Quantities in Chemical Reactions: Avogadro’s Number, Moles, Molar Mass, Molar Volume, Gas Density, and Percent Composition

Quantities in Chemical Reactions

Avogadro’s Number

Avogadro’s number is a fundamental constant in chemistry that defines the number of particles (atoms, molecules, or ions) in one mole of a substance.

• Definition: Avogadro’s number is 6.022 × 1023 particles per mole.

• Application: Used to convert between number of particles and moles.

• Example: 1 mole of H2O contains $6.022 \times 10^{23}$ molecules of water.

Mass, Moles, and Number of Molecules or Atoms Relations

Understanding the relationships between mass, moles, and number of particles is essential for quantitative chemical calculations.

• Mole: The SI unit for amount of substance, representing Avogadro’s number of entities.

• Conversions:

  • Mass to moles: $\text{moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}}$

  • Moles to number of particles: $\text{number of particles} = \text{moles} \times 6.022 \times 10^{23}$

  • Number of particles to moles: $\text{moles} = \frac{\text{number of particles}}{6.022 \times 10^{23}}$

• Example: Calculate the number of molecules in 18 g of H2O:

  • Moles of H2O: $\frac{18\ \text{g}}{18.02\ \text{g/mol}} = 1\ \text{mol}$

  • Number of molecules: $1\ \text{mol} \times 6.022 \times 10^{23} = 6.022 \times 10^{23}$ molecules

Molar Mass

Molar mass is the mass of one mole of a substance, expressed in grams per mole (g/mol).

• Definition: The sum of the atomic masses of all atoms in a molecule or formula unit.

• Calculation: Add the atomic masses from the periodic table for each element in the compound.

• Example: Molar mass of CO2:

  • C: 12.01 g/mol, O: 16.00 g/mol

  • Total: $12.01 + 2 \times 16.00 = 44.01$ g/mol

Molar Volume (at STP Conditions)

At standard temperature and pressure (STP: 0°C and 1 atm), one mole of any ideal gas occupies a specific volume.

• Definition: The molar volume at STP is 22.4 L/mol for an ideal gas.

• Equation: $\text{Volume (L)} = \text{moles} \times 22.4\ \text{L/mol}$

• Example: 2 moles of N2 gas at STP occupy $2 \times 22.4 = 44.8$ L.

Gas Density (Calculation, Units, Meaning)

Gas density is the mass per unit volume of a gas, typically expressed in g/L.

• Definition: $\text{Density} = \frac{\text{mass}}{\text{volume}}$

• At STP: $\text{Density} = \frac{\text{molar mass (g/mol)}}{22.4\ \text{L/mol}}$

• Units: grams per liter (g/L)

• Example: Density of O2 at STP:

  • Molar mass = 32.00 g/mol

  • Density = $\frac{32.00}{22.4} = 1.43$ g/L

Percent Composition

Percent composition expresses the mass percentage of each element in a compound.

• Definition: $\%\ \text{composition} = \frac{\text{mass of element in 1 mol of compound}}{\text{molar mass of compound}} \times 100\%$

• Calculation Steps:

  1. Find the molar mass of the compound.

  2. Find the total mass of each element in one mole of the compound.

  3. Divide the mass of each element by the molar mass and multiply by 100%.

• Example: Percent composition of H in H2O:

  • Mass of H in 1 mol = $2 \times 1.008 = 2.016$ g

  • Molar mass of H2O = 18.02 g/mol

  • Percent H = $\frac{2.016}{18.02} \times 100\% = 11.19\%$