta U = q + w$

• In bomb calorimetry, $w \approx 0$, so $\Delta U = q$.

Periodic Table

The periodic table organizes elements by increasing atomic number and similar chemical properties. It is essential for determining electron configurations, atomic masses, and other properties.

Summary Table: Test Structure

Question	Value
1	9
2	10
3	7
4	9
Significant Figures	Maximum Deduction of 1.5
Total	35

Additional info: These notes are based on a test covering thermochemistry, atomic structure, quantum theory, and related calculations, as indicated by the provided questions and formula sheets.