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?

Md Ariful Islam

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Md Ariful Islam

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

In your case, you know that this contains

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

To get 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 , 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 , 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, $"Na"_2"S"_2"O"_3$.

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