Convert From Atoms To Moles

ten.ii: Conversions Betwixt Moles and Atoms

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Big numbers or footling numbers?

Do y'all detest to type subscripts and superscripts? Fifty-fifty with a good word-processing plan, having to click on an icon to get a superscript and and so remembering to click off after you type the number can be a real hassle. If we did not know near moles and just knew about numbers of atoms or molecules (those big numbers that require lots of superscripts), life would be much more complicated and we would brand many more typing errors.

Conversions Betwixt Moles and Atoms

Conversions Betwixt Moles and Number of Particles

Using our unit conversion techniques, we can use the mole label to convert dorsum and forth betwixt the number of particles and moles.

Instance \(\PageIndex{1}\): Converting Number of Particles to Moles

The element carbon exists in 2 primary forms: graphite and diamond. How many moles of carbon atoms is \(4.72 \times 10^{24}\) atoms of carbon?

Solution

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

Known

number of \(\ce{C}\) atoms \(= 4.72 \times 10^{24}\)
\(ane\) mole \(= 6.02 \times 10^{23}\) atoms

Unknown

4.72 ten 10²⁴ = ? mol C

One conversion factor volition allow usa to catechumen from the number of \(\ce{C}\) atoms to moles of \(\ce{C}\) atoms.

Step two: Calculate.

\[iv.72 \times 10^{24} \: \text{atoms} \: \ce{C} \times \frac{1 \: \text{mol} \: \ce{C}}{half dozen.02 \times 10^{23} \: \text{atoms} \: \ce{C}} = 7.84 \: \text{mol} \: \ce{C}\nonumber \]

Pace 3: Think virtually your result.

The given number of carbon atoms was greater than Avogadro'south number, so the number of moles of \(\ce{C}\) atoms is greater than 1 mole. Since Avogadro's number is a measured quantity with three significant figures, the result of the adding is rounded to three significant figures.

Suppose that you want to know how many hydrogen atoms are in a mole of water molecules. Start, you demand to know the chemical formula for water, which is \(\ce{H_2O}\). There are two atoms of hydrogen in each molecule of h2o. How many atoms of hydrogen are in two water molecules? There are \(ii \times 2 = 4\) hydrogen atoms. How about in a dozen? In that example, a dozen is 12; so \(12 \times two = 24\) hydrogen atoms in a dozen water molecules. To get the answers (iv and 24), you lot multiply the given number of molecules by two atoms of hydrogen per molecule. And then, to find the number of hydrogen atoms in a mole of h2o molecules, the trouble can be solved using conversion factors:

\[i \: \text{mol} \: \ce{H_2O} \times \frac{half dozen.02 \times 10^{23} \: \text{molecules} \: \ce{H_2O}}{1 \: \text{mol} \: \ce{H_2O}} \times \frac{2 \: \text{atoms} \: \ce{H}}{i \: \text{molecule} \: \ce{H_2O}} = ane.20 \times 10^{24} \: \text{atoms} \: \ce{H}\nonumber \]

The get-go conversion factor converts from moles of particles to the number of particles. The second conversion gene reflects the number of atoms contained inside each molecule.

Figure \(\PageIndex{2}\): Ii water molecules comprise iv hydrogen atoms and two oxygen atoms. A mole of h2o molecules contains two moles of hydrogen atoms and one mole of oxygen atoms. (Credit: Ben Mills (Wikimedia: Benjah-bmm27); Source: http://commons.wikimedia.org/wiki/File:H2o-3D-assurance-A.png(opens in new window); License: Public Domain)

Case \(\PageIndex{2}\): Atoms, Molecules, and Moles

Sulfuric acid has the chemic formula \(\ce{H_2SO_4}\). A certain quantity of sulfuric acid contains \(4.89 \times 10^{25}\) atoms of oxygen. How many moles of sulfuric acid is the sample?

Solution:

Stride 1: List the known quantities and plan the problem.

Known

\(4.89 \times 10^{25} = \ce{O}\) atoms
\(1\) mole \(= 6.02 \times 10^{23}\) molecules \(\ce{H_2SO_4}\)

Unknown

mol of H₂And then_four molecules

Two conversion factors will be used. Commencement, convert atoms of oxygen to molecules of sulfuric acid. And then, convert molecules of sulfuric acrid to moles of sulfuric acid.

Stride 2: Calculate.

\[iv.89 \times x^{25} \: \text{atoms} \: \ce{O} \times \frac{1 \: \text{molecule} \: \ce{H_2SO_4}}{4 \: \text{atoms} \: \ce{O}} \times \frac{1 \: \text{mol} \: \ce{H_2SO_4}}{6.02 \times 10^{23} \: \text{molecules} \: \ce{H_2SO_4}} = xx.3 \: \text{mol} \: \ce{H_2SO_4}\nonumber \]

Step iii: Think about your result.

The original number of oxygen atoms was about 80 times larger than Avogadro'southward number. Since each sulfuric acid molecule contains four oxygen atoms, in that location are about 20 moles of sulfuric acid molecules.

Summary

Methods are described for conversions between moles, atoms, and molecules.

Review

What conversion factor would we demand to convert moles of helium to atoms of helium?
I desire to convert atoms to moles. My friend tells me to multiply the number of atoms by 6.02 × x²³ atoms/mole. Is my friend correct?
Why do you need to know the formula for a molecule in order to calculate the number of moles of one of the atoms?
How many atoms of fluorine are in five.half dozen×ten²² molecules of MgF_ii?