a drug is supplied as a 20 mg/ml solution in a 50 ml vial. you need to make 15 ml of a 10 mg/ml solution. how much concentrate and how much diluent are needed to obtain the desired final volume?
you need x ml of solution, and 15-x ml of water (0 mg/ml), so
20x + 0 = 10*15
x = 7.5
Since the concentration is being reduced by a factor of 2, the volume needs to be increased by that factor.
2 * 7.5 = 15
To determine how much concentrate (the 20 mg/ml solution) and how much diluent (the solvent used to dilute the solution) are needed to obtain the desired final volume of 15 ml with a concentration of 10 mg/ml, we can use the dilution formula:
C1V1 = C2V2
Where:
C1 = concentration of the initial solution
V1 = volume of the initial solution (concentrate)
C2 = concentration of the final solution
V2 = volume of the final solution
Let's calculate the amount of concentrate and diluent needed step by step:
1. Determine the amount of concentrate needed:
First, we need to find out how much drug is required to achieve the desired concentration.
C1V1 = C2V2
20 mg/ml (V1) = 10 mg/ml (15 ml)
V1 = (10 mg/ml * 15 ml) / 20 mg/ml
V1 = 7.5 ml
So, we need 7.5 ml of the concentrate (20 mg/ml solution).
2. Determine the amount of diluent needed:
To find the volume of diluent required, subtract the volume of concentrate from the desired final volume.
V2 - V1 = Amount of diluent
15 ml - 7.5 ml = 7.5 ml
Hence, you will need 7.5 ml of diluent.
To summarize:
To make the desired 15 ml solution with a concentration of 10 mg/ml, you will need:
- 7.5 ml of the 20 mg/ml concentrate
- 7.5 ml of diluent (solvent)