General Chemistry I: Key Concepts and Problem-Solving Strategies (Sample Exam 3 Study Guide)

Electrolytes and Solutions

Strong and Weak Electrolytes

Electrolytes are substances that conduct electricity when dissolved in water. They are classified as strong or weak based on their degree of ionization.

• Strong electrolytes dissociate completely into ions in solution (e.g., NaCl, KBr, HCl).

• Weak electrolytes only partially dissociate (e.g., acetic acid, NH3).

• Nonelectrolytes do not produce ions in solution (e.g., sugar, ethanol).

• Example: NaCl(s) → Na+(aq) + Cl-(aq)

Chemical Equilibrium

Dynamic Equilibrium

Chemical equilibrium occurs when the rates of the forward and reverse reactions are equal, and the concentrations of reactants and products remain constant over time.

• At equilibrium, no net change in the amount of reactants and products occurs.

• The equilibrium constant (K) expresses the ratio of product to reactant concentrations at equilibrium.

• General form: For a reaction aA + bB → cC + dD:

$K = \frac{[C]^c[D]^d}{[A]^a[B]^b}$

• Example: For 2H2O2(aq) → 2H2O(l) + O2(g), $K = \frac{[O_2]}{[H_2O_2]^2}$

Gas Laws and Calculations

Ideal Gas Law

The behavior of gases can be described by the ideal gas law:

$PV = nRT$

• P = pressure (atm), V = volume (L), n = moles, R = 0.0821 L·atm/(mol·K), T = temperature (K)

• Used to calculate unknown properties of gases under various conditions.

• Example: Calculate the pressure of 0.133 mol NH3 in a 7.50 L container at 460 °C (convert to Kelvin first).

Gas Law Relationships

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

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

• Combined Gas Law: $\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}$

• Dalton's Law of Partial Pressures: $P_{total} = P_1 + P_2 + ... + P_n$

Energy Diagrams and Activation Energy

Reaction Energy Profiles

Energy diagrams show the energy changes during a chemical reaction.

• Activation energy (Ea): The minimum energy required for a reaction to occur (height from reactants to the peak).

• ΔE (change in energy): The difference in energy between reactants and products.

• Exothermic reactions: Products have lower energy than reactants (ΔE < 0).

• Endothermic reactions: Products have higher energy than reactants (ΔE > 0).

Kinetic Molecular Theory and Properties of Gases

Kinetic Molecular Theory (KMT)

KMT explains the behavior of gases based on the motion of their particles.

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

• Collisions between gas particles are elastic (no energy lost).

• There are no significant attractive or repulsive forces between particles.

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

• Not a property: Explains the low density of gases compared to solids and liquids, but not the solubility of gases in water.

Stoichiometry and Limiting Reactants

Stoichiometric Calculations

Stoichiometry involves using balanced chemical equations to calculate quantities of reactants and products.

• Limiting reactant: The reactant that is completely consumed first, limiting the amount of product formed.

• Excess reactant: The reactant that remains after the reaction is complete.

• Example: For 4 Cr(s) + 3 O2(g) → 2 Cr2O3(s), determine the limiting reactant and amount of product formed given specific masses of Cr and O2.

Solution Concentrations and Dilutions

Percent by Mass and Molarity

• Percent by mass: $\text{Percent by mass} = \frac{\text{mass of solute}}{\text{mass of solution}} \times 100\%$

• Molarity (M): $M = \frac{\text{moles of solute}}{\text{liters of solution}}$

• Dilution equation: $M_1V_1 = M_2V_2$

• Example: Calculate the volume of 10.5 M NaOH needed to prepare 200. mL of 1.75 M NaOH.

Solubility and Precipitation

Solubility Rules

Solubility rules help predict whether a precipitate will form when two solutions are mixed.

• Most nitrate (NO3-) salts are soluble.

• Most chloride (Cl-) salts are soluble, except those of Ag+, Pb2+, and Hg22+.

• Phosphate (PO43-) salts are generally insoluble, except with alkali metals and NH4+.

• Example: Mixing AgNO3 and NaCl forms a precipitate of AgCl.

Colligative Properties: Osmotic Pressure

Osmotic Pressure

Osmotic pressure depends on the concentration of solute particles in solution.

• Higher concentration of ions leads to higher osmotic pressure.

• Example: 1 M CaCl2 produces 3 ions per formula unit (Ca2+ and 2 Cl-), so it has higher osmotic pressure than 1 M NaCl (2 ions).

Net Ionic Equations and Spectator Ions

Writing Net Ionic Equations

• Write the complete ionic equation, showing all strong electrolytes as ions.

• Identify and remove spectator ions (ions that do not participate in the reaction).

• The remaining species form the net ionic equation.

• Example: AgNO3(aq) + NaCl(aq) → AgCl(s) + NaNO3(aq)

• Net ionic: Ag+(aq) + Cl-(aq) → AgCl(s)

Sample Table: Comparison of Gas Law Variables

Variable	Symbol	Unit	Relationship
Pressure	P	atm	Inversely proportional to volume (Boyle's Law)
Volume	V	L	Directly proportional to temperature (Charles's Law)
Temperature	T	K	Directly proportional to volume and pressure
Moles	n	mol	Directly proportional to volume (Avogadro's Law)

Additional info:

• Some questions involve interpreting graphs (e.g., concentration vs. time for equilibrium), which require understanding of how reactant and product concentrations change over time.

• Calculations involving molarity, dilution, and stoichiometry are common and require careful unit conversions.

• Understanding the difference between exothermic and endothermic reactions is essential for interpreting energy diagrams and reaction enthalpy.