Unit 5: Percent Strength of Solutions

The strength of solutions is an important application of percents. A solution is a liquid that has had medication, minerals or other products dissolve in it. Percent strength refers to how much of a substance has been dissolved in a specific amount of liquid.

The key to percent strength is your knowledge of part-to-whole relationships: A percent is x parts to 100 total parts. Solution refers to a two-part substance: a solute that is the drug, mineral or product and a solvent or liquid that can be a variety of things depending on the medical application. Solutes will occur either as a dry drug measured in grams or as a liquid measured in milliliters. The total volume of the liquid is always in milliliters.

Example part 1:

A 15% drug solution has 15 parts of a drug to 100 parts solution. There are 15 grams of drug to 100 milliliters of solution. As a ratio, this would be shown as 15:100, or 2:20 in the reduced form.

Sometimes the solution will be given as a ratio rather than a percent. To express the solution strength as a percent, set up the problem as a proportion with 100 mL of the total solution. Remember that percent is always part of 100.

For example,

4% solution = 4 : 100 = 1 :25 = 1 gram of pure drug to 25 milliliters of solution

10% solution = 10 :100 = 1:10 = 1 gram of pure drug to 10 milliliters of solution

5% solution = 5 : 100 = 1 : 20 = 1 gram of pure drug to 20 milliliters of solution

Example part 2:

Percent strength 8% means that there are 8g of drug to 100 mL of solution. If the doctor orders 25 mL of an 8% solution, then a proportion may be used to ensure that the ratio of pure drug to solution represents 8%.

8g of drugs : 100 mL solution = x g of drug : 25 mL solution

After setting the proportion up, multiply the means and extremes to solve for x.

100x = 200

Divide both sides by 100 to get x alone.   200 divided by 100 = 2

x = 2g of drug

So, to make a 25 mL of an 8% solution using this ratio of pure drug to solution, 2g of pure drug to 25 mL of solution are required. This keeps the percent strength of the medication consistent with the doctor's order for an 8% strength solution. Note that the amount of mixed solution changes, not the percent strength itself.

Example part 3:

Ten grams of drug are in 25 mL of solution. What is the percent strength of this medication?

To convert this ratio to a percent, write it as a proportion and then solve for x.

10g : 25 mL :: x g : 100 mL

Multiply the means and the extremes to get 25x = 1,000

Divide both sides to get x alone. 1,000 divided by 25 = 40, so the answer is 40% strength.

Complete the following practice problems:

1) The doctor has ordered a 5% saline solution to be prepared. How many grams of pure drug will be needed to make each of these amounts of solution at 5% strength?

a) 25 mL of solution                          c) 65 mL of solution

b) 35 mL of solution                          d) 125 mL of solution

 

2) Nine milligrams of pure drug are in 100 mL of solution.

a) What is the percent strength of the solution?

b) How many milligrams of drug are in 75 mL of that solution?

 

3) 15 grams of pure drug are in 50 mL.

a) What is the percent strength of the solution?

b) How many grams of pure drug are in 200 mL of the solution?

 

4) A 12% strength solution has been prepared.

a) How many grams of medication is in the 12% strength solution?

b) How many milliliters of solution are in this 12% strength solution?

c) Express this solution as a simplified ratio.

d) How much pure drug is needed to create 35.5 mL of this solution? Round to the nearest tenth. Your answer will be in grams.

e) How much pure drug is needed to create 80 mL of this solution? Your answer will be in grams.

f) If you have 60 mL of solution, how many grams of pure drug will you have in order to keep the 12%? Round to the nearest tenth. Your answer will be in grams.

 

5) A 0.09% strength solution has been prepared.

a) How many grams of medication is in the 0.09% strength solution?

b) How many milliliters of solution are in this 0.09% strength solution?

c) Express this solution as a simplified ratio.

d) How much pure drug is needed to create 54 mL of this solution? Round to the nearest hundredth. Your answer will be in grams.

e) How much pure drug is needed to create 24 mL of this solution? Round to the nearest hundredth. Your answer will be in grams.

f) If you have 50 mL of solution, how many grams of pure drug will you have in order to keep the 0.09% solution? Round to the nearest hundredth. Your answer will be in grams.

 

6) A 78% strength solution has been prepared.

a) How many grams of medication is in the 78% strength solution?

b) How many milliliters of solution are in this 78% strength solution?

c) Express this solution as a simplified ratio.

d) How much pure drug is needed to create 65.5 mL of this solution? Round to the nearest tenth. Your answer will be in grams.

e) How much pure drug is needed to create 90 mL of this solution? Round to the nearest tenth. Your answer will be in grams.

f) If you have 450 mL of solution, how many grams of pure drug will you have in order to keep the 78%? Your answer will be in grams.

 

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