Solution hints.

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:

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.