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Wize University Chemistry Textbook > Stoichiometry

Atoms, Molecules, and the Mole!

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Moles

When someone says they want a dozen donuts, roses, or eggs we know they mean they want 12. A mole in chemistry also tells us the amount of something.


  • Just like how a dozen of something = 12, 1 mole of something =6.02x1023 molecules
  • 6.02x1023 is referred to as Avagadro's number (NA)

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Wize Tip
You should memorize Avagadro's number since it is not always provided on exams! We'll soon see that you need to know it to solve problems :)
NA=6.02×1023  molecules/mole\boxed{\bold{N_A=6.02\times 10^{23}\ \bold{\text{ molecules/mole}}}}

We use the unit "moles" to help make very small amounts more measurable. A mole is just like any other unit!

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There are 2 Equations Related to Moles:


n=mM\boxed{n=\frac{m}{M}} n=NNA\boxed{n=\frac{N}{N_{A_{ }}}}

n=# of moles
m=mass (g)
M=molar mass (g/mol)
N=# of molecules or atoms
NA=Avagadro's number=6.02x1023 molecules

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Example #1:

If we are told that a sample of CO2(s) weighs 11g, how many moles are present?

m=11g, n=?
n=m/M
We are given m but need to solve for M:
M=12g/mol + 2(16g/mol)
M=44g/mol

n=m/M
n=11g/44g/mol
n=0.25moles!


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Example #2

We have 2 moles of CO2 present in our sample, how many molecules are there?

n=2 moles, N=? NA=6.02x1023
n=N/NA
N=n(NA)
N=2(6.02x1023)
N=1.2x1024 molecules

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Example #3

How many oxygen atoms there in 1 mole of CO2?

1) Find Number of Molecules In the Sample

n=N/NA N=? (how many molecules are there)
N=n(NA)
N=1(6.02x1023)
N=6.02x1023 molecules



2) Find the Number of O atoms in the Sample

In each molecule there are
2
O atoms.
Therefore to find the number of O atoms:
# of molecules in sample x
2
O atoms/molecule =# of O atoms
# of O atoms=
6.02x1023 x2=1.2x1024 atoms!


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Example: Calculate the Number of Molecules of Ethyl Mercaptan


The volatile liquid ethyl mercaptan,C2H6S,{\small\text{C}_2\text{H}_6\text{S},}is one of the most odoriferous substances known. It is added to natural gas to make gas leaks detectable. (d = 0.84 g/mL; MW = 62.1 g/mol)
  1. How manyC2H6S,{\small\text{C}_2\text{H}_6\text{S},}molecules are contained in a 3.0 μL{\small \mu L} sample?
N=? V=3 uL d=0.84 g/mL M=62.1g/mol NA=6.02x1023

n=N/NA
N=n(NA)
Need to solve for moles first before we can use this equation.

n=m/M need the mass before we can solve for moles
d=m/V
m=dV
density is given in g/mL so the V needs to be in mL so the units cross out and we have a mass in g.
1uL=1x10-6L
3uL=3x10-6L
Now we need to convert into mL:
1000mL=1L
V=3x10-3mL
m=dV
m=(0.84g/mL)(3x10-3mL)
m=2.52x10-3 g

n=m/M now solve for moles
n=2.52x10-3g / 62.1 g/mol
n=4.05797x10-5 moles

Finally since we have the total moles in the sample, we can solve for the total molecules:
N=n(NA)
N=4.05797x10-5 moles (6.02x1023 molecules/mole)
N= 2.4x1019 molecules

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  1. In the same 3.0 µL sample, how many C and H atoms are there?

#C atoms=2.4×1019molecules×2 C atomsmolecules=4.8×1019 C atoms\# \text{C atoms} = 2.4\times10^{19} \text{molecules}\times\dfrac{2\text{ C atoms}}{\text{molecules}} = 4.8\times10^{19}\text{ C atoms}

#H atoms=2.4×1019molecules×6 H atomsmolecules=1.4×1020 H atoms\# \text{H atoms} = 2.4\times10^{19} \text{molecules}\times\dfrac{6\text{ H atoms}}{\text{molecules}} = 1.4\times10^{20}\text{ H atoms}

Practice: Converting Mass to Number of Atoms

Calculate the number of nitrogen atoms in 2.25 g of bismuth(III) nitrate.

Practice: Finding the Number of Moles of Iron

Calculate the number of moles of iron atoms in 14.1 g of iron oxide, Fe2O3
Extra Practice
Combustion, Stoichiometry
What mass of KClO3 is required to produce proper amount of O2 needed to achieve complete combustion of 78.88 g CH4?
2 KClO3 → 2 KCl + 3 O2
Given that the molar mass of X is 170.12 g mol-1, how many molecules of X are present in a tablet that contains 100 mg of X?
Calculate the molar mass of H2O
Chemical reactions: Limiting Reagent & Percent Yield
Iron oxidizes when exposed to oxygen to form iron oxide according to the following equation:
Fe (s) + O2 (g) ​→ Fe2​O3​ (s)
352g of pure iron is exposed to 12.0 mols of O2, and after a period of time, 46.7 g of iron oxide (rust) is collected.
Molecules: Molar mass
Calculate the number of moles of each compound:
a. 18.5 g of MgCO3
b. 2.36 g of NF3
Stoichiometry: Chemical formula
How many carbon atoms are in 10.00 mL of ethanol ( CH3CH2OH)?
The density of ethanol is 0.789 g/mL.
Practice: Finding the Number of Moles of Iron
Calculate the number of moles of Iron atoms in 14.1 g of iron oxide, Fe2O3
Introduction to General Chemistry
Answer the following questions concerning benzoic acid (C7H6O2).
a) Calculate the number of moles in a 7.50 x 10-2 g sample of benzoic acid.
b) Calculate the number of molecules of benzoic acid in the 7.50 x 10-2 g sample.
Stoichiometry: Moles, atomic mass
Acetominophen (C8H9NO2) is a common drug used to treat pain and fever. It is the main component of common trade names such as Tylenol.
a) Calculate the molar mass of acetominophen.
b) How many moles of acetominophen are there in 250.0 g of this compound?
Converting Mass to Number of Atoms
Calculate the number of nitrogen atoms in 2.25 g of bismuth(III) nitrate. (Enter your answer in scientific notation in nitrogen atoms, for example 1.23⋅10181.23\cdot10^{18})
How many grams of oxygen are in 22 mL of water? Remember that the density of water is 1.0 g/mL
How many moles of ammonia (NH3) are in 2.4g of ammonia?
Chemical formula: Moles
Which of the following quantities is not equivalent to 5 mg of sodium bicarbonate,NaHCO3?
Stoichiometry: Finding the Number of Moles of Iron
Calculate the number of moles of iron atoms in 14.1 g of iron oxide, Fe2O3
Atoms: Avogadro's Number
How many C\text{C} atoms are there in 260 g of H2CO3\text{H}_2\text{CO}_3?
Stoichiometry: Molar mass and Avogadro's Number
How many hydrogen atoms are in exactly 2 g of hydrazinium sulfate, N2H6SO4?