# A component of protein called serine has an approximate molar mass of 100 g/mole. If the percent composition is as follows, what is the empirical and molecular formula of serine?

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The percent composition is: C=34.95% H = 6.844% O=46.56% and N=13.59%.

The percent composition is: C=34.95% H = 6.844% O=46.56% and N=13.59%.

##### 1 Answer

#### Explanation:

Here's a great example of a problem that allows you to use a bit of *logic* to find the *molecular formula* **first**, then backtrack to find the *empirical formula*.

Notice that you are given the **molar mass** of serine, which is said to be **approximately** equal to

That means that you can expect the actual molar mass of serine to be either a little smaller than

You can pick a **one mole** of a compound, the number of moles of each element **must** come out to be **integers**.

*Why?*

*Because one molecule of a compound will always contain whole numbers of atoms of each constituent element.*

So, if you were to pick a

#"34.95 g " -># carbon#"6.844 g " -># hydrogen#"46.56 g " -># oxygen#"13.59 g " -># nitrogen

Use the **molar mass** of each element to determine how may *moles* of each you get in **one mole** of serine

#"For C: " 34.95 color(red)(cancel(color(black)("g"))) * "1 mole C"/(12.011color(red)(cancel(color(black)("g")))) = "2.91 moles C"#

#"For H: " 6.844color(red)(cancel(color(black)("g"))) * "1 mole H"/(1.00794color(red)(cancel(color(black)("g")))) = "6.80 moles H"#

#"For O: "46.56color(red)(cancel(color(black)("g"))) * "1 mole O"/(15.9994color(red)(cancel(color(black)("g")))) = "2.91 moles O"#

#"For N: " 13.59color(red)(cancel(color(black)("g"))) * "1 mole N"/(14.00674color(red)(cancel(color(black)("g")))) = "0.97 moles N"#

You can stop the calculations at this point and say that since these values must be **rounded up** to give **integers**, the molecular mass of serine is a little bigger than

Since you're still in the *approximately* equal to **round these values** to the *nearest integer* to get

#"For C: " 2.91 ~~ "3 moles C"#

#"For H: " 6.80 ~~ "7 moles H"#

#"For O: " 2.91 ~~ "3 moles O"#

#"For N: " 0.97 ~~ "1 mole N"#

Therefore, if **one mole** of serine contains that many moles of each element, you can say that its **molecular formula** is

#color(green)("C"_3"H"_7"N"_1"O"_3 implies "C"_3"H"_7"NO"_3) -># molecular formula

Since **smallest whole number ratio** that can exist between these values, this will also be serine's **empirical formula**

#color(green)("C"_3"H"_7"NO"_3) -># empirical formula

If you want to test this result, simply divide the number of moles of each element you found in the *smallest value* of the group to get the compound's *empirical formula*.

Once you know the empirical formula, you can determine the molecular formula by using the