The symbol #"M"# represents molarity, which is #"moles of solute"/"liters of solution"#.

A #"0.10 M"# solution is said to be #0.10# molar.

When diluting a solution, use the following equation:

#M_1V_2=M_2V_2#

where #M_1# and #M_2# are the initial and final molarity, and #V_1# and #V_2# are the initial and final volume.

When calculating dilutions involving molarity, the volume must be in liters, so #"100 mL"# will be converted into liters.

**Organize your data:**

**Known**

#M_1="40 M"#

#M_2="2 M"#

#V_2=100 color(red)cancel(color(black)("mL"))xx(1"L")/(1000color(red)cancel(color(black)("mL")))="0.1 L"#

**Unknown**

#V_1#

**Solution**

Rearrange the equation to isolate #V_1#. Insert your data into the equation and solve.

#V_1=(M_2V_2)/M_1#

#V_1=(2color(red)cancel(color(black)("M"))xx0.1"L")/(40color(red)cancel(color(black)("M")))="0.005 L"# or #"5 mL"#