As a fundamental concept in chemistry, the molar mass is essential for understanding the relationships between mass, moles, and Avogadro’s number. In the following post, we’ll cover the basics, including how to find molar mass, its relationship to Avogadro’s number and moles, and how to convert mass into moles.
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What We Review
Avogadro’s Number and the Mole
Avogadro’s number is a fundamental constant that represents the number of particles (atoms, molecules, ions) in one mole of a substance. Specifically, the number is defined as 6.022 \times 10^{23} particles per mole, and it is named after the Italian scientist Amedeo Avogadro.
Avogadro’s Number
N_A = 6.022 \times 10^{23}
The Mole and its Relationship to Avogadro’s Number
A mole is a unit of measurement that is used to express the amount of a substance in chemistry. One mole of a substance contains Avogadro’s number of particles. For instance, one mole of carbon dioxide (CO_2) contains 6.022 \times 10^{23} molecules of CO_2.
Using Avogadro’s Number
You can see that by using Avogadro’s number, we can calculate the number of particles in a given number of moles of a substance. For example, let’s say we have 2 moles of carbon. We can use Avogadro’s number to determine the number of atoms in 2 moles of carbon:
2\text{ moles } C \cdot 6.022 \times 10^{23}\text{ atoms per mole} = 1.2044 \times 10^{24}\text{ atoms } C
Similarly, we can use Avogadro’s number to determine the number of molecules in a given number of moles of a substance. For example, let’s say we have 3 moles of water (H_2O). We can use Avogadro’s number to determine the number of water molecules in 3 moles of water:
3\text{ moles }H_2O \cdot 6.022 \times 10^{23}\times \text{ molecules per mole}
= 1.8066 \times 10^{24}\text{ molecules }H_2O
In summary, by using Avogadro’s number, we can convert between the number of particles in a substance and the amount of the substance in moles. This allows us to make calculations that relate the mass, volume, and number of particles of a substance, which are important concepts in chemistry.
For a more in-depth view of Avogadro’s number and the mole, check out the following TED-Ed video:
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Molar Mass
Molar mass is the mass of one mole of a substance and is expressed in grams per mole (\text{g/mol}). Chemists denote molar mass with the symbol \text{M}. It is a useful quantity in chemistry because it allows us to relate the mass of a substance to the number of particles present in it.
How to Find Molar Mass Using the Periodic Table
The molar mass of an element is equal to its atomic mass in atomic mass units (\text{amu}) converted to grams per mole. For example, the molar mass of carbon is 12.01\text{ g/mol}, which is the atomic mass of carbon (12.01\text{ amu}) converted to grams per mole.
How to Find Molar Mass of a Compound
To calculate the molar mass of a compound, we need to add up the molar masses of all the elements in the compound. For example, the molar mass of water (H_2O) can be calculated by adding up the molar masses of two hydrogen atoms and one oxygen atom. The atomic mass of hydrogen is 1.01\text{ amu}, and the atomic mass of oxygen is 16.00\text{ amu}. Therefore:
2 \times 1.01\text{ g/mol (for hydrogen)} + 1 \times 16.00\text{ g/mol (for oxygen)}
= 18.02 \text{ g/mol}
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Practice Finding Molar Mass
Example 1: Simple Compound
Let’s walk step-by-step for finding the molar mass of calcium chloride (CaCl_2):
- First, write out the chemical formula for the compound. In this case, the formula for calcium chloride is CaCl_2.
- Then, find the atomic mass of each element in the compound. You can find the atomic mass of each element on the periodic table. For calcium (Ca), the atomic mass is 40.08\text{ g/mol}. For chlorine (Cl), the atomic mass is 35.45\text{ g/mol}.
- Next, multiply the atomic mass of each element by the number of atoms of that element in the compound. In this case, there is one calcium atom (Ca) and two chlorine atoms (Cl) in calcium chloride. So, we multiply the atomic mass of calcium (40.08\text{ g/mol}) by 1, and the atomic mass of chlorine (35.45\text{ g/mol}) by 2:
- Calcium (Ca): 40.08\text{ g/mol} \times 1 = 40.08\text{ g/mol}
- Chlorine (Cl): 35.45\text{ g/mol} \times 2 = 70.90 \text{g/mol}
- Lastly, add the atomic masses of each element in the compound to get the molar mass of the compound. In this case, we add the atomic masses of calcium and chlorine to get the molar mass of calcium chloride:
Molar mass of CaCl_2 = 40.08\text{ g/mol} + 70.90\text{ g/mol} = 110.98\text{ g/mol}
So the molar mass of calcium chloride (CaCl_2) is 110.98\text{ g/mol}.
Example 2: Complex Compound
For our second example, let’s find the molar mass of glucose, which has the chemical formula C_6H_{12}O_6.
- First, write down the chemical formula of the compound.
C_6H_12O_6
- Then, look up the atomic masses of each element in the periodic table.
