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?

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, #"Na"_2"S"_2"O"_3#.