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These types of problems usually start with a stock solution of a particular concentration and you need to dilute it to a particular volume to make a new, more dilute solution. The key equation here is:
M1V1 = M2V2
Remember that number of moles you are working with is constant whether in the stock solution or in the more dilute new solution. Since molarity times volume equals moles, that it what the equation above is talking about. M1V1 is the molarity (moles per liter) times the volume of the stock solution and M2V2 is the molarity times the volume of the new solution. So you are usually given three of the variables in the problem and you simply plug them in and solve for the missing fourth variable.
In terms of actual laboratory practice to make a new solution from a stock solution, first you calculate how many milliliters of the stock solution that you need to make the new solution. Then measure out the required number of mL's of the stock solution in a graduated cylinder and pour into into a new flask. Then add fresh water (or whatever solvent you are working with) to the flask until the level reaches the required number of mL's of the new solution. Then stir the solution to mix evenly. Now you have a new, more dilute solution of a know concentration.
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