 Serial dilutions are used to accurately make really dilute solutions and are used throughout science not just chemistry such as microbiology and medicine. So let's look at an example. As before we start with our equation m1 v1 equals m2 v2. For the first dilution m1 equals one mole v1 equals 10 moles m2 we do not know and v2 equals 20 moles because we have already added 10 moles of water to dilute it by half. Substitute in these values and you get 1 times 10 equals m2 times 20. So 10 equals 20 m2 and rearranging means m2 equals 0.5. Now on to our second dilution m1 equals 0.5 v1 equals 20 mole m2 we do not know and v2 equals 40 mole because we have already added 20 mole of water to dilute it by half again. Substitute in these values and we get 0.5 times 20 equals m2 times 40. So 10 equals 40 m2 and rearranging means m2 equals a quarter. And finally our third dilution m1 equals a quarter v1 equals 40 mole m2 we do not know v2 equals 80 mole because we have already added another 40 mole of water to dilute it again by half. And substituting in these values gives us a quarter times 40 equals m2 times 80. So 10 equals 80 m2 and rearranging gives us m2 equals a eighth which is 0.125 moles. So after three dilutions the concentration of the hydrochloric acid is 0.125 moles. See zero dilutions are just as easy as playing all dilutions. All you need to remember is that good old m1 v1 equals m2 v2. Take your time show you're working and you'll fly through dilution questions. There is just one tiny thing more to know about dilutions and that is how we label them. Let's look at colonies of bacteria for this. So we take one mole of our bacteria colony and add it to 9 mole of broth. This gives us a 1 to 10 dilution. If we then take one mole of this 1 to 10 dilution and add it to 9 mole of broth we now have a 1 to 100 dilution. And if we take one more of this 1 to 100 dilution and add it to 9 mole of broth we now have a 1 to 1000 dilution. Or even just a plain old chemistry experiment. So there you have dilutions. They are very important to many professions especially doctors. And thanks to the good old m1 v1 equals m2 v2 equation they are very simple to calculate.