# Ibuprofen, a common pain remedy, has an empirical formula of C_7H_9O and a molar mass of approximately 218.078 grams per mole. What is the molecular formula of ibuprofen?

Dec 17, 2016

${C}_{14} {H}_{18} {O}_{2}$

#### Explanation:

The empirical formula is the simplest ratio of Ibuprofen, which in this case is 7:9:1.

To find the molecular formula, you need to find an integer, or a number which you multiply the empirical formula ratio with. To do this, just know this simple equation:

n$=$ Molar mass of MF$\div$Molar mass of EF

'n' represents the numerical integer.

Since the molar mass of the molecular formula is given to you (218.078 grams), all we need to find is the molar mass of the empirical formula. The empirical formula has 7 carbon atoms, 9 hydrogen atoms and 1 oxygen atom.

As a result, our calculation would look like this:

(7 x 12.011) + (9 x 1.008) + (1 x 16)

We would get something near 109.149. Now back to our equation for the integer, we simply divide the given molar mass by the molar mass of the empirical formula, and we would get something around 1.99.

Keep in mind that in molecular/ empirical formula problems, the integer is always rounded to the nearest whole number unless it is too far away (i.e, 1.5) (which in that case, it is multiplied by another whole number). However, in our problem, 1.99 is close enough to 2 that we can call it 2.

Now that we have our integer, we simply multiply each ratio whole number from the empirical formula with 2. As a result, we get ${C}_{14} {H}_{18} {O}_{2}$.