Water operator math tutorial
Percent Strength of a Solution
Find pounds of chemical in a tank of solution from its volume and percent strength.
A one percent solution holds 10,000 mg/L of chemical. Percent strength questions ask how many pounds of actual chemical you have in a given volume.
Convert the percent to a decimal, then multiply by the weight of the water, using 8.34 lb/gal.
The formula
lb chemical = volume (gal) × 8.34 lb/gal × (percent strength ÷ 100)
| Variable | Unit |
|---|---|
| Solution volume | gal |
| Percent strength | % |
| Result: Chemical | lb |
Conversion factors used: 8.34 lb per gallon of water; 1% = 10,000 mg/L.
Applies to: Water Treatment, Water Distribution, Wastewater Treatment.
Common exam tip: Percent to decimal means divide by 100. 12.5% is 0.125.
Calculator
Chemical
521.25 lb
- 1. 12.5% ÷ 100 = 0.125
- 2. 500 gal × 8.34 × 0.125 = 521.25 lb
For instructional use. Results assume the standard conversion factors shown on this page. Actual field calculations may need chemical strength, density, temperature, and other adjustments, so check your plant’s procedures.
Worked examples
Example 1
500 gal of a 12.5% solution.
- 12.5% ÷ 100 = 0.125
- 500 gal × 8.34 × 0.125 = 521.25 lb
Answer: 521.25 lb
Example 2
200 gal of a 5% solution.
- 5% ÷ 100 = 0.05
- 200 gal × 8.34 × 0.05 = 83.4 lb
Answer: 83.4 lb
Common mistakes
Wrong result: 52,125 lb
not converting the percent to a decimal
Wrong result: 62.5 lb
leaving out the 8.34 lb/gal
Practice questions
1. 1,000 gal of a 10% solution. Pounds of chemical?
- A83,400 lb
- B100 lb
- C8,340 lb
- D834 lb
Show answer and explanation
Correct answer: D. 10% ÷ 100 = 0.1 1,000 gal × 8.34 × 0.1 = 834 lb Answer: 834 lb. A common slip is not converting the percent to a decimal, which gives 83,400 lb.
2. 350 gal of a 15% solution. Pounds of chemical?
- A437.85 lb
- B43,785 lb
- C52.5 lb
- D4,378.5 lb
Show answer and explanation
Correct answer: A. 15% ÷ 100 = 0.15 350 gal × 8.34 × 0.15 = 437.85 lb Answer: 437.85 lb. A common slip is not converting the percent to a decimal, which gives 43,785 lb.
3. 120 gal of a 25% solution. Pounds of chemical?
- A25,020 lb
- B250.2 lb
- C30 lb
- D2,502 lb
Show answer and explanation
Correct answer: B. 25% ÷ 100 = 0.25 120 gal × 8.34 × 0.25 = 250.2 lb Answer: 250.2 lb. A common slip is not converting the percent to a decimal, which gives 25,020 lb.
Where this formula applies
This calculation can appear in the disciplines below. Exact exam coverage depends on your state, certification level, and official exam outline.
Water Treatment
Water Distribution
Wastewater Treatment
Study guides
Keep going with the full guide
Water Operator Math Made Simple walks through operator math step by step and includes printable references plus a full practice exam.
Water Operator Math Made Simple
A Step-by-Step Guide to the Math Every Water Operator Needs to Know