ppm-to-weight conversion

Problem set: 6 worked problems

Each problem is original, authored from the underlying non-copyrightable relationship, with the full worked solution and the exact slip that produces each wrong answer. Work the problem before opening the solution. For a timed, randomized run with a per-topic score, use the free knowledge practice test.

Watch for This is the pure-weight core of every dose. Two constants collide here: 8.34 (pounds per gallon of water) and 7.48 (gallons per cubic foot). Using 7.48 in a weight problem is the signature error. The result is the PURE weight, before any product-purity adjustment.

1. How many pounds of a pure chemical raise 50,000 gallons by 10 ppm?

   • A 3.74 lb
   • B 41.7 lb
   • C 0.42 lb
   • D 4.17 lb
   Show the worked solution

   Correct answer: D. 4.17 lb

   Pounds = 50,000 x 10 x 8.34 / 1,000,000 = 4,170,000 / 1,000,000 = 4.17 lb. Using 7.48 (gallons per cubic foot) instead of 8.34 gives 3.74 lb, a volume conversion misused as a weight; a lost zero in the million gives 41.7.

   Source: Public relationship: pure lb = gallons x ppm x 8.34 / 1,000,000 (8.34 lb per gallon of water)

2. How many pounds of a pure chemical raise 20,000 gallons by 5 ppm?

   • A 8.34 lb
   • B 83.4 lb
   • C 0.75 lb
   • D 0.83 lb
   Show the worked solution

   Correct answer: D. 0.83 lb

   Pounds = 20,000 x 5 x 8.34 / 1,000,000 = 834,000 / 1,000,000 = 0.83 lb. Using 7.48 gives 0.75 lb; misplacing the decimal on the million gives 8.34 or 83.4.

   Source: Public relationship: pure lb = gallons x ppm x 8.34 / 1,000,000

3. How many pounds of a pure chemical raise 100,000 gallons by 1 ppm?

   • A 0.083 lb
   • B 83 lb
   • C 8.34 lb
   • D 0.83 lb
   Show the worked solution

   Correct answer: D. 0.83 lb

   Pounds = 100,000 x 1 x 8.34 / 1,000,000 = 834,000 / 1,000,000 = 0.83 lb. This is a useful benchmark: it takes about 0.83 lb of pure chemical to move 100,000 gallons by 1 ppm, so scale it up or down from there.

   Source: Public relationship: pure lb = gallons x ppm x 8.34 / 1,000,000

4. How many ounces of a pure chemical raise 40,000 gallons by 2 ppm?

   • A About 6.7 oz
   • B About 21 oz
   • C About 1.3 oz
   • D About 10.7 oz
   Show the worked solution

   Correct answer: D. About 10.7 oz

   Pounds = 40,000 x 2 x 8.34 / 1,000,000 = 0.667 lb. Convert to ounces with 16: 0.667 x 16 = 10.7 oz. Using 10 instead of 16 gives 6.7 oz, the base-10 habit that ruins ounce answers.

   Source: Public relationship: pure lb = gallons x ppm x 8.34 / 1,000,000; 16 oz per lb

5. How many pounds of cyanuric acid (a product measured at full strength) raise 60,000 gallons by 30 ppm?

   • A 1.5 lb
   • B 150 lb
   • C 13.5 lb
   • D 15.0 lb
   Show the worked solution

   Correct answer: D. 15.0 lb

   Pounds = 60,000 x 30 x 8.34 / 1,000,000 = 15,012,000 / 1,000,000 = 15.0 lb. Cyanuric acid is added at full strength (product factor 1.0), so the pure weight is also the product weight here. Using 7.48 gives 13.5 lb.

   Source: Public relationship: pure lb = gallons x ppm x 8.34 / 1,000,000; cyanuric acid factor 1.0

6. In the ppm-to-weight formula, what does the number 8.34 represent?

   • A The number of gallons in one cubic foot
   • B The number of ounces in one pound
   • C Parts per million per gallon
   • D The weight in pounds of one US gallon of water
   Show the worked solution

   Correct answer: D. The weight in pounds of one US gallon of water

   8.34 is the weight of one US gallon of water in pounds, which is why it converts a volume of water into a weight of dissolved chemical. The gallons-per-cubic-foot conversion is 7.48, and pounds-to-ounces is 16; mixing them up is the most common dosing error.

   Source: Fixed physical constant: one US gallon of water weighs about 8.34 pounds