General Chemistry: Mole Calculations, Solutions, Gas Laws, and Intermolecular Forces

Stoichiometry and Mole Calculations

Calculating Number of Molecules

Stoichiometry involves quantitative relationships in chemical reactions. Calculating the number of molecules in a given mass of a substance is a fundamental skill in general chemistry.

• Mole: The SI unit for amount of substance, defined as containing Avogadro's number of entities (6.022 × 1023).

• Avogadro's Number: $6.022 \times 10^{23}$ particles/mol.

• Conversion: To find the number of molecules, first convert grams to moles, then multiply by Avogadro's number.

• Formula: $\text{Number of molecules} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \times 6.022 \times 10^{23}$

• Example: Calculate the number of molecules in 32.11 g of NH3.

Calculating Molar Mass

The molar mass of a compound is the mass in grams of one mole of that substance.

• Molar Mass: Sum of the atomic masses of all atoms in a formula unit (g/mol).

• Example: For Pb(NO3)2, add the atomic masses of Pb, N, and O accordingly.

Stoichiometry in Chemical Reactions

Mass-Mass Calculations

Stoichiometry allows calculation of the mass of products or reactants in a chemical reaction using balanced equations.

• Balanced Equation: Required to relate moles of reactants and products.

• Steps:

  1. Convert mass of given substance to moles.

  2. Use mole ratio from balanced equation.

  3. Convert moles of desired substance to mass.

• Example: Calculate the mass of water formed when 19.3 g of hydrogen reacts: $2\ \mathrm{H}_2 + \mathrm{O}_2 \rightarrow 2\ \mathrm{H}_2\mathrm{O}$

Solution Preparation and Molarity

Molarity (M) is a measure of concentration, defined as moles of solute per liter of solution.

• Formula: $M = \frac{n}{V}$ where $n$ = moles of solute, $V$ = volume in liters.

• Preparation: To prepare a solution of known molarity, calculate the required mass of solute using molar mass and desired volume.

• Example: Calculate the mass of KOH needed to make 355 mL of 0.22 M KOH.

• Example: Find the molarity of a solution with 8.45 g of KI in 0.250 L.

Gas Laws

Charles's Law

Charles's Law describes the direct relationship between the volume and temperature of a gas at constant pressure.

• Formula: $\frac{V_1}{T_1} = \frac{V_2}{T_2}$

• Temperature: Must be in Kelvin ($K = ^\circ C + 273.15$).

• Example: Calculate the new volume of a gas when temperature changes, keeping pressure constant.

Avogadro's Law

Avogadro's Law states that equal volumes of gases at the same temperature and pressure contain equal numbers of molecules.

• Formula: $\frac{V_1}{n_1} = \frac{V_2}{n_2}$

• STP Conditions: Standard Temperature and Pressure (0°C, 1 atm): 1 mol gas = 22.4 L.

Ideal Gas Law

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

• Formula: $PV = nRT$ where $P$ = pressure (atm), $V$ = volume (L), $n$ = moles, $R = 0.0821\ \mathrm{L \cdot atm \cdot K^{-1} \cdot mol^{-1}}$, $T$ = temperature (K).

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

• Example: Calculate the volume occupied by 0.600 mol of nitrogen gas at 3.00 atm and 30°C.

Gas Compression and Pressure-Volume Relationships

When the volume of a gas changes at constant temperature, the pressure changes inversely (Boyle's Law).

• Formula: $P_1V_1 = P_2V_2$

• Example: If 23.2 L of neon gas at 2.1 atm is compressed to 18.1 L, calculate the new pressure.

Intermolecular Forces

Types of Intermolecular Forces

Intermolecular forces are the forces of attraction between molecules, affecting physical properties like boiling and melting points.

• Dispersion Forces (London Dispersion): Present in all molecules, especially significant in nonpolar molecules.

• Dipole-Dipole Forces: Occur between polar molecules with permanent dipoles.

• Hydrogen Bonding: A special type of dipole-dipole interaction, occurs when hydrogen is bonded to N, O, or F.

• Ionic Forces: Occur between ions (positive and negative charges).

Table: Types of Intermolecular Forces

Molecule/Atom A	Molecule/Atom B	Type of Attraction
No +/- Charges	No +/- Charges	Dispersion Forces (London Dispersion Forces)
δ- / δ+	δ- / δ+	Dipole-Dipole
δ- / δ+ with H bound to N, O, or F	δ- / δ+ with H bound to N, O, or F	Hydrogen Bonding (Type of Dipole-Dipole)
+ / -	+ / -	Ionic

Key Constants and Conversions

• Avogadro's Number: $6.022 \times 10^{23}$

• STP (Standard Temperature and Pressure): 0°C (273.15 K), 1 atm, 1 mol gas = 22.4 L

• Gas Constant (R): $0.0821\ \mathrm{L \cdot atm \cdot K^{-1} \cdot mol^{-1}}$

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