# Naphthalene (moth balls) contains 93.71% carbon and 6.29% hydrogen. Its molecular mass is 128 g mol-1, calculate its molecular formula?

Aug 17, 2017

${C}_{10} {H}_{8}$

#### Explanation:

Assuming that is a mass amount, divide each proportion by the atomic weight of the component. Normalize to obtain the empirical formula and then use the molecular mass to determine the actual molecular formula.
$\frac{93.91}{12} = 7.83$ relative moles of carbon
$\frac{6.29}{1} = 6.29$ relative moles of hydrogen

Ratio of C:H is 7.83:6.29 or 1.2. Nearest whole multiple is 5, resulting in ratio of 6:5. 6-C and 5-H would have a molecular weight of $\left(6 \times 12\right) + \left(5 \times 1\right) = 77$ The actual molecular weight is 128, so the formula must be $\frac{128}{77} = 1.67 \times {C}_{6} {H}_{5}$.
${C}_{10} {H}_{8}$

Subsequent note on Whole Multiple:
A chemical compound MUST have whole numbers of atoms - we can't have a compound with a "partial" atom! The observed/calculated math just gives us ratios of the mass. We need to insure that our final mass contains WHOLE atoms. Thus, when we find our molar ratio of C:H is 7.83:6.29 or 1.2:1 we need to convert that to one with whole numbers in the numerator as well as the denominator.

In this case, with the denominator already "normalized" at 1, we only need to find a factor to make the 1.2 a whole number. The key that 0.2 part - we need to make it $1.0$.
0.2 xx ? = 1.0
 ? = 1.0/0.2 = 5 Applying this to our original $\frac{1.2}{1}$ ratio we obtain:
$5 \times \frac{1.2}{1} = \frac{6}{5}$ So, our atomic molar ratio is 6-C and 5-H, as used in the rest of the original answer derivation.