# Elemental analysis of a compound showed that it consisted of 81.82% carbon and 18.18% hydrogen by mass, how many hydrogen atoms appear in the empirical formula of the compound?

Nov 12, 2015

8 $H$ atoms

#### Explanation:

For this kind of problem, we have to assume that you have 100g unknown sample (since the percentages add up to 100%).

Thus, masses are C = 81.82 g; H = 18.18 g

Since chemical formulas deal with number of moles more than their respective weights, we need to multiply the masses with their respective atomic weights to get the number of moles.

$C$ = $81.82 \cancel{g}$ x $\frac{\text{1 mol}}{12.01 \cancel{g}}$ = 6.81 mol $C$

$H$ = $18.18 \cancel{g}$ x $\frac{\text{1 mol}}{1.01 \cancel{g}}$ = 18 mol $H$

Next, to get the ratio of atoms to each other, we would need to divide the number of moles by the smallest number of mole.

$C$ = $\left(6.81 \cancel{\text{mol")/(6.81 cancel "mol}}\right)$ = 1

$H$ = $\left(18.18 \cancel{\text{mol")/(6.81 cancel "mol}}\right)$ = $\textcolor{red}{2.64}$

Now, since the number of $H$ atoms is too far to round off, we need to find a factor that we can multiply to BOTH atoms to get the accurate ratio. In this case, the factor is 3.

$C$ = 1 x 3 = $3$

$H$ = 2.64 x 3 = $7.92 \approx 8$

Therefore, the empirical formula is ${C}_{3} {H}_{8}$.