GOB Chemistry Study Guide: Solutions, Nuclear Reactions, Intermolecular Forces, and Quantum Numbers

Solutions

Calculating Molarity

Molarity (M) is a measure of concentration, defined as the number of moles of solute per liter of solution.

• Definition: Molarity (M) = moles of solute / liters of solution

• Formula:

$M = \frac{\text{moles of solute}}{\text{liters of solution}}$

• Example: To prepare a solution by dissolving 15.0 g of NaOH in enough water to make 250 mL (0.250 L):

  • Calculate moles of NaOH: $\text{moles} = \frac{15.0\ g}{40.00\ g/mol} = 0.375\ mol$

  • Calculate molarity: $M = \frac{0.375\ mol}{0.250\ L} = 1.50\ M$

Preparing a Solution of Known Molarity

To prepare a specific volume and molarity of a solution, calculate the required mass of solute.

• Formula: $\text{mass} = M \times V \times \text{molar mass}$

• Example: To prepare 500 mL (0.500 L) of 0.200 M KCl:

  • Moles needed: $0.200\ M \times 0.500\ L = 0.100\ mol$

  • Mass needed: $0.100\ mol \times 74.55\ g/mol = 7.46\ g$

Saturated, Unsaturated, and Supersaturated Solutions

Solutions can be classified based on the amount of solute dissolved at a given temperature.

• Saturated Solution: Contains the maximum amount of solute that can dissolve at a specific temperature. Additional solute will not dissolve.

• Unsaturated Solution: Contains less solute than the maximum amount; more solute can still dissolve.

• Supersaturated Solution: Contains more solute than is normally possible at that temperature; unstable and can precipitate excess solute.

• Example: Dissolving sugar in water: If no more sugar dissolves and crystals form, the solution is saturated. If all sugar dissolves, it is unsaturated. If more sugar is dissolved by heating and then cooled, forming crystals, it is supersaturated.

Nuclear Reactions

Alpha Decay of Uranium-238

Alpha decay is a type of radioactive decay where an unstable nucleus emits an alpha particle (helium-4 nucleus).

• Balanced Nuclear Equation:

$^{238}_{92}\text{U} \rightarrow ^{234}_{90}\text{Th} + ^{4}_{2}\text{He}$

• Explanation: Uranium-238 loses 2 protons and 2 neutrons, forming thorium-234 and an alpha particle.

Fission vs. Fusion

Both are nuclear processes that release energy, but they differ in mechanism and application.

• Fission: Splitting of a heavy nucleus into smaller nuclei, releasing energy. Example: $^{235}\text{U}$ fission in nuclear reactors.

• Fusion: Combining of light nuclei to form a heavier nucleus, releasing energy. Example: Fusion of hydrogen isotopes in the sun: $^{2}\text{H} + ^{3}\text{H} \rightarrow ^{4}\text{He} + n$

Radioactive Decay and Half-Life

The half-life is the time required for half of a radioactive sample to decay.

• Formula: $N = N_0 \left(\frac{1}{2}\right)^{t/t_{1/2}}$

• Example: If 80.0 g of an isotope with a 6.0 h half-life is present, how much remains after 18 hours?

  • Number of half-lives: $\frac{18\ h}{6.0\ h} = 3$

  • Amount remaining: $80.0\ g \times (1/2)^3 = 80.0\ g \times 1/8 = 10.0\ g$

Intermolecular Forces

Main Types and Strength Ranking

Intermolecular forces are attractions between molecules, affecting physical properties like boiling point.

• London Dispersion Forces: Weakest; present in all molecules, especially nonpolar ones.

• Dipole-Dipole Forces: Moderate; occur between polar molecules.

• Hydrogen Bonding: Strongest; occurs when H is bonded to N, O, or F.

• Strength Ranking: London dispersion < dipole-dipole < hydrogen bonding

Boiling Point Comparison: H2O vs. H2S

• H2O has a higher boiling point than H2S because water molecules form strong hydrogen bonds, while H2S only exhibits weaker dipole-dipole and London dispersion forces.

• Example: Boiling point of H2O: 100°C; H2S: -60°C

Why Ice Floats on Water

• Hydrogen bonding in ice creates an open, hexagonal structure, making ice less dense than liquid water.

• Result: Ice floats because its molecules are held further apart than in liquid water.

Quantum Numbers

The Four Quantum Numbers

Quantum numbers describe the properties and location of electrons in atoms.

• Principal Quantum Number (n): Indicates energy level (shell); n = 1, 2, 3, ...

• Angular Momentum Quantum Number (l): Indicates subshell (shape); l = 0 to n-1

• Magnetic Quantum Number (ml): Orientation of orbital; ml = -l to +l

• Spin Quantum Number (ms): Electron spin; ms = +1/2 or -1/2

Possible Values for n = 3, l = 2

• For n = 3, l = 2: This is a 3d subshell.

• Possible ml values: -2, -1, 0, +1, +2

• Possible ms values: +1/2 or -1/2 for each ml