# 4.3: Mole-Mass Conversions

As described in the previous section, molar mass is expressed as “grams per mole”. The word per in this context implies a mathematical relationship between grams and mole. Think of this as a ratio. The fact that a per relationship, ratio, exists between grams and moles implies that you can use dimensional analysis to interconvert between the two. For example, if we wanted to know the mass of 0.50 mole of molecular hydrogen (H2) we could set up the following equations:

The known molar mass of H2 is:

$\left ( \frac{2.06g\: H_{2}}{1\: mol\: H_{2}} \right )$

We are given that we have 0.50 moles of H2 and we want to find the number of grams of H2 that this represents. To perform the dimensional analysis, we arrange the known and the given so that the units cancel, leaving only the units of the item we want to find.

$(0.5mol\: H_{2})\times \left ( \frac{2.06g\: H_{2}}{1\: mol\: H_{2}} \right )=x\, g\: H_{2}=1.0g\: H_{2}$

Exercise $$\PageIndex{1}$$

1. Determine the mass of 0.752 mol of H2 gas.
2. How many moles of molecular hydrogen are present in 6.022 grams of H2?
3. If you have 22.414 grams of Cl2, how many moles of molecular chlorine do you have?

We can also use what is often called a per relationship (really just a ratio) to convert between number of moles and the number to things (as in 6.02 x 1023 things per mole). For example, if we wanted to know how many molecules of H2 are there in 3.42 moles of H2 gas we could set up the following equations:

The known ratio of molecules per mole is :

$\left ( \frac{6.02\times 10^{23}molecules\: H_{2}}{1\: mol\: H_{2}} \right )$

We are given that we have 3.42 moles of H2 and we want to find the number of molecules of H2 that this represents. To perform the dimensional analysis, we arrange the known and the given so that the units cancel, leaving only the units of the item we want to find.

$(3.42mol\: H_{2})\times \left ( \frac{6.02\times 10^{23}molecules\: H_{2}}{1\: mol\: H_{2}} \right )=x\: molecules\: H_{2}=2.06\times 10^{24}\: molecules\: H_{2}$

And finally, we can combine these two operations and use the per relationships to convert between mass and the number of atoms or molecules. For example, if we wanted to know how many molecules of H2 are there in 6.022 grams of H2 gas we could set up the following series of equations:

The known molar mass of H2 is

$\left ( \frac{2.016gH_{2}}{1molH_{2}} \right )$

The known ratio of molecules per mole is ${\displaystyle \left({\frac {6.{\text{02 }}\times {\text{ 10}}^{\text{23}}{\text{ }}molecules{\text{ H}}_{\text{2}}}{1{\text{ }}mol{\text{ H}}_{\text{2}}}}\right)}$

$\left ( \frac{6.02\times 10^{23}molecules\: H_{2}}{1\: mol\: H_{2}} \right )$

We are given that we have 6.022 grams of H2 and we want to find the number of molecules of H2 that this represents. As always, to perform the dimensional analysis, we arrange the known ratios and the given so that the units cancel, leaving only the units of the item we want to find.

$(6.022gH_{2})\times \left ( \frac{1molH_{2}}{2.016gH_{2}}\right )\times \left ( \frac{6.02\times 10^{23}molecules\: H_{2}}{1\: mol\: H_{2}} \right )=x\; molecules\; H_{2}=1.80\times 10^{24}$

Exercise $$\PageIndex{1}$$

1. A sample of molecular chlorine is found to contain 1.0 x 1020 molecules of Cl2. What is the mass (in grams) of this sample?
2. How many moles of sand, silicon dioxide (SiO2), and how many molecules of sand are found in 1.00 pound (454g) of sand?
3. You add 2.64 x 1023 molecules of sodium hydroxide (Drano™; NaOH), to your drain. How many moles are this and how many grams?

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