A Solution-Making Trick

   If you have a choice, the faster and more precise way of making solutions is diluting another solution (rather than weighing out solid and then dissolving in water).

   This is for when you use one solution to make another:

  1. Make sure that the stock solution is more concentrated than what you want to make.

  2. Make a fraction of the two concentrations that is less than one. (You don't have to remember this, but it means you put the stock solution's concentration on the bottom. Just remember to make a fraction that is less than one.)

  3. Multiply the volume of what you want to make by the fraction. That gives you the amount of stock solution you need to use.

EXAMPLE

   You have a stock solution of 4% sucrose, and you want to make 200 mL of 2% sucrose.

  1. Yes, the stock solution is more concentrated than what you want to make.

  2. Fraction: 2%/4% = ½ (notice that the units, the percents, cancel and vanish)

  3. Multiply: 200 mL x ½ = 100 mL

  4. Add more water up to 200 mL (q.a. 200 mL)

The logic in the rule's steps.

  1. If the stock solution's concentration were lower than you need, the only thing you could do is boil away some of its water to raise its concentration. This is not a QUICK method. The stock must be more concentrated than what you need!

  2. You must have a fraction that is less than one because were you to do it the other way around and use a fraction that was greater than one - look what'll happen in the next step where you multiply your desired total volume by the bigger-than-one fraction - you'd be using more volume of the stock than what you want to have as your final volume. Your fraction must be less than one!

ANOTHER EXAMPLE

   You have a stock solution of 4 M NaCl and you want to make 800 mL of 1 M NaCl.

  1. Yes, 4M is greater than 1 M.

  2. Fraction: 1M/4M = 1/4

  3. Multiply: 800 mL x 1/4 = 200 mL

  4. q.a. 800 mL

YET ANOTHER EXAMPLE

   You have a stock solution of 1 M NaCl, and you want to make 200 mL of 2 M NaCl.

  1. No, the stock's 1M is not more than 2 M, so STOP! We must find an alternative way, such as dissolving solid NaCl into water.

   BE PREPARED for a problem like this, which more closely imitates reality.

   You need to make 250 mL of a 1.5% solution of NaCl and you go into the stockroom and find the following bottles on the shelf: solid NaCl, 1% NaCl, 2% NaCl, 3% NaCl and 2% sucrose. Life always gives you lots of choices! What is the fastest and least error-prone method for making what you want? Answer: grab the 3% NaCl bottle because you get an easy fraction (1.5%/3% = ½). Thus

250 mL x ½ = 125 mL So you take 125 mL of the 3% and make it up to 250 mL with water, voila! you have 250 mL of 1.5% NaCl.

Sure, you could have used the 2%, but think of the fraction:
1.5%/2% (this'll slow down most people) = 3/4
250 mL x 3/4 (another slow-down where error can be easily made!)....