Solutions, Concentrations, and Dilutions

A 20% solution has been diluted to 400mL and is now a 5% solution. What was the beginning volume of the 20% solution?

(20%)(x) = (5%)(400mL)

x = 100mL

The pharmacist gives the technician 1000mL of a 20% solution. How many 1 ounce bottles (1 ounce = 30mL) can be filled, if the solution is diluted to make a 2% solution?

(20%)(1000mL) = (2%)(x)

(0.2)(1000mL) = (0.02)(x)

200 = (0.02)(x)

x = 10,000

10,000/30mL = 333.3 bottles can be filled

A technician is given 120mL of a 50% (W/V) potassium chloride solution and is told to add 300mL of sterile water to it. What will the final (W/V) percentage concentration be of the solution?

(final volume or weight of finished product) x (% strength) = mL or grams of solution to be dissolved

300mL + 120mL = 420mL

(50%)(120mL) = (x)(420mL)

(0.5)(120mL) = (x)(420mL)

60 = 420x

x = 0.14

0.14 x 100 = 14% final concentration of solution

A pharmacy receives an order for 280mL of a 5% salicylic acid solution. How many grams of salicylic acid powder are needed to make the solution?

(5%)(280mL) = x grams

(0.5)(280mL) = 14 grams are needed, to make the solution

How many mL of a 3% (W/V) solution will be necessary to make 6 ounces (180mL) of a 1:200 (0.5%) solution?

(3%)(x) = (0.5%)(180mL)

(0.03)(x) = (0.005)(180mL)

0.03x = 0.9

x = 30mL is needed to make 6 ounces of a 1:200 solution

The pharmacist has weighted out 15g of coal tar and given it to the technician with the instructions to compound a 1% ointment. What will be the final weight of the correctly compounded prescription?

(1%)(x) = 15g

(0.01)(x) = 15g

x = 1500g final weight

How many 5 grain tablets (5 grains = 325mg) are needed to make 500mL of a 1:200 (0.5%) solution?

(0.5%)(500mL) = x grams

(0.005)(500mL) = 2.5g are needed

2.5g = 2500mg

2500mg / 325mg = 7.7 tablets

8 tablets are needed

How many mL of a 10% (W/V) solution can be prepared from 150mL of a 32% (W/V) soltuion?

(32%)(150mL) = (10%)(x)

(0.32)(150mL) = (0.1)(x)

48 = 0.1x

x = 480mL can be prepared

How many mg of hydrocortisone are in 5g of ointment taken from a 120g ointment tube of 1% hydrocortisone?

5g = 50mg

If 60mL of a 70% (V/V) solution is diluted to 240mL, what is the percentage strength (V/V)?

(70%)(60mL) = (x)(240mL)

(0.7)(60mL) = (x)(240mL)

42 = 240x

x = 0.175

x = 17.5%

What is the initial concentration, expressed as a percent, of a 200mL solution which was diluted to 840mL with final concentration of 15%?

(x)(200mL) = (15%)(840mL)

(x)(200mL) = (0.15)(840mL)

200x = 126

x = 0.63

x = 63%