# Question #d7129

##### 1 Answer

#### Explanation:

The first thing to do here is to pick a sample of this compound and calculate how many moles of each constituent element it contains.

Since you're dealing with the compound's **percent composition**, you can pick a *per cent*, **for every** **of compound**

#"39.97 g C"# #"13.41 g H"# #"46.62 g N"#

To convert these values to *moles*, use the **molar masses** of the three elements. You will have

#"For C: " 39.97color(red)(cancel(color(black)("g"))) * "1 mole C"/(12.011color(red)(cancel(color(black)("g")))) = "3.3278 moles C"#

#"For H: " 13.41 color(red)(cancel(color(black)("g"))) * "1 mole H"/(1.008color(red)(cancel(color(black)("g")))) = "13.306 moles H"#

#"For N: " 46.62 color(red)(cancel(color(black)("g"))) * "1 mole N"/(14.007color(red)(cancel(color(black)("g")))) = "3.3283 moles N"#

Next, figure out the **mole ratios** that exist between the three elements by dividing all values by the *smallest one*. You will have

#"For C: " (3.3278 color(red)(cancel(color(black)("moles"))))/(3.3278color(red)(cancel(color(black)("moles")))) = 1#

#"For H: " (13.306 color(red)(cancel(color(black)("moles"))))/(3.3278color(red)(cancel(color(black)("moles")))) = 3.9984 ~~ 4#

#"For N: " (3.3283color(red)(cancel(color(black)("moles"))))/(3.3278color(red)(cancel(color(black)("moles")))) = 1.0002 ~~ 1#

Now, the **empirical formula** of a compound tells you the **smallest whole number ratio** that exists between its constituent elements.

In this case, you know that you have

#"C : H : N = 1 : 4 : 1"#

Since

#color(darkgreen)(ul(color(black)("C"_1"H"_4"N"_1 implies "CH"_4"N")))#