Dilution of solids
Pharmacy personnel will often go to a stock solution to obtain the amount of active ingredient that is needed to make a preparation. This is especially true if the amount required is so small that it cannot be accurately weighed on a torsion balance.
It is easier to measure an amount of stock solution than to set up a balance, weigh the ingredients, and compound the entire product. The use of stock preparations is an important aspect of pharmacy.
2-8. FORMULAS: In order for these formulas to work:
a. Volumes and weights must be expressed in the same units.
b. Concentrations must be expressed in the same units.
c. Formula: V C = V1 C1
(1) V = Volume of stock preparation
(2) C = Concentration of stock preparation
(3) V1 = Volume of desired preparation
(4) C1 = Concentration of desired preparation
d. Formula: W C = W1 C1
(1) W = Weight of stock preparation
(2) C = Concentration of stock preparation
(3) W1 = Weight of desired preparation
(4) C1 = Concentration of desired preparation
EXAMPLE PROBLEMS
a. How many milliliters of a 2% stock solution of potassium permanganate
(KMn04) would be needed to compound the following prescription?
USE THESE STEPS:
Step 1: Write the formula.
V C = V1 C1
Step 2: Substitute values.
(X) (2%) = (120 ml) (.02%)
Step 3: Check units.
(a) Units of concentration are both percent.
(b) X will have the same units as the volume on the other side of the equal sign. In this case "milliliters."
Step 4: Solve for X.
2 X = 2.4
X = 1.2 ml (answer)
NOTE: To compound the prescription: Obtain 1.2 milliliters of the 2% stock
solution of potassium permanganate, place it in a graduate, and "q.s." to 120
ml with distilled water.
b. How many grams of 14% zinc oxide ointment can be made from one pound
of 20% zinc oxide ointment?
USE THESE STEPS:
Step 1: W C = W1 C1
Step 2 & 3: (X) (14%) = (454 g) (20%)
Step 4: 14 X = 9080 X = 648.57142 grams (answer) (can be rounded to 648.57 grams)
NOTE: The one lb was changed to 454 grams because the answer is to be grams
c. How many milliliters of 10% povidone-iodine (Betadine??) solution would be
needed to make 4 liters of a 1:2000 Betadine??solution?
USE THESE STEPS:
Step 1: V C = V1 C1
Step 2: (X) (10%) = (4 L) ( 1 ) 2000
Step 3: (a) Change 4 liters to milliliters
(b) Change 10% to a ratio by placing the 10 over 100.
(X) (10) = (4000 ml) ( 1 ) 100 2000
NOTE: At this point, use the rule of mathematics that states that if both sides of the equal sign are multiplied by the same number, the sides will still be equal. The easiest way to simplify an equation having ratios on both sides of the equal
sign is to multiply both sides of the equal sign by the larger denominator. In
this case the larger denominator is 2000; therefore, multiply both sides by 2000.
(X) (20,000) = (4000 ml) (2000)
100 2000
*200 X = 4000 ml
X = 20 ml
*When zeros trail whole numbers on both sides of the equal sign, an equal number of zeros may be cancelled on each side without changing the value of the equation.
d. How many milliliters of a 1:200 silver nitrate solution would be needed to
make 2000 ml of a 1:4000 solution?
V C = V1 C1
(X) ( 1 ) = (2000 ml) ( 1 )
200 4000
(X) (4000) = (2000 ml) (4000)
200 4000
20 X = 2000 ml
X = 100 ml
e. Practical Exercises. Work the following problems and check your answers
with the correct answers found in d (page 2-34).
(1) (a) How many milliliters of a 3% hydrogen peroxide solution would be needed to make 120 ml of 1% hydrogen peroxide solution?
(b) How many milliliters of water should be added?
(2) How many milliliters of a 5% potassium hydroxide solution would be needed to make 60 ml of a 2% potassium hydroxide solution?
(3) (a) How many milliliters of a 1:1000 epinephrine HCl solution are needed to make 30 ml of 1:5000 solution?
(b) How many milliliters of water would be added
(4) How many milliliters of a 1:50 stock solution should be used to prepare one liter of a 1:4000 solution?