Mole Calculations and Molar Mass: Ibuprofen as a Case Study

Mole Calculations and Molar Mass

Ibuprofen: An Anti-Inflammatory Compound

Ibuprofen is a commonly used anti-inflammatory drug. Understanding its chemical properties, such as molar mass and the relationship between moles, mass, and number of atoms, is essential in GOB Chemistry. The following study notes address key concepts using ibuprofen as an example.

1. Molar Mass of Ibuprofen

The molar mass of a compound is the mass of one mole of its molecules, expressed in grams per mole (g/mol). It is calculated by summing the atomic masses of all atoms in the molecular formula.

• Definition: The mass (in grams) of one mole of a substance.

• Formula: For a compound, add the atomic masses of each element multiplied by the number of atoms of that element in the formula.

• Example: The molecular formula of ibuprofen is C13H18O2.

Calculation:

• Carbon (C): 13 atoms × 12.01 g/mol = 156.13 g/mol

• Hydrogen (H): 18 atoms × 1.008 g/mol = 18.144 g/mol

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

Total molar mass:

$156.13\ \text{g/mol} + 18.144\ \text{g/mol} + 32.00\ \text{g/mol} = 206.27\ \text{g/mol}$

Additional info: The molecular formula for ibuprofen is C13H18O2.

2. Mass-Mole Conversions

To convert between grams and moles, use the molar mass as a conversion factor.

• Formula: $\text{mass (g)} = \text{moles} \times \text{molar mass (g/mol)}$

• Example: How many grams are in 0.525 mole of ibuprofen?

Calculation:

$0.525\ \text{mol} \times 206.27\ \text{g/mol} = 108.29\ \text{g}$

3. Calculating Moles of an Element in a Compound

To find the number of moles of a specific element (e.g., carbon) in a given mass of a compound:

• First, calculate the moles of the compound.

• Then, multiply by the number of atoms of the element per molecule.

• Formula: $\text{moles of element} = \text{moles of compound} \times \text{number of atoms of element per molecule}$

• Example: How many moles of C are in 12.0 g of ibuprofen?

Step 1: Calculate moles of ibuprofen:

$\text{moles of ibuprofen} = \frac{12.0\ \text{g}}{206.27\ \text{g/mol}} = 0.0582\ \text{mol}$

Step 2: Calculate moles of C:

$0.0582\ \text{mol ibuprofen} \times 13 = 0.757\ \text{mol C}$

4. Atoms and Moles: Avogadro's Number

Avogadro's number ($6.022 \times 10^{23}$) relates the number of particles (atoms, molecules) to moles.

• Formula: $\text{number of atoms} = \text{moles} \times \text{Avogadro's number} \times \text{number of atoms per molecule}$

• To find moles of ibuprofen containing a specific number of C atoms, rearrange the formula:

• $\text{moles of ibuprofen} = \frac{\text{number of C atoms}}{\text{Avogadro's number} \times 13}$

• Example: How many moles of ibuprofen contain $1.22 \times 10^{23}$ atoms of C?

Calculation:

$\text{moles of ibuprofen} = \frac{1.22 \times 10^{23}}{6.022 \times 10^{23} \times 13} = 0.0156\ \text{mol}$

Summary Table: Key Relationships

Quantity	Formula	Example (Ibuprofen)
Molar Mass	$\sum (\text{atomic mass} \times \text{number of atoms})$	206.27 g/mol
Mass to Moles	$\text{moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}}$	$\frac{12.0}{206.27} = 0.0582$ mol
Moles to Mass	$\text{mass (g)} = \text{moles} \times \text{molar mass}$	$0.525 \times 206.27 = 108.29$ g
Moles of Element	$\text{moles of element} = \text{moles of compound} \times \text{atoms per molecule}$	$0.0582 \times 13 = 0.757$ mol C
Moles from Atoms	$\text{moles} = \frac{\text{atoms}}{\text{Avogadro's number} \times \text{atoms per molecule}}$	$\frac{1.22 \times 10^{23}}{6.022 \times 10^{23} \times 13} = 0.0156$ mol