Molar Mass, Mole Calculations, and Chemical Composition: Applications in GOB Chemistry

Mole Calculations and Chemical Composition

Molecular Formula and Molar Mass

Understanding the molecular formula and molar mass of a compound is fundamental in chemistry, as these concepts allow chemists to relate the mass of a substance to the number of particles (atoms or molecules) it contains.

• Molecular Formula: The molecular formula shows the exact number and type of atoms in a molecule. For example, dipyrithione has the formula C10H8N2O2S2.

• Molar Mass: The molar mass is the mass of one mole of a substance, expressed in grams per mole (g/mol). It is calculated by summing the atomic masses of all atoms in the molecular formula.

Example Calculation:

• For dipyrithione (C10H8N2O2S2):

  • Carbon (C): 10 atoms × 12.01 g/mol = 120.10 g/mol

  • Hydrogen (H): 8 atoms × 1.008 g/mol = 8.064 g/mol

  • Nitrogen (N): 2 atoms × 14.01 g/mol = 28.02 g/mol

  • Oxygen (O): 2 atoms × 16.00 g/mol = 32.00 g/mol

  • Sulfur (S): 2 atoms × 32.07 g/mol = 64.14 g/mol

  • Total molar mass = 120.10 + 8.064 + 28.02 + 32.00 + 64.14 = 252.32 g/mol

Calculating Moles from Mass

The number of moles in a given mass of a substance can be calculated using the formula:

$\text{Moles} = \frac{\text{Mass (g)}}{\text{Molar Mass (g/mol)}}$

• Example: To find the number of moles in 10.0 g of a compound with a molar mass of 252.32 g/mol:

• $\text{Moles} = \frac{10.0\ \text{g}}{252.32\ \text{g/mol}} = 0.0396\ \text{mol}$

Application: Dipyrithione in Dandruff Shampoo

Dipyrithione is used as an antibacterial and antifungal agent. The following questions illustrate how to apply mole and mass relationships to real-world chemical problems.

1. What is the molar mass of dipyrithione?

   • As calculated above, the molar mass is 252.32 g/mol.

2. How many moles of dipyrithione are in 25.0 g?

   • $\text{Moles} = \frac{25.0\ \text{g}}{252.32\ \text{g/mol}} = 0.0991\ \text{mol}$

3. How many moles of C are in 25.0 g of dipyrithione?

   • First, calculate moles of dipyrithione: 0.0991 mol (from above).

   • Each mole of dipyrithione contains 10 moles of C.

   • $\text{Moles of C} = 0.0991\ \text{mol dipyrithione} \times 10 = 0.991\ \text{mol C}$

4. How many moles of dipyrithione contain $8.2 \times 10^{24}$ atoms of N?

   • Each mole of dipyrithione contains 2 moles of N atoms.

   • Number of N atoms per mole of dipyrithione: $2 \times 6.022 \times 10^{23} = 1.2044 \times 10^{24}$ atoms N per mole.

   • $\text{Moles of dipyrithione} = \frac{8.2 \times 10^{24}\ \text{atoms N}}{1.2044 \times 10^{24}\ \text{atoms N/mol}} = 6.81\ \text{mol}$

Summary Table: Dipyrithione Calculations

Quantity	Value	Formula Used
Molar mass of dipyrithione	252.32 g/mol	Sum of atomic masses
Moles in 25.0 g	0.0991 mol	$\frac{25.0}{252.32}$
Moles of C in 25.0 g	0.991 mol	0.0991 mol × 10
Moles of dipyrithione for $8.2 \times 10^{24}$ N atoms	6.81 mol	$\frac{8.2 \times 10^{24}}{2 \times 6.022 \times 10^{23}}$

Key Terms

• Mole (mol): The SI unit for amount of substance, representing $6.022 \times 10^{23}$ particles (Avogadro's number).

• Molar Mass: The mass of one mole of a substance, in grams per mole.

• Molecular Formula: The actual number of each type of atom in a molecule.