# A certain ionic compound is found to contain .012 mol of sodium, .012 mol of sulfur, and .018 mol of oxygen. What is its empirical formula?

Nov 13, 2015

${\text{Na"_2"S"_2"O}}_{3}$

#### Explanation:

A compound's empirical formula tells you what the smallest whole number ratio between the elements that make up that compound is.

In your case, you know that this ionic compound contains

• $0.012$ moles of sodium
• $0.012$ moles of sulfur
• $0.018$ moles of oxygen

To get the mole ratio that exists between these elements in the compound, divide these numbers by the smallest one

"For Na: " (0.012color(red)(cancel(color(black)("moles"))))/(0.012color(red)(cancel(color(black)("moles")))) = 1

"For S: " (0.012color(red)(cancel(color(black)("moles"))))/(0.012color(red)(cancel(color(black)("moles")))) = 1

"For O: " (0.018color(red)(cancel(color(black)("moles"))))/(0.012color(red)(cancel(color(black)("moles")))) = 1.5

Now, since you can't have fractional numbers as mole ratios, you will need to find the smallest whole number ratio that satisfies the condition $1 : 1 : 1.5$.

Notice that if you multiply all the numbers by $2$, you can get rid of oxygen's fractional number and still keep the ratio $1 : 1 : 1.5$. This means that the empirical formula of the compound will be

("Na"_1"S"_1"O"_1.5)_2 implies "Na"_2"S"_2"O"_3

For ionic compounds, the empirical formula is always the same as the chemical formula, which is why you cn say that your unknown compound is actually sodium thiosulfate, ${\text{Na"_2"S"_2"O}}_{3}$.