General Chemistry 161 – Practice Exam 2 Study Notes

General Chemistry 161 – Practice Exam 2 Study Notes

Introduction

This study guide summarizes key concepts, equations, and problem types found in a typical General Chemistry college-level exam. It covers stoichiometry, gas laws, solution chemistry, redox reactions, and more, providing definitions, formulas, and examples to aid in exam preparation.

Helpful Equations and Conversions

• Temperature Conversions:

  • Fahrenheit to Celsius: $^\circ F = 1.8(^\circ C) + 32$

  • Celsius to Kelvin: $K = ^\circ C + 273.15$

• Gas Constant (R):

  • $R = 0.08206 \; L \cdot atm \cdot mol^{-1} \cdot K^{-1}$

  • $R = 8.314 \; J \cdot mol^{-1} \cdot K^{-1}$

• Root Mean Square Speed:

  • $u_{rms} = \sqrt{\frac{3RT}{M}}$

  • Where $M$ is the molar mass in kg/mol, $R$ is the gas constant, and $T$ is temperature in Kelvin.

• Van der Waals Equation (for real gases):

  • $\left[ P + a \left( \frac{n}{V} \right)^2 \right] (V - nb) = nRT$

  • Where $a$ and $b$ are substance-specific constants, $n$ is moles, $V$ is volume, $P$ is pressure, $R$ is the gas constant, and $T$ is temperature.

Standard Atmospheric Pressure Conversions

Unit	Abbreviation	Value
Atmosphere	atm	1.00
Millimeters of mercury	mm Hg	760
Torr	Torr	760
Pascals	Pa	101,325
Kilopascals	kPa	101.325

Common Polyatomic Ions

Per_ate	Chlorate	Bromate	Iodate	Sulfate	Nitrate	Phosphate	Carbonate
ClO4-	BrO4-	IO4-	SO42-	NO3-	PO43-	CO32-
ClO3-	BrO3-	IO3-	SO32-	NO2-	PO33-	CO22-

Stoichiometry and Chemical Reactions

Balancing Chemical Equations

Balancing chemical equations ensures the law of conservation of mass is obeyed. Each side of the equation must have the same number of atoms of each element.

• Steps:

  1. Write the unbalanced equation.

  2. Count the number of atoms of each element on both sides.

  3. Add coefficients to balance the atoms.

  4. Check your work.

• Example: $\mathrm{Mg} + \mathrm{O}_2 \rightarrow \mathrm{MgO}$ Balanced: $2\mathrm{Mg} + \mathrm{O}_2 \rightarrow 2\mathrm{MgO}$

Limiting Reactant and Theoretical Yield

The limiting reactant is the reactant that is completely consumed first, limiting the amount of product formed. The theoretical yield is the maximum amount of product that can be formed from the limiting reactant.

• Steps to Find Limiting Reactant:

  1. Convert all given quantities to moles.

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

  3. The reactant that produces the least is the limiting reactant.

• Percent Yield: $\text{Percent Yield} = \frac{\text{Actual Yield}}{\text{Theoretical Yield}} \times 100\%$

Solution Chemistry

Molarity

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

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

• Example: Dissolving 0.468 g of MgI2 in enough water to make 50.0 mL of solution. First, convert grams to moles, then divide by volume in liters.

Precipitation Reactions

When two aqueous solutions are mixed, an insoluble solid (precipitate) may form. Use solubility rules to predict the formation of a precipitate.

• Example: Mixing $\mathrm{K}_2\mathrm{SO}_4$ and $\mathrm{Ba(NO}_3)_2$ forms insoluble $\mathrm{BaSO}_4$.

Titration

Titration is a technique to determine the concentration of a solution by reacting it with a solution of known concentration.

• Formula: $M_1V_1 = M_2V_2$ (for 1:1 stoichiometry)

• For other stoichiometries, use mole ratios from the balanced equation.

Redox Reactions

Oxidation and Reduction

Oxidation is the loss of electrons; reduction is the gain of electrons. The oxidizing agent is reduced, and the reducing agent is oxidized.

• Example: $\mathrm{Cr}_2\mathrm{O}_7^{2-} + 2\mathrm{Cr}^{3+} + 2\mathrm{OH}^- \rightarrow 2\mathrm{CrO}_4^{2-} + 3\mathrm{H}_2\mathrm{O}$

• Assign oxidation numbers to identify which species is oxidized and which is reduced.

Gas Laws

Ideal Gas Law

The ideal gas law relates pressure, volume, temperature, and moles of a gas.

• Equation: $PV = nRT$

• Variables: P = pressure (atm), V = volume (L), n = moles, R = gas constant, T = temperature (K)

Partial Pressure and Dalton’s Law

The total pressure of a gas mixture is the sum of the partial pressures of each component.

• Equation: $P_{\text{total}} = P_1 + P_2 + \ldots + P_n$

• Collecting Gas Over Water: Subtract vapor pressure of water from total pressure to find the pressure of the collected gas.

Gas Stoichiometry

Use the ideal gas law to relate the volume of gases in chemical reactions at non-standard conditions.

Graham’s Law of Effusion

The rate of effusion of a gas is inversely proportional to the square root of its molar mass.

• Equation: $\frac{\text{Rate}_1}{\text{Rate}_2} = \sqrt{\frac{M_2}{M_1}}$

Root Mean Square Speed

The root mean square speed of gas molecules is given by:

• $u_{rms} = \sqrt{\frac{3RT}{M}}$

• Where $M$ is the molar mass in kg/mol.

Periodic Table and Atomic Structure

The periodic table organizes elements by increasing atomic number and groups elements with similar chemical properties into columns. It is essential for determining atomic masses, valence electrons, and predicting chemical behavior.

Practice Problem Types

• Identifying major contributors to global warming (e.g., CO2, CH4, N2O, etc.)

• Stoichiometry calculations (moles, limiting reactant, theoretical yield, percent yield)

• Balancing chemical equations

• Solution concentration and dilution problems

• Precipitation and solubility rules

• Redox reactions and assigning oxidation numbers

• Gas law calculations (ideal gas law, partial pressures, gas stoichiometry, effusion)

• Interpreting graphs of molecular speed distributions

Additional Info

• Always use the periodic table for atomic masses and element identification.

• Refer to the provided polyatomic ion table for correct formulas and charges.

• For gas law problems, ensure all units are consistent (e.g., convert Celsius to Kelvin, pressure to atm or kPa as needed).