Disinfectant Batch Concentration and Dosing Tolerance
A building-services technician is preparing disinfectant for a 4-gallon sprayer batch. The concentrate label specifies a dilution of 1 part concentrate to 15 parts water and states that the concentrate contains 12.5% active ingredient by volume. The only measuring vessel on hand is a 12 fl oz graduated cup, and the bucket is marked in gallons (1 gal = 128 fl oz). The site health-and-safety sheet requires the working solution to stay between 7,500 ppm and 8,200 ppm of active ingredient; outside that band the solution is either ineffective or irritating to skin. The technician's dosing pump is rated to deliver the set volume with a relative error of up to 3% in either direction, and the technician rounds the concentrate measure to the nearest 0.1 fl oz using the cup's markings. Water is added up to the 4-gallon mark after the concentrate, so the total batch volume is fixed at 4 gallons regardless of small dosing errors.
1. Determine the volume of concentrate, in fluid ounces, needed for one 4-gallon batch, and express that amount in terms of cup-fills.
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Convert the batch volume first. 4 gal × 128 fl oz/gal = 512 fl oz of finished solution.
Apply the ratio. A 1:15 dilution means 1 part concentrate to 15 parts water, so the batch is 16 equal parts: 1 part concentrate + 15 parts water. Concentrate = 512 ÷ 16 = 32 fl oz; water = 512 − 32 = 480 fl oz (15 × 32, consistent).
Convert to cup-fills. 32 ÷ 12 = 2.667, so the technician fills the 12 fl oz cup twice (24 fl oz) and then measures 8.0 fl oz in the same cup, using the graduations to hit 32.0 fl oz.
Common error to avoid: dividing 512 by 15 instead of 16. That gives 34.1 fl oz and a solution that is about 6% too strong, which matters at the upper ppm limit.
2. Compute the active-ingredient concentration of the working solution in ppm and decide whether it meets the specification.
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Active ingredient in the concentrate dose: 32 fl oz × 0.125 = 4.00 fl oz of active ingredient.
Concentration in the batch (volumes treated as additive, which the label's mixing instructions assume): 4.00 ÷ 512 = 0.0078125 as a volume fraction.
Convert to ppm: 0.0078125 × 1,000,000 = 7,812.5 ppm.
Compare with the band 7,500–8,200 ppm: 7,812.5 sits inside the band, about 312 ppm above the floor and 387 ppm below the ceiling.
Sanity check via the alternative route: the concentrate is 125,000 ppm active; diluting by a factor of 16 gives 125,000 ÷ 16 = 7,812.5 ppm. Both routes agree, so the batch as specified is compliant.
3. Using the pump's ±3% relative error, test whether every batch stays inside the 7,500–8,200 ppm band. State the margin to each limit in terms of concentrate volume.
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Worst cases on the concentrate volume (water volume fixed at 512 fl oz total):
- High: 32 × 1.03 = 32.96 fl oz → active = 32.96 × 0.125 = 4.12 fl oz → 4.12 ÷ 512 × 1,000,000 = 8,047 ppm. Below 8,200 ✓
- Low: 32 × 0.97 = 31.04 fl oz → active = 3.88 fl oz → 3.88 ÷ 512 × 1,000,000 = 7,578 ppm. Above 7,500 ✓
So the ±3% pump is acceptable - but the margins are asymmetric. Find the concentrate volumes that would exactly hit each limit:
- Ceiling: 8,200 ppm needs 8,200 ÷ 1,000,000 × 512 ÷ 0.125 = 33.59 fl oz, i.e. +4.97% over 32 fl oz.
- Floor: 7,500 ppm needs 7,500 ÷ 1,000,000 × 512 ÷ 0.125 = 30.72 fl oz, i.e. −4.00%.
Judgement: the pump has roughly 1 percentage point of headroom on the low side and 2 points on the high side. Any recalibration drift beyond about 4% under-dosing silently produces a sub-potency batch that still looks and smells correct, so the technician should verify pump output by weight at the start of each shift rather than rely on the label setting alone.