Often in this course, you will be given a concentrated stock solution and you will need to dilute it to the desired working concentration. Fortunately, this is easy! Just follow the equation:
where C represent concentration and V represents volume. The subscript 1 refers to the starting solution (what you are given) and subscript 2 refers to what you need to make.
For example, suppose you are given a 1 M sucrose solution (this is C1), and you need to make a 50 mM (0.050 M) solution (this is C2). You will first need to decide how much of the final solution you need (this is V2). Suppose we want to make 10 milliliters (ml) of the working solution. The equation becomes:
1M * (V1) = 0.050M * (10ml)
Solving for V1, we see that we need 0.5 ml of 1M sucrose to make 10 ml of a 50mM solution. The remainder of the solution (10 ml - 0.5 ml = 9.5 ml) should be deionized water.
Important: Keep the units consistent. Notice that we put in a volume in ml, this means that the volume we calculate is also in ml. Notice also that we converted mM to M so that concentrations on both sides of the equation were in M.