A pharmacy technician is making a 50% solution, how many mL of a 38% stock solution should be added to one pint of a 82% solution? ( just need to know how to set this problem up please)
just keep track of the amount of solute present. The amounts must add up to the total in the final solution. Remember to watch the units; a pint is 473mL.
.38x + .82(473) = .50(x+473)
To set up this problem, we need to determine the amount of a 38% stock solution that needs to be added to one pint (which is equivalent to 473.18 mL) of an 82% solution to make a 50% solution.
Let's use the subscripts "A" and "B" to represent the two solutions:
Solution A: 82% (one pint)
Solution B: 38% (unknown amount in mL)
We know that the resulting mixture after adding Solution B to Solution A should be a 50% solution. This means that the amount of solute (active ingredient) in the resulting mixture should be equal to 50% of the total volume of the resulting mixture.
To solve this problem, we can use the following equation:
Percent of Solution A × Volume of Solution A + Percent of Solution B × Volume of Solution B = Percent of Resulting Mixture × Total Volume of Resulting Mixture
In this equation:
- Percent of Solution A = 82% = 0.82 (since 82% is equivalent to 0.82)
- Volume of Solution A = 473.18 mL (one pint)
- Percent of Solution B = 38% = 0.38
- Volume of Solution B = unknown
- Percent of Resulting Mixture = 50% = 0.50
- Total Volume of Resulting Mixture = Volume of Solution A + Volume of Solution B
By plugging in the given values and solving for the unknown (Volume of Solution B), you can determine how many mL of the 38% stock solution should be added to one pint of the 82% solution to obtain a 50% solution.