# Question d7129

Jun 15, 2017

$\text{CH"_4"N}$

#### 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 $\text{100-g}$ sample and say that it contains--remember, per cent, %, simply means for every $\text{100 g}$ of compound

• $\text{39.97 g C}$
• $\text{13.41 g H}$
• $\text{46.62 g N}$

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

$\text{For C: " 39.97color(red)(cancel(color(black)("g"))) * "1 mole C"/(12.011color(red)(cancel(color(black)("g")))) = "3.3278 moles C}$

$\text{For H: " 13.41 color(red)(cancel(color(black)("g"))) * "1 mole H"/(1.008color(red)(cancel(color(black)("g")))) = "13.306 moles H}$

$\text{For N: " 46.62 color(red)(cancel(color(black)("g"))) * "1 mole N"/(14.007color(red)(cancel(color(black)("g")))) = "3.3283 moles N}$

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

$\text{C : H : N = 1 : 4 : 1}$

Since $1 : 4 : 1$ is the smallest whole number ratio that you can have here, you can say that the empirical formula of the compound is

$\textcolor{\mathrm{da} r k g r e e n}{\underline{\textcolor{b l a c k}{\text{C"_1"H"_4"N"_1 implies "CH"_4"N}}}}$