General Chemistry: Stoichiometry, Solutions, Electron Configuration, and Periodic Trends

Stoichiometry and Limiting Reactants

Stoichiometric Calculations

Stoichiometry involves the calculation of reactants and products in chemical reactions using balanced chemical equations. It is essential for determining the quantities of substances consumed and produced.

• Mole-to-mole relationships: Use coefficients from the balanced equation to relate moles of different substances.

• Percent yield: The ratio of actual yield to theoretical yield, expressed as a percentage.

Example: Given the reaction $4FeS_2 + 11O_2 \rightarrow 2Fe_2O_3 + 8SO_2$, if you start with 8.200 g of FeS2 and produce 0.0885 moles of Fe2O3 at 23.6% yield, you can calculate the moles of FeS2 used and the theoretical yield.

• Key formula: $\text{Percent yield} = \frac{\text{Actual yield}}{\text{Theoretical yield}} \times 100$

Limiting Reactant

The limiting reactant is the substance that is completely consumed first in a chemical reaction, thus determining the maximum amount of product that can be formed.

• Calculate moles of each reactant.

• Use stoichiometry to determine which reactant produces the least amount of product.

• The reactant that produces the least product is the limiting reactant.

Example: For $2Al + Fe_2O_3 \rightarrow 2Fe + Al_2O_3$, if you react 0.70 moles of Al with 0.34 moles of Fe2O3, determine the limiting reactant by comparing the required and available moles.

Solutions and Molarity

Calculating Molarity

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

• Formula: $M = \frac{\text{moles of solute}}{\text{volume of solution in L}}$

• To find moles: $\text{moles} = M \times V$

Example: If you dissolve 30.0 g of a compound in water to make 0.750 mol in 150.0 mL, the molar mass is $\frac{30.0\,g}{0.750\,mol} = 40.0\,g/mol$.

Solution Dilution

When solutions are diluted, the number of moles of solute remains constant, but the volume increases, decreasing the concentration.

• Formula: $M_1V_1 = M_2V_2$

Example: Mixing 40.0 mL of 0.300 M NaOH with 120.0 mL of water results in a final concentration of $C_2 = \frac{(0.300\,M)(0.0400\,L)}{0.1600\,L} = 0.0750\,M$.

Chemical Nomenclature and Formula Writing

Writing Names and Formulas

Chemical nomenclature is the system for naming chemical compounds and writing their formulas.

Name	Formula
dinitrogen tetroxide	N2O4
potassium carbonate	K2CO3
iron (III) sulfate	Fe2(SO4)3
sulfur trioxide	SO3

Electron Configuration and Energy Levels

Electron Configuration

Electron configuration describes the arrangement of electrons in an atom's orbitals. For ions, electrons are removed from the highest principal quantum number (n) first.

• Example: Ti2+: $1s^2 2s^2 2p^6 3s^2 3p^6 3d^2$

• Condensed notation uses the previous noble gas: [Ar] $3d^2$

Energy Level Diagrams

Energy level diagrams visually represent the arrangement of electrons in orbitals. Transitions between levels correspond to absorption or emission of photons.

• Emission: Electron drops to a lower energy level, releasing a photon.

• Absorption: Electron moves to a higher energy level, absorbing a photon.

Periodic Trends

Trends in the Periodic Table

Elements show periodic trends in properties such as atomic radius, ionization energy, and electronegativity.

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

• Ionization energy: Decreases down a group, increases across a period.

• Electronegativity: Increases across a period, decreases down a group.

Example: For C, Fe, Mo, and Pd, the order of atomic radius is: Mo > Pd/Cr > Fe (Mo has the largest radius due to lower effective nuclear charge and higher principal quantum number).

Comparing Elements

Rank	Ionization Energy	Electronegativity	Radius
Largest	C	C	Sr
Smallest	Sr	Sr	C

Empirical and Molar Mass Calculations

Empirical Formula and Molar Mass

The empirical formula represents the simplest whole-number ratio of elements in a compound. Molar mass is the mass of one mole of a substance.

• Formula: $\text{Molar mass} = \frac{\text{mass (g)}}{\text{moles}}$

Example: If 12.5 g of P2S5 contains 0.263 mol S, use the molar mass to relate grams and moles.

Summary Table: Electron Configurations

Symbol	Full Configuration	Condensed Configuration
Si	1s2 2s2 2p6 3s2 3p2	[Ne] 3s2 3p2
Nb	1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s1 4d4	[Kr] 5s1 4d4
As3-	1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6	[Kr]

Additional info:

• Some answers include explanations for why certain periodic trends occur, such as the effect of electron repulsion in O− vs. N.

• Energy diagrams illustrate both emission and absorption transitions, with arrows indicating electron movement between orbitals.