# Empirical Formula As of Feb. 4, 2013, the Canadian Penny will be phased out of circulation over a 6-year period. This may cause you to look through your change jar at home and sort out all of the pennies from the other coins. Imagine that you reached into your change jar and pulled out a handful of coins. You dropped this handful of coins on your table and found you had 10 pennies and 5 quarters. What would be the ratio of pennies to quarters? Since you have double the amount of pennies than you have quarters we can say that the ratio between pennies and quarters is, That was a pretty simple example, so lets try a more difficult one. Imagine that you pulled out another handful of coins, dumped them onto the table and counted up the pennies and quarters. This time you found that somehow you had 29.54 pennies and 19.77 quarters (Not exactly sure how you had 0.54 of a penny and 0.77 of a quarter, but you did). What would be the ratio of pennies to quarters? This example isn’t as immediately obvious as the other one. How could we solve this problem? To determine any ratio, all you need to do is compare the two numbers to each other by dividing the larger number by the smaller number. Let’s try this with our pennies and quarters.

Once again, we end up with a ratio of, Ratios can also be used to help us understand chemical compounds. Often times, chemists are concerned with the lowest whole number ratio of elements in a chemical compound, which we call the empirical formula. Calculating an empirical formula of a compound is just like calculating ratios.

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# Here’s an example of calculating empirical formula:

A compound containing only carbon, hydrogen and nitrogen has a percent composition of 62.1 % C, 13.8 % H, and 24.1 % N. What is the empirical formula of this compound?

Just like in the example with the coins we need to compare the quantities of each element to each other. However, we can only compare the quantities if the quantities are in units of the mole. We cannot convert from a percent to a mole so we will first change our percent signs to grams.

If we assume that we have 100 g total of this compound, than we would have 62.1 g of carbon, 13.8 g of hydrogen and 24.1 g of nitrogen.

Now we can convert these quantities into moles,   .

Now that we have each quantity in units of the mole, we can compare them to each other. Just as with any ratio, we can take each number and divide it by the smaller number, . .

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So the ratio of carbon, nitrogen and hydrogen is, .

Finally we can turn this ratio into an empirical formula by ratios as subscripts, 