How many moles of sulfur atoms are there in 5.0 g of sulfur? 8.3 x 10-24 mol. 2.7 x 10-22 mol. But wait, what actually is a mole? The mole is the SI unit of the measurement for the amount of a substance. In one mole of matter, there is precisely 6.4 × 10²³ (using scientific notation) atoms, molecules, or anything else. This tremendous value refers to Avogadro's number.
Even with a good word-processing program, having to click on an icon to get a superscript, and then remembering to click off after you type the number can be a real hassle. If we did not know of moles, and instead just knew of numbers of atoms or molecules (big numbers that require lots of superscripts), life would be much more complicated; we would certainly make more typing errors.
Conversions Between Moles and Atoms
Conversions Between Moles and Number of Particles
Using our unit conversion techniques, we can use the mole label to convert back and forth between the number of particles and moles.
Example (PageIndex{1})
The element carbon exists in two 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})
- (1) mole (= 6.02 times 10^{23}) atoms
Unknown
- (4.72 times 10^{24} = ?) atoms (ce{C})
One conversion factor will allow us to convert from the number of (ce{C}) atoms to moles of (ce{C}) atoms.
Step 2: Calculate.
[4.72 times 10^{24} : text{atoms} : ce{C} times frac{1 : text{mol} : ce{C}}{6.02 times 10^{23} : text{atoms} : ce{C}} = 7.84 : text{mol} : ce{C}]
Step 3: Think about your result.
The given number of carbon atoms was greater than Avogadro's 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 calculation is rounded to three significant figures.
Suppose that you want to know how many hydrogen atoms are in a mole of water molecules. First, you need to know the chemical formula for water, which is (ce{H_2O}). There are two atoms of hydrogen in each molecule of water. How many atoms of hydrogen are in two water molecules? There are (2 times 2 = 4) hydrogen atoms. How about in a dozen? In that case, a dozen is 12; so (12 times 2 = 24) hydrogen atoms in a dozen water molecules. To get the answers (4 and 24), you multiply the given number of molecules by two atoms of hydrogen per molecule. So, to find the number of hydrogen atoms in a mole of water molecules, the problem can be solved using conversion factors:
[1 : text{mol} : ce{H_2O} times frac{6.02 times 10^{23} : text{molecules} : ce{H_2O}}{1 : text{mol} : ce{H_2O}} times frac{2 : text{atoms} : ce{H}}{1 : text{molecule} : ce{H_2O}} = 1.20 times 10^{24} : text{atoms} : ce{H}]
The first conversion factor converts from moles of particles to the number of particles. The second conversion factor reflects the number of atoms contained within each molecule.
How to add new page in word shortcut. Example (PageIndex{2})
Sulfuric acid has the chemical 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?
Excel for dummies free. Solution:
Step 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
- (text{mol}) of (ce{H_2SO_4}) molecules
Two conversion factors will be used. First, convert atoms of oxygen to molecules of sulfuric acid. Then, convert molecules of sulfuric acid to moles of sulfuric acid.
Step 2: Calculate.
[4.89 times 10^{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}} = 20. : text{mol} : ce{H_2SO_4}]
Step 3: Think about your result. Wordpress web developer.
The original number of oxygen atoms was about 80 times larger than Avogadro's number. Since each sulfuric acid molecule contains 4 oxgyen atoms, there are about 20 moles of sulfuric acid molecules.
Summary
- Methods are described for conversions between moles, atoms, and molecules.
Contributors and Attributions
CK-12 Foundation by Sharon Bewick, Richard Parsons, Therese Forsythe, Shonna Robinson, and Jean Dupon.
Lets say you have 2.5 moles of Au (Gold) and you’re really curious as to how many atoms of gold are in that sample. What should we do? Well just remember what Chemistry Cat says about MOLE PROBLEMS:
For any element or compound, 1 mole is equal to Avogadro’s Number of particles of that element or compound.
1 mole = 6.022 x 10²³
Atoms To Moles Chemistry
So, lets start plugging into a factor label equation the same way we did for Moles to Grams equations.
2.5 mole Au atoms -> __________ Au atoms
Since 1 mole is equal to Avogadro’s number, we can put that into our formula as…
6.022 x 10²³ Au atoms
1 mole Au atoms
So lets put this value into our formula and see if we can make this work…
2.5 mole Au atoms x 6.022 x 10²³ Au atoms
11 mole Au atoms
We can cross out the “mole Au atoms” units so the only unit remaining is “Au atoms“. So…
Atoms To Moles Co2
2.5 x 6.022 x 10²³ Au atoms = 1.506 x 1024 Au atoms
___________Easy! When you go from grams to moles you MULTIPLY BY THE ATOMS!_______________
But, what if I want to go from atoms to moles??? EASY!!! DIVIDE BY AVOGADRO’S NUMBER!
How many moles of Zn is 2.75 x 1024 atoms of Zn?
2.75 x 1024 Zn atoms x 1 mole Zn atoms= 4.57 mole Zn atoms
1 6.022 x 10²³ Zn atoms
Atoms To Moles Conversion Factor
Since, 1 mole of any element = Avogadro’s number of atoms (or molecules), you can flip the equation to work for you! Since we have moles on the top left of the formula, we want moles on the bottom right so they can cancel out!
Your homework for tonight is to finish the second 10 problems (the back side) of the Moles Conversions Worksheet (found on semester 1 Docs). You can also watch the Voicethread on mole conversions using the App or the semester 1 Notes Page.