Even v a good word-processing program, having to click on an icon to obtain a superscript, and also then remembering to click turn off after you kind the numbercan be a genuine hassle. If us did not understand ofmoles, and instead just knew of numbers of atoms or molecule (big numbers the require many superscripts), life would be much an ext complicated;we would certainly make much more typing errors.

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Conversions in between Moles and number of Particles

Using our unit conversion techniques, we can use the mole brand to convert ago and forth between the variety of particles and also moles.

Example (PageIndex1)

The aspect carbon exist in two major forms: graphite and diamond. How numerous moles the carbon atoms is (4.72 imes 10^24) atoms of carbon?


Step 1: perform the well-known quantities and also plan the problem.


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


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

One conversion variable will allow us to transform from the number of (ceC) atoms to moles 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 about your result.

The given number of carbon atoms was better than Avogadro"s number, for this reason the number of moles the (ceC) atom is higher than 1 mole. Due to the fact that Avogadro"s number is a measured quantity with three far-ranging figures, the result of the calculate is rounded to three far-ranging figures.

Suppose that you wantto know how numerous hydrogen atoms space in a mole the water molecules. First, you require to recognize the smashville247.netical formula because that water, i beg your pardon is (ceH_2O). There room two atoms of hydrogen in each molecule the water. How many atoms the hydrogen room in two water molecules? There space (2 imes 2 = 4) hydrogen atoms. How around in a dozen? In that case, a dozen is 12;so (12 imes 2 = 24) hydrogen atoms in a dozen water molecules. To gain the answer (4 and also 24), you main point the given number of molecules by two atoms the hydrogen every molecule. So, to find the variety of hydrogen atoms in a mole that water molecules, the difficulty canbe resolved using counter 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 first conversion factor converts from mole of corpuscle to the number of particles. The 2nd conversion variable reflects the number of atoms contained within each molecule.

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