Many chemicals are stored in concentrated solutions called stock solutions for the purpose of taking up less volume. For example, hydrochloric acid may be stored in a 12 molar stock solution. For an actual experiment, you may not want 12 molar hydrochloric acid, so you may need to prepare a dilute solution from a concentrated solution. For this process, we can use the equation M1 V1 = M2 V2. If we multiply the molarity of a solution by its volume, we end up with moles of solute. What this equation is showing is that all of our moles of solute in the dilute solution must come from the concentrated solution. The process of diluting means we're adding more solvent, but we're not changing our moles of solute. This equation only works with solution dilution because our moles of solute are constant. If we wanted to create 3 liters of 0.5 molar calcium chloride from a 10 molar calcium chloride stock solution, we would calculate that we need 150 milliliters of concentrated solution to obtain the necessary 1.5 moles of calcium chloride in our dilute solution. Then we would dilute this 150 milliliters of concentrated stock solution to a total volume of 3 liters. Let's practice. We want to create 2 liters of 1.5 molar hydrochloric acid from a 12 molar stock solution. We want to know what volume of stock solution is needed and what volume of water is needed, assuming a linear addition of volumes. First, we'll calculate the volume of stock solution using the equation M1 V1 = M2 V2. We'll assign the dilute solution to M1 V1 and the concentrated stock solution to M2 V2. We're solving for the volume of concentrated stock solution. Rearranging our equation and adding our numbers, we'll need 0.25 liters of concentrated stock solution. Next, we'll calculate the volume of water we need, assuming a linear addition of volumes. To create our dilute solution, we're adding together a volume of stock solution and a volume of water. We can rearrange the equation to solve for our volume of water. We want 2 liters of dilute solution, and we're using 0.25 liters of concentrated stock solution. So, we should need to add about 1.75 liters of water.