Mole Conversions

Definitions & Key takeaways

Moles are a type of unit conversion used in chemistry to measure the amount of substances. One mole is equal to 6.022 x 10^23 atoms, molecules or other particles. By converting from moles to grams, liters, and other units, chemists can calculate the mass or volume of a given substance. This is especially useful when dealing with solutions and chemical reactions. Mole conversions are an important part of understanding and working with chemistry, so it's important to become familiar with them.

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Moles are a counting unit that make it easier for chemists to work with large numbers. Just as we say that one dozen eggs is equal to 12 eggs.
We can say that one mole of atoms is equal to 6.02 times 10 to the 23rd atoms, 6.02 times 10 to the 23rd is called Avogadro's number.
An essential skill in chemistry is being able to convert between mass moles and number of atoms. Suppose we start with two moles of helium and we want to figure out how many grams of helium we have to convert between grams and moles.
We need to use the molar mass. The molar mass is the mass of one mole of an element and is found on the periodic table.
If we look this number up for helium, we find that helium has a molar mass of 4.0 g per mole. So one mole of helium has a mass of 4.0 g.
We can use the molar mass as a conversion factor. Two moles of helium times 4 g of helium per mole of helium is equal to 8 g of helium.
Notice how moles of helium cancels out. Let's consider a related problem in which we're given 8.0 g of helium.
And we wanna calculate the number of moles of helium. For this problem, we wanna divide by the molar mass.
So 8.0 g of helium divided by 4.0 g per mole gives us 2.0 moles of helium. Notice how the grams cancel out to give us moles as our unit.
We can also do this problem by multiplying with one over the molar mass, which gives us 8.0 g of helium times one mole of helium per 4.0 g of helium.
Once again, grams cancel out to give moles. So the answer is 2.0 moles of helium.
So to recap to convert moles to grams, we multiplied by the molar mass to convert grams to moles. We divided by the molar mass.
Here's a table to help us keep track of how to do the different conversions. We can also use the number of moles to calculate the number of atoms that are present.
For example, let's say we have 0.500 moles of silver. And we wanna know how many atoms of silver we have.
Once again, we need a conversion factor from Avogadro's number. We know that one mole of silver atoms is equal to 6.0 two times 10 to the 23rd silver atoms.
So if we multiply 0.500 moles of silver by the conversion factor of 6.02 times 10 to the 23rd atoms of silver per one mole of silver moles of silver cancel.
And we get 3.01 times 10 to the 23rd atoms of silver. Now, let's consider a related problem.
We start with a known number of atoms and we wanna find out how many moles we have. For example, let's say we start out with 3.01 times 10 to the 23rd atoms of silver.
This time we need to divide by Avogadro's number 3.01 times 10 to the 23rd atoms of silver divided by 6.02 times 10 to the 23rd atoms of silver per mole of silver gives 0.500 moles of silver.
Notice how the atoms of silver cancel out to give moles of silver as our units. So to convert moles to atoms, we multiply by Avogadro's number to convert atoms to moles, we divide by Avogadro's number.
If we add conversions using Avogadro's number to our table, we now have a way of converting between grams, moles and atoms.
Now, our table isn't limited to only atoms. For example, we could also use the table to find the number of molecules in a sample of methane gas.
Methane has the chemical formula CH four, let's say we have 48.0 g of methane. And our goal is to figure out how many molecules of methane we have.
Since we're starting with the mass. Our first step is to convert this amount to moles.
Our next step will then be to convert moles to molecules. We start by going from mass to moles.
Looking at our conversion table, we can see that we need to divide by the molar mass of methane. Looking at the periodic table, the molar mass of carbon is 12.0 and the molar mass of hydrogen is 1.0.
Since methane has the chemical formula ch four, the molar mass of methane is four times one plus one times 12, which adds up to a total molar mass of 16.0 g per mole, dividing 48.0 GMS by 16.0 g per mole gives us 3.00 moles of methane.
Now that we have moles, we need to find the number of molecules. We look again at our chart and we see that to convert moles to molecules, we need to multiply by Avogadro's number multiplying 3.00 moles by 6.02 times 10 to the 23rd gives 1.81 times 10 to the 24th molecules of methane.
Now let's do an example with an ionic compound. Suppose we have 1 44.5 g of zinc nitrate.
And our goal is to figure out how many moles we have, we look at our table which says that going from mass to moles requires dividing by the molar mass.
That means we need to find the molar mass of zinc nitrate. Looking at the chemical formula for zinc nitrate, we know that for every zinc, there are two nitrogens and six oxygens.
The molar mass of zinc is 65.4 g per mole. The molar mass of nitrogen is 14.0 g per mole, which we have to multiply by two.
The molar mass of oxygen is 16.0 which we need to multiply by six. Adding up these numbers gives a molar mass of 1 89.4 g per mole.
For zinc nitrate, we started out with 1 44.5 g of zinc nitrate. We divide this number by the molar mass of 1 89.4 g per mole.
The grams cancel out and we find that we have 0.7629 moles of zinc nitrate. All right.
As a quick recap, moles can be used to convert between grams and number of particles to convert between grams and moles.
We use the molar mass as a conversion factor to convert between moles and number of particles. We use Avogadro's number as a conversion factor.