A doctor needs to administer 2 mL of a 100 mg/mL solution to a 200-pound patient. However, the doctor has the solution available only in 20 mg/mL strength. What volume of the 20 mg/mL solution would be needed to administer the desired dose?

2 ml of 100 mg/ml is 200 mg

to get 200 mg he needs 10 ml of the weaker solution

To find the volume of the 20 mg/mL solution needed, we can use the concept of the equivalence of concentrations.

First, let's calculate the amount of the active ingredient, which is 100 mg, required for the desired dose. We can use the following formula:

Amount of active ingredient = Concentration × Volume

Given that the desired dose is 2 mL and the desired concentration is 100 mg/mL, we can calculate the amount of active ingredient required:

Amount of active ingredient = 100 mg/mL × 2 mL = 200 mg

Now, we need to find the volume of the 20 mg/mL solution that contains 200 mg of the active ingredient. We can use the formula mentioned earlier:

Volume = Amount of active ingredient / Concentration

Using the values we have, we can calculate:

Volume = 200 mg / 20 mg/mL = 10 mL

Therefore, the doctor would need to administer 10 mL of the 20 mg/mL solution to achieve the desired dose.