How do you find the factor 'n' to determine the molecular formula from the empirical formula, using an example like CH2 and a molecular mass of 70?

Here's a detailed explanation:

• Empirical Formula: This is the simplest whole-number ratio of atoms in a compound. For example, if a compound has 2 carbons and 4 hydrogens, its empirical formula is $\text{CH}_2$.
• Molecular Formula: This is the actual number of atoms of each element in a molecule of the compound. For the example above, if the actual molecule has 4 carbons and 8 hydrogens, its molecular formula is $\text{C}_4\text{H}_8$. Notice that $\text{C}_4\text{H}_8$ is $(\text{CH}_2)_4$.

The molecular formula is always a whole-number multiple of the empirical formula. This whole number is what we call 'n'.

$$\text{Molecular Formula} = (\text{Empirical Formula})_n$$

To find 'n', we use the masses:

$$n = \frac{\text{Molecular mass}}{\text{Empirical formula mass}}$$

In :

1. We found the empirical formula in part (a) to be $\text{CH}_2$.
2. We calculated the empirical formula mass of $\text{CH}_2$: $(1 \times 12) + (2 \times 1) = 14 \text{ g/mol}$.
3. The problem statement gives the molecular mass as $70 \text{ g/mol}$.

So, to find 'n':

$$n = \frac{70 \text{ g/mol}}{14 \text{ g/mol}} = 5$$

This means the actual molecule is 5 times larger than the empirical formula unit. Therefore, the molecular formula is $(\text{CH}_2)_5$, which simplifies to $\text{C}_5\text{H}_{10}$.