Understanding the Mole Concept

The Mole

• The atomic mass of an element is mass of one atom, expressed in atomic mass units (amu).
• $1 \mathrm{amu} = 1.66054 \times 10^{-24} \mathrm{g}$
• The molar mass is the mass of one mole of a substance expressed in grams per mole (g/mol).
• The molar mass of an element is numerically equal to its atomic mass in amu.
• Example: Sodium's atomic mass is 22.99 amu; its molar mass is 22.99 g/mol.
• One mole of any substance contains the same number of particles (Avogadro's number): approximately $6.022 \times 10^{23}$.
• $1 \mathrm{~mol} = 6.022 \times 10^{23} \text{ particles}$
• The mole allows conversion between mass, number of particles, and volume (for gases).

Calculations Involving the Mole

• To find how many moles are in 25.0 g of potassium chromate ($\mathrm{K_2CrO_4}$), divide the given mass by the molar mass (194.2 g/mol)
• Moles of $\mathrm{K_2CrO_4}$= 0.129 mol
• To find how many grams of gold (Au) are in 15.3 moles, multiply the number of moles by the molar mass of Au (196.97 g/mol).
• Grams of Au = 3013.6 g
• To find how many atoms are in 10.0 g of lead (Pb), first find the number of moles by dividing the given mass by the molar mass of Pb (207.2 g/mol).
• Moles of Pb = 0.0483 mol
• Multiply the number of moles by Avogadro's number ($6.022 \times 10^{23} \mathrm{~atoms/mol}$)
• Atoms of Pb = $2.91 \times 10^{22}$ atoms

Chemical Formulas

• The formula mass of a compound is the sum of the atomic masses of all the atoms in its formula.
• The formula mass of water $(\mathrm{H_2O})$ is 18.02 amu.

Percent Composition from Formulas

• The percent composition of a compound is the percentage by mass of each element in the compound.
• $\text{Percent composition of element} = \frac{(\text{number of atoms of element}) \times (\text{atomic mass of element})}{\text{formula mass of compound}} \times 100%$
• In potassium chromate $(\mathrm{K_2CrO_4})$, % K = 40.27%, % Cr = 26.78%, and % O = 32.96%.

Empirical and Molecular Formulas

• The empirical formula is the simplest whole-number ratio of atoms in a compound.
• The molecular formula is the actual number of atoms of each element in a molecule.

Steps for Determining Empirical Formula

• Convert mass percentages to grams, assuming a 100 g sample.
• Convert grams to moles by dividing the mass of each element by its molar mass.
• Find the simplest whole-number ratio by dividing each mole value by the smallest mole value.
• Write the empirical formula using the whole-number ratios as subscripts.

Steps for Determining Molecular Formula

• Calculate the empirical formula mass.
• Calculate the ratio between molecular and empirical formula mass:$\frac{\text{Molecular formula mass}}{\text{Empirical formula mass}} = \text{integer}$
• Multiply the subscripts in the empirical formula by this integer to obtain the molecular formula.

Empirical and Molecular Formula Example

• For a compound with the composition Na: 29.1%, S: 40.5%, O: 30.4%, and a molecular mass of 158 g/mol, the empirical formula is $\mathrm{Na_2S_2O_3}$.
• The molecular formula is the same as the empirical formula: $\mathrm{Na_2S_2O_3}$.