Often, scientists and lab technicians express the concentration of a diluted solution in terms of a ratio to the original -- a 1:10 ratio, for example, meaning that the final solution has been diluted tenfold. Don't let this frighten you; it's just a different form of a simple equation. You, too, can calculate ratios between solutions. Here's how to set about solving these kinds of problems.

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Determine what information you have and what you need to find. You might have a solution of known starting concentration and be asked to dilute it by some set ratio -- 1:10, for example. Or you might have the concentration of two solutions and need to determine the ratio between them.

If you have a ratio, convert it into a fraction. 1:10 becomes 1/10, for example, while 1:5 becomes 1/5. Multiply this ratio by the original concentration to determine concentration of the final solution. If the original solution has 0.1 mole per liter and the ratio is 1:5, for example, the final concentration is (1/5)(0.1) = 0.02 moles per liter.

Use the fraction to determine how much of the original solution should be added to a given volume when diluting.

Let's say, for example, that you have a 1 molar solution and need to do a 1:5 dilution to prepare a 40 mL solution. Once you convert the ratio to a fraction (1/5) and multiply it by the final volume, you have the following:

(1/5)(40 mL) = 8 mL

meaning you need 8 mL of the original 1 molar solution for this dilution.

If you need to find the ratio of concentration between two solutions, just turn it into a fraction by placing the original solution in the denominator and the dilute solution in the numerator.

Example: You have a 5 molar solution and a diluted 0.1 molar solution. What is the ratio between these two?

Answer: (0.1 molar) / (5 molar) is the fractional form.

Next, multiply or divide both numerator and denominator of the fraction by the smallest number that will convert them to a whole-number ratio. The whole goal here is to get rid of any decimal places in numerator or denominator.

Example: (0.1 / 5) can be multiplied by 10/10. Since any number over itself is just another form of 1, you are merely multiplying by 1, so this is mathematically acceptable.

(10/10)(0.1 / 5) = 1/50

If the fraction had been 10 / 500, on the other hand, you could have divided both numerator and denominator by 10 -- essentially dividing by 10 over 10 -- to reduce to 1 / 50.

Change the fraction back into a ratio.

Example: 1/50 converts back to 1 : 50.

#### Things You'll Need

#### References

- "Biochemical Techniques, Laboratory Manual"; Aaron Coleman, Meredith Gould and Jose Luis Stephano; 2010
- Miramar College: Dilutions

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