Question

The tranquilizer valium is sold in 2.0 ml syringes that contain 50.0 mg of drug per 1.0 ml of liquid (50.0 mg/1.0 ml). if a physician prescribes 22 mg of this drug, how many milliliters should be administered?

Answer 1

To administer 22 mg of the tranquilizer Valium, 0.44 ml should be administered.

Step-by-step explanation:

To find out how many milliliters of the tranquilizer Valium should be administered when the physician prescribes 22 mg of the drug, we need to use the given information about the concentration of the drug. The concentration is 50.0 mg of drug per 1.0 ml of liquid. So, we can set up a proportion to solve for the unknown amount of liquid:

(50.0 mg/1.0 ml) = (22 mg/x ml)

Cross multiplying gives us:

50.0x = 22 * 1.0

Dividing both sides by 50.0 gives us:

x = 0.44 ml

Therefore, 0.44 ml of Valium should be administered.

Answer 2

The approach to determining the answer to this problem is to use the proper dimensional analysis. To determine the volume of the drug that should be administered, we divide the given mass in prescription by the concentration of drug.

V = (22 mg)/ (50.0 mg / 1.0 mL)

Simplifying,

V = 0.44 mL

Answer: 0.44 mL