Another Solution-Making Trick

    In the previous trick, you needed to find out how much of a starting solution you need to use to get to the one you wanted to make up. In this page, you will see a very similar trick used to determine either the starting concentration or the finished concentration.

    As before, this is for when you use one solution to make another:

  1. Make sure that the stock solution is less in volume than the final solution.

  2. For determining the final concentration: Make a fraction of the two volumes that is less than one and multiply that by the starting concentration. Doesn't this comply with the rule learned earlier that the final concentration must be less than the starting one?

  3. For determining the starting concentration, flip the former fraction upside down to make a fraction that is larger than one. Multiply that times the final concentration. Again, that'll make the starter more concentrated than the final.

EXAMPLES

    You have used 100 mL of a stock solution of 4 % sucrose, and you have made 200 mL of unknown % sucrose. What is the final concentration.

  1. Yes, the stock solution is less in volume than what you want to make.

  2. Fraction: 100 mL/200 mL = ½ (notice that the units, the milliliters, cancel and vanish).

  3. Multiply: 4% x ½ = 2%

    For a second example: You have used 100 mL of a starting solution of unknown concentration, and you have made 200 mL of 2% sucrose. What was the concentration of the starting solution?

  1. Yes, the stock solution is less in volume than what you made
  2. Since the starter must be more concentrated than the final, your fraction must be greater than one. Thus 200 mL/100 mL = 2.
  3. 2 x 2% = 4%, which is the starter concentration.

    GOLDEN RULE: Remember that concentrations and volumes are like on a seesaw - when one is high, the other is low. In the case of starting solutions, the concentration must be high and volume low COMPARED WITH those values of the final solution.