A farm product contains a 12.5% w/v concentrate of tiamulin hydrogen fumarate, used to treat swine dysentery when diluted as a medicated drinking water.

Question

Altering Strength, Stock Solutions, and Alligation Calculations

How many gallons of medicated water may be prepared from a liter of concentrate if

the final product is to contain 227 mg of tiamulin hydrogen fumarate per gallon?

Answer 1

Let me abbreviate tiamulin hydrogen fumarate as THF

12.5% w/v means 12.5 g THF per 100 mls of solution.

We want 227 mg of THF per gallon of solution.

We need to make a few conversions to find how many gallons of THF can be made.

Conversion factors:

1000 ml = 1 L

3.785 L = 1 gallon (gal)

What we have:

12.5 g TFH / 100 ml = 125 g / L x 3.785 L / 1 gal = 33.0 g / gal = 33,000 mg / gal

H₂O as diluent = 0 mg THF / gal

What we want:

227 mg / gal

We can use V1C1 = V2C2 to find V2

V1 = 1 L x 1 gal / 3.785 L = 0.264 gal

C1 = 33,000 mg / gal

V2 = ? gal

C2 = 227 mg / gal

(0.264 gal)(33,000 mg/gal) = (V2)(227 mg/gal)

V2 = 38.38 gallons = 38.4 gallons can be prepared

or

Using alligation:

Have.........Need........Parts

0..............................32,773

................227...................

33,000......................227

So, 227 parts would = 1 liter and 32,773 parts would = 144.4 L = ~ 38.2 gallons