General Chemistry Study Guide: Chemical Reactions, Solutions, and Gases

Useful Equations and Reference Data

Key Equations in General Chemistry

These equations are fundamental for solving problems in chemical reactions, solutions, and gas laws. They are commonly used in introductory college chemistry courses.

• Percent Yield: $\%\ \text{yield} = \frac{\text{actual}}{\text{theoretical}} \times 100\%$

• Molarity: $M = \frac{n}{V}$ where $n$ is moles of solute and $V$ is volume of solution in liters.

• Molar Mass: $\text{Molar Mass (M)} = \frac{m}{n}$ where $m$ is mass and $n$ is moles.

• Ideal Gas Law: $PV = nRT$ $R = 0.08206\ \text{L atm mol}^{-1}\text{K}^{-1}$

• Partial Pressure (Dalton's Law): $P_{\text{total}} = P_1 + P_2 + P_3 + \ldots$

• Density of a Gas: $d = \frac{PM}{RT}$

• Root Mean Square Velocity: $u_{rms} = \sqrt{\frac{3RT}{M}}$

• Temperature Conversion: $K = ^\circ C + 273.15$

• Standard Pressure: $760\ \text{mm Hg} = 1\ \text{atm}$

Solubility Rules for Ionic Compounds in Water

General Solubility Guidelines

Solubility rules help predict whether an ionic compound will dissolve in water. Exceptions are important for identifying precipitates in reactions.

Compounds Containing the Following Ions Are Generally Soluble	Exceptions
Li+, Na+, K+, and NH4+	None
NO3- and C2H3O2-	None
Cl-, Br-, and I-	With Ag+, Hg22+, or Pb2+
SO42-	With Sr2+, Ba2+, Pb2+, Ag+, or Ca2+

Compounds Containing the Following Ions Are Generally Insoluble	Exceptions
OH- and S2-	With Li+, Na+, K+, NH4+, or Ca2+, Sr2+, Ba2+ (slightly soluble)
CO32- and PO43-	With Li+, Na+, K+, NH4+

The Periodic Table of the Elements

Organization and Use

The periodic table arranges elements by increasing atomic number and groups elements with similar chemical properties into columns. It is essential for identifying element symbols, atomic numbers, and periodic trends such as electronegativity, atomic radius, and ionization energy.

• Groups: Vertical columns (e.g., alkali metals, halogens, noble gases)

• Periods: Horizontal rows

• Metals, Nonmetals, Metalloids: Classification based on physical and chemical properties

• Common Ion Charges: Indicated for many elements (e.g., Na+, Cl-)

Chemical Reactions and Chemical Quantities

Balancing Chemical Equations

Balancing equations ensures the conservation of mass and atoms in a chemical reaction. Each side of the equation must have the same number of each type of atom.

• Steps to Balance:

  1. Write the unbalanced equation.

  2. Count atoms of each element on both sides.

  3. Add coefficients to balance atoms.

  4. Check your work.

• Example: $6\ \text{H}_2O + 4\ \text{CO}_2 \rightarrow 4\ \text{H}_2O + 6\ \text{CO}_2$

Stoichiometry and Limiting Reactants

Stoichiometry involves calculating the amounts of reactants and products in chemical reactions. The limiting reactant is the substance that is completely consumed first, limiting the amount of product formed.

• Steps:

  1. Convert quantities to moles.

  2. Use mole ratios from the balanced equation.

  3. Identify the limiting reactant.

  4. Calculate theoretical yield.

• Example: $\text{Al}_2S_3 (s) + 6\ \text{H}_2O (l) \rightarrow 2\ \text{Al(OH)}_3 (s) + 3\ \text{H}_2S (g)$

Percent Yield

Percent yield compares the actual amount of product obtained to the theoretical maximum possible.

• Formula: $\%\ \text{yield} = \frac{\text{actual}}{\text{theoretical}} \times 100\%$

• Example: If 28.65 g of Fe is produced from a reaction with a theoretical yield of 50.0 g, the percent yield is $\frac{28.65}{50.0} \times 100\% = 57.3\%$.

Solutions and Aqueous Reactions

Solution Concentration: Molarity

Molarity (M) is the most common unit of concentration, defined as moles of solute per liter of solution.

• Formula: $M = \frac{n}{V}$

• Example: Dissolving 97.7 g LiBr in enough water to make 750.0 mL solution. Molar mass of LiBr = 86.85 g/mol. $n = \frac{97.7}{86.85} = 1.125\ \text{mol}$ $M = \frac{1.125}{0.750} = 1.50\ \text{M}$

Precipitation, Acid-Base, and Redox Reactions

Types of reactions in aqueous solutions include precipitation (formation of insoluble products), acid-base (transfer of protons), and redox (transfer of electrons).

• Precipitation Reaction: Occurs when two soluble salts form an insoluble product. Example: $\text{Na}_2\text{SO}_4 (aq) + \text{BaCl}_2 (aq) \rightarrow \text{BaSO}_4 (s) + 2\text{NaCl} (aq)$

• Acid-Base Reaction: Involves transfer of H+ ions. Example: $\text{HCl} (aq) + \text{NaOH} (aq) \rightarrow \text{NaCl} (aq) + \text{H}_2O (l)$

• Redox Reaction: Involves transfer of electrons; oxidation states change. Example: $\text{Zn} (s) + \text{Cu}^{2+} (aq) \rightarrow \text{Zn}^{2+} (aq) + \text{Cu} (s)$

Solubility and Strong Electrolytes

Strong electrolytes dissociate completely in water, conducting electricity well. Weak electrolytes only partially dissociate.

• Strong Electrolytes: Most soluble ionic compounds, strong acids, and strong bases.

• Weak Electrolytes: Weak acids and bases, some molecular compounds.

Gases and Gas Laws

Properties and Laws of Gases

Gas laws describe the relationships between pressure, volume, temperature, and amount of gas. They are essential for predicting gas behavior under different conditions.

• Boyle's Law: $P_1V_1 = P_2V_2$ (at constant T and n)

• Charles's Law: $\frac{V_1}{T_1} = \frac{V_2}{T_2}$ (at constant P and n)

• Avogadro's Law: $\frac{V_1}{n_1} = \frac{V_2}{n_2}$ (at constant P and T)

• Ideal Gas Law: $PV = nRT$

• Dalton's Law of Partial Pressures: $P_{\text{total}} = P_1 + P_2 + \ldots$

Kinetic Molecular Theory

This theory explains the behavior of gases based on the motion of particles. Key postulates include:

• Gases consist of tiny particles in constant, random motion.

• Collisions between particles are perfectly elastic.

• The volume of gas particles is negligible compared to the container.

• The average kinetic energy is proportional to temperature in Kelvin.

Gas Stoichiometry and Real Gases

Gas stoichiometry uses the ideal gas law to relate moles, volume, and pressure. Real gases deviate from ideal behavior at high pressures and low temperatures.

• Example: Calculate the volume of H2 gas produced from a reaction at given temperature and pressure using $PV = nRT$.

Answer Key Table

Purpose

This table provides the correct answers for the multiple-choice questions from Chapters 4, 5, and 6, useful for self-assessment and review.

Chapter 4	Chapter 5	Chapter 6
1. A	11. A	21. C
2. B	12. D	22. C
3. C	13. B	23. C
4. D	14. C	24. C
5. B	15. D	25. E
6. C	16. C	26. D
7. A	17. A	27. E
8. A	18. D	28. B
9. E	19. B	29. B
10. D	20. D	30. A

Additional info:

• Some equations and rules have been expanded for clarity and completeness.

• Examples and context have been added to make the notes self-contained and suitable for exam preparation.