CHM 1101 Exam 3 Study Guide: Gases, Thermochemistry, and Quantum-Mechanical Model of the Atom

Chapter 6 – Gases

Gas Laws and Calculations

The behavior of gases can be described using mathematical relationships known as gas laws. These laws relate the volume, pressure, temperature, and amount of gas.

• Ideal Gas Law: The ideal gas law relates the four variables of a gas: $PV = nRT$, where P is pressure, V is volume, n is moles, R is the gas constant, and T is temperature in Kelvin.

• Density and Molar Mass: The density ($d$) of a gas can be calculated using $d = \frac{PM}{RT}$, where M is molar mass.

• Stoichiometry: Gas volumes in reactions can be calculated using stoichiometric relationships and the ideal gas law.

• Example: Calculate the volume of 2.0 mol of O2 at 1.00 atm and 273 K: $V = \frac{nRT}{P} = \frac{2.0 \times 0.0821 \times 273}{1.00} = 44.8 \text{ L}$

Partial Pressure and Mole Fraction

In a mixture of gases, each gas exerts a partial pressure proportional to its mole fraction.

• Dalton’s Law: $P_{\text{total}} = P_1 + P_2 + \ldots + P_n$

• Mole Fraction: $X_i = \frac{n_i}{n_{\text{total}}}$

• Partial Pressure: $P_i = X_i \times P_{\text{total}}$

• Example: If a mixture contains 2 mol O2 and 3 mol N2, $X_{O_2} = \frac{2}{5} = 0.4$

Ideal vs. Real Gases

The ideal gas law assumes gases behave ideally under most conditions, but deviations occur at high pressure and low temperature.

• Ideal Gas: Assumes no intermolecular forces and negligible volume of gas particles.

• Real Gas: Deviates from ideal behavior due to intermolecular forces and finite particle volume.

• Conditions: Ideal gas law applies best at low pressure and high temperature.

Kinetic Molecular Theory

This theory explains the behavior of gases based on the motion of particles.

• Assumptions:

  • Gas particles are in constant, random motion.

  • Collisions are elastic (no energy lost).

  • Volume of particles is negligible compared to container.

  • No intermolecular forces between particles.

Root Mean Square Speed and Molar Mass

The speed of gas particles depends on temperature and molar mass.

• Root Mean Square Speed: $v_{\text{rms}} = \sqrt{\frac{3RT}{M}}$

• Relationship: Higher temperature increases $v_{\text{rms}}$; higher molar mass decreases $v_{\text{rms}}$.

Standard Temperature and Pressure (STP)

STP is a reference condition for gas measurements.

• STP: 0°C (273.15 K) and 1 atm pressure.

• Molar Volume: At STP, 1 mol of an ideal gas occupies 22.4 L.

Chapter 7 – Thermochemistry

Internal Energy, Heat, and Work

Thermochemistry studies energy changes in chemical reactions.

• Internal Energy ($\Delta E$): $\Delta E = q + w$, where q is heat and w is work.

• Work: For expansion/compression, $w = -P\Delta V$

• System and Surroundings: The system is the part studied; the surroundings are everything else.

Endothermic vs. Exothermic Reactions

Reactions can absorb or release heat.

• Endothermic: Absorbs heat ($q > 0$); surroundings cool down.

• Exothermic: Releases heat ($q < 0$); surroundings warm up.

Calorimetry

Calorimetry measures heat changes in reactions.

• Coffee-cup Calorimeter: Measures heat at constant pressure.

• Bomb Calorimeter: Measures heat at constant volume.

• Heat Calculation: $q = mC\Delta T$, where m is mass, C is heat capacity, \Delta T is temperature change.

Heat Capacity and Thermochemistry Calculations

• Specific Heat Capacity ($C$): Amount of heat required to raise 1 g of substance by 1°C.

• Use in Calculations: $q = mC\Delta T$

Hess’s Law and Enthalpy of Formation

Hess’s Law allows calculation of reaction enthalpy from known enthalpies.

• Hess’s Law: The enthalpy change for a reaction is the sum of enthalpy changes for individual steps.

• Enthalpy of Formation ($\Delta H_f$): Enthalpy change when 1 mol of compound forms from elements.

• Reaction Enthalpy: $\Delta H_{\text{rxn}} = \sum \Delta H_f^{\text{products}} - \sum \Delta H_f^{\text{reactants}}$

Chapter 8 – The Quantum-Mechanical Model of the Atom

Properties of Light and Energy Calculations

Light has both wave and particle properties. Its energy, wavelength, and frequency are related.

• Speed of Light: $c = \lambda \nu$, where c is speed, \lambda is wavelength, \nu is frequency.

• Energy of Photon: $E = h\nu = \frac{hc}{\lambda}$

• Example: Calculate energy for $\lambda = 500 \text{ nm}$: $E = \frac{6.626 \times 10^{-34} \times 3.00 \times 10^8}{500 \times 10^{-9}}$

Bohr Model and Its Limitations

The Bohr model describes electrons in fixed orbits but fails to explain many atomic behaviors.

• Incorrectness: Cannot explain multi-electron atoms or electron cloud behavior.

Energy Changes in Hydrogen Atom

Electron transitions in hydrogen involve quantized energy changes.

• Energy Change: $\Delta E = -2.18 \times 10^{-18} \left( \frac{1}{n_f^2} - \frac{1}{n_i^2} \right )$

• Example: Calculate $\Delta E$ for $n_i = 3$ to $n_f = 2$.

de Broglie Wavelength

Particles have wave-like properties; wavelength depends on mass and velocity.

• de Broglie Equation: $\lambda = \frac{h}{mv}$

Quantum Numbers and Orbitals

Quantum numbers describe electron properties and locations.

• Principal Quantum Number (n): Energy level; $n = 1, 2, 3, \ldots$

• Angular Momentum (l): Subshell shape; $l = 0$ (s), $1$(p), $2$ (d), $3$ (f)

• Magnetic Quantum Number (ml): Orientation; $m_l = -l$ to $+l$

• Spin Quantum Number (ms): Electron spin; $m_s = +\frac{1}{2}$ or $-\frac{1}{2}$

• Maximum Orbitals: In a subshell, number of orbitals = $2l + 1$

• Maximum Electrons: In a subshell, number of electrons = $2(2l + 1)$

Heisenberg’s Uncertainty Principle

It is impossible to know both the position and momentum of an electron precisely.

• Uncertainty Principle: $\Delta x \cdot \Delta p \geq \frac{h}{4\pi}$

Development of Quantum Mechanics

Quantum mechanics developed through key experiments and theories.

• Important Events: Blackbody radiation, photoelectric effect, atomic spectra, de Broglie hypothesis.

Electromagnetic Spectrum

The electromagnetic spectrum includes all types of electromagnetic radiation.

• Regions: Gamma rays, X-rays, ultraviolet, visible, infrared, microwave, radio.

• Locations: Visible light ranges from about 400 nm (violet) to 700 nm (red).

Atomic Orbitals and Electron Capacity

Atomic orbitals have characteristic shapes and electron capacities.

• s orbital: Spherical; 1 orbital; max 2 electrons.

• p orbital: Dumbbell-shaped; 3 orbitals; max 6 electrons.

• d orbital: Complex shape; 5 orbitals; max 10 electrons.

Subshell	Number of Orbitals	Maximum Electrons
s	1	2
p	3	6
d	5	10
f	7	14

Additional info: These notes expand on the study guide by providing definitions, formulas, and examples for each topic, ensuring a self-contained review for exam preparation.