- Carbon (C) = 12.01\text{ g/mol}
- Hydrogen (H) = 1.01\text{ g/mol}
- Oxygen (O) = 16.00\text{ g/mol}
- Next. multiply the atomic mass of each element by the number of atoms of that element in the compound.
- 6\text{ carbon atoms} \times 12.01\text{ g/mol} = 72.06\text{ g/mol}
- 12\text{ hydrogen atoms} \times 1.01\text{ g/mol} = 12.12\text{ g/mol}
- 6\text{ oxygen atoms} \times 16.00\text{ g/mol} = 96.00\text{ g/mol}
- Lastly, add up the molar masses of each element in the compound:
72.06\text{ g/mol} + 12.12\text{ g/mol} + 96.00\text{ g/mol} = 180.18\text{ g/mol}
Therefore, the molar mass of glucose (C_6H_{12}O_6) is 180.18\text{ g/mol}.
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Converting Between Mass and Moles
How to Convert Mass into Moles
Once we have determined the molar mass of a substance, we can use it to convert a given mass of the substance into the number of moles. This can be useful for determining the amount of a substance needed for a chemical reaction, or for calculating the mass of a product formed in a reaction.
To convert mass into moles, we use the following formula:
\text{moles} = \text{mass (in grams)} /\text{molar mass}
On the other hand, we can also find the mass for a given amount of moles using:
\text{mass} = \text{moles} \times \text{molar mass}
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Example 1: Simple Compound
Let’s say we have 25\text{ grams} of sodium chloride (NaCl), and we want to convert it to moles. First, we’ll find the molar mass as follows:
- 1\text{ sodium atom} \times 22.99\text{ g/mol} = 22.99\text{ g/mol}
- 1\text{ chlorine atom} \times 35.45\text{ g/mol} = 35.45\text{ g/mol}
Adding these up gives us 58.44\text{ g/mol}.
Then we can use the formula to calculate the number of moles of sodium chloride:
\text{moles} = \dfrac{25\text{ g}}{58.44\text{ g/mol}} = 0.428\text{ moles}
Therefore, we have 0.428\text{ moles} of sodium chloride in 25\text{ grams} of sodium chloride.
Example 2: Complex Compound
In our next example, we will find the mass of 2.5\text{ moles} of calcium carbonate (CaCO_3).
First, identify the molar mass of the compound.
- Calcium has a molar mass of 40.08\text{ g/mol}
- Carbon has a molar mass of 12.01\text{ g/mol}
- Oxygen has a molar mass of 16.00\text{ g/mol}
1\text{ calcium atom} \times 40.08\text{ g/mol} + 1\text{ carbon atom} \times 12.01\text{ g/mol} + 3\text{ oxygen atoms} \times 16.00\text{ g/mol}
= 100.09\text{ g/mol}
Then, use the formula for finding mass using moles:
\text{mass} = \text{moles} \times \text{molar mass}
Next, plug in the given values and solve for mass:
\text{mass} = 2.5\text{ moles} \times 100.09\text{ g/mol} = 250.23\text{ g}
Therefore, the mass of 2.5\text{ moles} of calcium carbonate is 250.23\text{ g}.
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Example 3: Finding the Mass of a Number of Molecules
For our last example, let’s pull all of these concepts together to determine the mass of a certain number of a given molecule.
Let’s say we have 2.5 \times 10^{24} molecules of glucose (C_6H_{12}O_6). We want to find the mass of this amount of glucose.
First, find the molar mass of glucose by adding up the atomic masses of all the atoms in the molecule:
- 6\text{ carbon atoms} \times 12.01\text{ g/mol} = 72.06\text{ g/mol}
- 12\text{ hydrogen atoms} \times 1.01\text{ g/mol} = 12.12\text{ g/mol}
- 6\text{ oxygen atoms} \times 16.00\text{ g/mol} = 96.00\text{ g/mol}
Therefore the molar mass of glucose is 180.18\text{ g/mol}.
Then, use Avogadro’s number to find the number of moles of glucose:
2.5 \times 10^{24} \text{ molecules} \times (1\text{ mole}/6.022 \times 10^{23}\text{ molecules}) = 4.15\text{ moles}
Next, use the formula \text{mass} = \text{moles} \times\text{molar mass} to find the mass of 4.15\text{ moles} of glucose:
\text{mass} = 4.15\text{ moles} \times 180.18\text{ g/mol} = 748.4\text{ g}
Therefore, the mass of 2.5 \times 10^{24}\text{ molecules} of glucose is 748.4\text{ g}.
Conclusion
In conclusion, understanding molar mass is an essential concept in chemistry as it allows us to relate the amount of a substance to the number of particles present in it. We learned about Avogadro’s number and how it relates to the mole, which is a unit used to express the amount of a substance. We also learned how to calculate the molar mass of a compound using the periodic table and how to convert mass into moles. The lessons learned in this post will continue through the study of chemical reactions and equations.
