The pharmacy stocks a 90% w/v solution of drug 'w'. you need to prepare 200ml of a 5mg/ml solution for a patient. what volume of the stock solution will you need?

A concentration that is reported in 90% w/v solution means that there is 90 mg of solute in every 100 mL of solution. Technically, the units can be anything as long as the mass and volume have the same metric measurement. In this case, we use the 'milli' metric system, so it is in mg/mL.

By obeying the Law of Conservation of Mass, there must be the same amount of solute in the 90%w/v as it is in the new 200 mL solution. Therefore, you must equate the two equations in ratio and proportion:

90mg/100mL = 5 mg/ x mL

where x is the amount of volume in liters that we should get from the stock solution. Solving the equation, we determine x to be equal to 5.56 mL. Therefore, this means that we get 5.56 mL of the 90% w/v stock solution, then dilute it with water up to the 200-mL mark.