Question

Question #d7129

Answer 1

`"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 `"100-g"` sample and say that it contains--remember, per cent, `%`, simply means for every `"100 g"` 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 `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

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