Even through a an excellent word-processing program, having actually to click on an symbol to obtain a superscript, and then remembering to click off after you form the numbercan it is in a real hassle. If we did not understand ofmoles, and also instead just knew of number of atoms or molecule (big numbers the require many superscripts), life would be much much more complicated;we would certainly make an ext typing errors.

You are watching: Convert atoms of carbon to moles of carbon

## Conversions between Moles and number of Particles

Using ours unit conversion techniques, we deserve to use the mole label to convert back and forth between the number of particles and moles.

Example (PageIndex1)

The facet carbon exists in two main forms: graphite and also diamond. How many moles the carbon atom is (4.72 imes 10^24) atoms of carbon?

Solution

Step 1: perform the known quantities and plan the problem.

Known

variety of (ceC) atoms (= 4.72 imes 10^24) (1) mole (= 6.02 imes 10^23) atoms

Unknown

(4.72 imes 10^24 = ?) atom (ceC)

One conversion element will permit us to transform from the variety of (ceC) atoms to mole of (ceC) atoms.

Step 2: Calculate.

<4.72 imes 10^24 : extatoms : ceC imes frac1 : extmol : ceC6.02 imes 10^23 : extatoms : ceC = 7.84 : extmol : ceC>

Step 3: Think around your result.

The given number of carbon atom was better than Avogadro"s number, therefore the number of moles of (ceC) atom is greater than 1 mole. Due to the fact that Avogadro"s number is a measured amount with three far-reaching figures, the result of the calculate is rounded come three significant figures.

Suppose the you wantto understand how numerous hydrogen atoms are in a mole of water molecules. First, you need to recognize the gaianation.netistry formula because that water, i m sorry is (ceH_2O). There space two atom of hydrogen in each molecule of water. How numerous atoms the hydrogen space in 2 water molecules? There room (2 imes 2 = 4) hydrogen atoms. How about in a dozen? In the case, a dozen is 12;so (12 imes 2 = 24) hydrogen atom in a dozen water molecules. To get the answer (4 and 24), you multiply the given variety of molecules by 2 atoms the hydrogen per molecule. So, to uncover the variety of hydrogen atoms in a mole that water molecules, the trouble canbe addressed using switch factors:

<1 : extmol : ceH_2O imes frac6.02 imes 10^23 : extmolecules : ceH_2O1 : extmol : ceH_2O imes frac2 : extatoms : ceH1 : extmolecule : ceH_2O = 1.20 imes 10^24 : extatoms : ceH>

The very first conversion variable converts from moles of particles to the variety of particles. The 2nd conversion factor reflects the number of atoms consisted of within each molecule.

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Figure (PageIndex1): 2 water molecules contain 4 hydrogen atoms and also 2 oxygen atoms. A mole the water molecules has 2 mole of hydrogen atoms and 1 mole the oxygen atoms.