# How can molarity be used as a conversion factor?

Jun 15, 2014

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

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

$\text{0.5 mol"/"1 L}$ or $\text{1 L"/"0.5 mol}$

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 solute 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 × $\text{1.20 mol NaCl"/"1 L}$ = 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 × $\text{1 L"/"3.0 mol NaCl}$ = 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: $2 M N a C l = \frac{2 m o l N a C l}{1 L s o l u t i o n}$

$0.5 L \left(\frac{2 m o l N a C l}{1 L s o \setminus l \setminus n}\right) = 1 m o \setminus l \setminus e N a C l$