# I need help with Subscripts for empirical formula, how do i know which number to multiply so that I get a whole number?

##### 2 Answers
Mar 10, 2015

When you have to calculate a compound's empirical formula from its percent composition, there are a few tricks to use to help you deal with decimal mole ratios between the atoms that comprise your compound.

Now, I assume you know how to get to this point, so I won't show you the whole approach. Let's assume you have a compound containing $\text{A}$, $\text{B}$ ,and $\text{C}$, and you determine the mole ratios between these elements to be

$\text{A} : 2.33$
$\text{B} : 1$
$\text{C} : 1.67$

In such cases it is very useful to use mixed fractions. Mixed fractions are a combination of a whole number and a regular (or proper) fraction.

In this case, $2.33$ is equal to 2 and 1/3, or 7/3, and $1.67$ is equal to 1 and 2/3, or 5/3. This makes the ratios equal to

$\text{A": "7/3}$
$\text{B} : 1$
$\text{C": "5/3}$

Now multiply all of them by 3 to get rid of the denominator and you'll get the empirical formula

${A}_{7} {B}_{3} {C}_{5}$

If you get enough practice with empirical formulas you'll be able to "see" the answer faster. For example, if you have a compound comporised of $\text{X}$, $\text{Y}$, and $\text{Z}$, and the mole ratio looks like this

$\text{X} : 1.33$
$\text{Y} : 1$
$\text{Z} : 1$

It will become obvious in time that you have to multiply all of them by 3 to get all-whole numbers and an empirical formula of

${X}_{4} {Y}_{3} {Z}_{3}$

Notice that the mixed fractions method is useful in this case as well, since 1.33 is actually 1 and 1/3, or 4/3.

As a conclusion, it takes a little practice to be able to determine which numbers can be written in a useful way as mixed fractions, so spend some time on getting this skill down.

SIDE NOTE I assume you know how to get around mixed fractions, so I won't detail how I got 7/3 or 4/3.

Mar 10, 2015

After you divide by the smallest amount of moles if you end up with a number ending in .25 then multiply all numbers by 4. If you end up with a number ending in .33 then multiply all numbers 3. If you end up with a number ending in .20 then multiply all numbers by 5. If you end up with a number ending in .5 then multiply all numbers by 2.