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# How can molarity be used as a conversion factor?

A conversion factor is a fraction that represents the relationship between two different units. A conversion factor is ALWAYS equal to 1.

is an example of a conversion factor. For example, if the molarity is 0.5 mol/L, the conversion factor is either

##"0.5 mol"/"1 L"## or ##"1 L"/"0.5 mol"##

You can use whichever one gives you the correct units for the answer, because each conversion factor equals 1.

**Molarity can be used as a conversion factor because it provides the number of moles of dissolved in in the volume (liters) of solution.**

**Example 1: Volume of solution to moles of solute**

How many moles of NaCl would you need to prepare 400 mL of a 1.20 mol/L solution of sodium chloride?

**Solution 1**

0.400 L × ##"1.20 mol NaCl"/"1 L"## = 0.480 mol NaCl

Notice that we use the conversion factor with "L" on the bottom. This makes the units cancel and gives an answer with the units of "mol NaCl".

**Example 2: Moles of solute to volume of solution**

What is the volume of a 3.0 mol/L NaCl solution that contains 6.0 mol of NaCl?

**Solution 2**

6.0 mol NaCl × ##"1 L"/"3.0 mol NaCl"## = 2.0 L

Here we use the conversion factor with "mol NaCl" on the bottom. This makes the units cancel and gives an answer with the units of "L".

**Example 3**

How many moles of NaCl are dissolved in 0.5L of 2M NaCl?**

**Solution 3**

Note: ##2M NaCl = (2 mol NaCl) / (1 L solution)##

##0.5 L (( 2 mol NaCl) / (1 L so\l\n) ) = 1 mo\l\e NaCl##