concentrate and diluent

Question

Prepare 15 mL of a 50 mg/mL cefazolin dilution from a stock of 1 g/5 mL. How many milliliters of diluent and stock solution will be needed?
concentrate: 3.75 mL and diluent: 11.25 mL
concentrate: 2.25 mL and diluent: 12.75 mL
concentrate: 3 mL and diluent: 12 mL
concentrate: 4.15 mL and diluent: 10.85 mL

Prepare one dose of 0.6 mg gentamicin in 2 mL diluted from a stock solution of 20 mg/mL. How much gentamicin and how much diluent is used?
concentrate: 0.3 mL and diluent: 1.7 mL
concentrate: 0.03 mL and diluent: 1.97 mL
concentrate: 0.08 mL and diluent: 1.92 mL
concentrate: 0.22 mL and diluent: 1.78 mL

 

You need 50 mL of 5% dextrose for a patient. You have 70% dextrose 1000 mL on hand. How much concentrate will you need? How much diluent?
concentrate: 37 mL and diluent: 13 mL
concentrate: 3.57 mL and diluent: 46.43 mL
concentrate: 5.37 mL and diluent: 44.63 mL
concentrate: 47 mL and diluent: 3 mL

Answer 1

1.

Stock = 1 g / 5 mL = 1000 mg / 5 mL = 200 mg/mL

Suppose you need a mL of concentrate, and b mL of diluent:

a + b = 15 (mL)

15mL * 50 mg/mL = a * stock = a * 200 mg/mL

So a = 15 * 50 / 200 = 3.75 (mL)

Therefore b = 15 - a = 11.25 (mL)

 

2.

To get 0.6 mg of gentamicin from a stock solution of 20 mg/mL, you need 0.6 / 20 = 0.03 mL of concentrate.

Therefore you need 2 mL - 0.03 mL = 1.97 mL of diluent.

 

3.

Suppose you need a mL of stock, and b mL of diluent.

50 x 5% = a * 70%

So a = 50 * 5% / 70% = 3.57 (mL)

Therefore b = 50 - a = 46.43 (mL)