General Chemistry Study Guide: Chemical Reactions, Solutions, and Gas Laws

Chemical Reactions and Stoichiometry

Exchange (Double Replacement) Reactions

Exchange reactions, also known as double replacement or metathesis reactions, involve the swapping of ions between two compounds to form new products. These reactions are common in aqueous solutions and often result in the formation of a precipitate, gas, or water.

• Definition: An exchange reaction occurs when the cations and anions of two ionic compounds switch partners.

• General Equation: $AB + CD \rightarrow AD + CB$

• Example: $\text{AgNO}_3 (aq) + \text{NaCl} (aq) \rightarrow \text{AgCl} (s) + \text{NaNO}_3 (aq)$

Precipitation and Solubility

When a product of a reaction falls out of solution, it is called a precipitate. Precipitation occurs when the product is insoluble in water.

• Key Term: Precipitate – a solid formed from a solution during a chemical reaction.

• Common Precipitates: Silver chloride (AgCl), barium sulfate (BaSO4), lead(II) iodide (PbI2).

• Application: Precipitation reactions are used in qualitative analysis to identify ions in solution.

Writing Chemical Equations

For reactions in aqueous solutions, it is important to write balanced molecular, complete ionic, and net ionic equations.

• Molecular Equation: Shows all reactants and products as compounds.

• Complete Ionic Equation: Shows all strong electrolytes as ions.

• Net Ionic Equation: Shows only the species that actually participate in the reaction.

• Example:

  • Molecular: $\text{Na}_2\text{SO}_4 (aq) + \text{BaCl}_2 (aq) \rightarrow \text{BaSO}_4 (s) + 2\text{NaCl} (aq)$

  • Complete Ionic: $2\text{Na}^+ (aq) + \text{SO}_4^{2-} (aq) + \text{Ba}^{2+} (aq) + 2\text{Cl}^- (aq) \rightarrow \text{BaSO}_4 (s) + 2\text{Na}^+ (aq) + 2\text{Cl}^- (aq)$

  • Net Ionic: $\text{Ba}^{2+} (aq) + \text{SO}_4^{2-} (aq) \rightarrow \text{BaSO}_4 (s)$

Acid-Base Reactions and Neutralization

Stoichiometry of Neutralization

Neutralization reactions occur when an acid reacts with a base to produce water and a salt. The stoichiometry depends on the number of acidic and basic protons and hydroxide ions.

• General Equation: $\text{Acid} + \text{Base} \rightarrow \text{Salt} + \text{Water}$

• Example: $\text{HCl} (aq) + \text{NaOH} (aq) \rightarrow \text{NaCl} (aq) + \text{H}_2\text{O} (l)$

• Stoichiometry: The number of moles of acid and base required depends on their valency (monoprotic, diprotic, etc.).

• Salt Formation: The salt formed is composed of the cation from the base and the anion from the acid.

Complete and Net Ionic Equations for Neutralization

• Complete Ionic Equation: $\text{H}^+ (aq) + \text{Cl}^- (aq) + \text{Na}^+ (aq) + \text{OH}^- (aq) \rightarrow \text{Na}^+ (aq) + \text{Cl}^- (aq) + \text{H}_2\text{O} (l)$

• Net Ionic Equation: $\text{H}^+ (aq) + \text{OH}^- (aq) \rightarrow \text{H}_2\text{O} (l)$

Gases and Their Properties

Ideal Gas Law

The behavior of gases is described by the ideal gas law, which relates pressure, volume, temperature, and amount of gas.

• Equation: $PV = nRT$

• Variables:

  • P: Pressure (atm, torr, Pa)

  • V: Volume (L)

  • n: Moles of gas

  • R: Universal gas constant ($0.0821 \text{ L atm mol}^{-1} \text{K}^{-1}$)

  • T: Temperature (K)

• Simple Gas Laws:

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

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

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

Standard Temperature and Pressure (STP)

• Standard Temperature: 0°C or 273.15 K

• Standard Pressure: 1 atm or 760 torr

• Molar Volume at STP: 22.4 L/mol

Partial Pressures and Dalton's Law

In a mixture of gases, each gas exerts a pressure independently of the others. The total pressure is the sum of the partial pressures.

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

• Mole Fraction: $X_i = \frac{n_i}{n_{\text{total}}}$

• Partial Pressure: $P_i = X_i \times P_{\text{total}}$

Gas Effusion and Graham's Law

Effusion is the process by which gas molecules escape through a small hole. Graham's law relates the rate of effusion to the molar mass of the gases.

• Graham's Law: $\frac{\text{Rate}_1}{\text{Rate}_2} = \sqrt{\frac{M_2}{M_1}}$

• Application: Used to determine the molar mass of an unknown gas by comparing its rate of effusion to a known gas.

• Example: If helium effuses twice as fast as an unknown gas, the unknown gas has a molar mass four times that of helium.

Sample Table: Comparison of Gas Laws

Law	Equation	Variables Held Constant
Boyle's Law	$P_1V_1 = P_2V_2$	n, T
Charles's Law	$\frac{V_1}{T_1} = \frac{V_2}{T_2}$	n, P
Avogadro's Law	$\frac{V_1}{n_1} = \frac{V_2}{n_2}$	P, T
Ideal Gas Law	$PV = nRT$	None

Worked Example: Gas Law Calculation

• Problem: An inflated balloon has a volume of 5.45 L at 1.00 atm and 32°C. If the pressure drops to 0.21 atm and the temperature to 15°C, what is the final volume?

• Solution:

  • Convert temperatures to Kelvin: $T_1 = 32 + 273.15 = 305.15$ K, $T_2 = 15 + 273.15 = 288.15$ K

  • Use combined gas law: $\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}$

  • Plug in values: $\frac{1.00 \times 5.45}{305.15} = \frac{0.21 \times V_2}{288.15}$

  • Solve for $V_2$

Additional info:

• Some questions reference specific chemical reactions and calculations, which are standard in General Chemistry topics such as stoichiometry, solution chemistry, and gas laws.

• Effusion and molar mass determination are covered under Ch.9 - Gases and Their Properties.

• Precipitation and neutralization reactions are covered under Ch.4 - Chemical Reactions and Stoichiometry and Ch.14 - Acid-Base Equilibria.