Final answer:
Prepare 1 gallon of 0.05% w/v solution from a 10% w/v stock solution, 18.93 milliliters of the stock solution is required. This calculation uses the dilution equation C1V1 = C2V2 after converting 1 gallon to milliliters.
Step-by-step explanation:
To determine how many milliliters of a 10% w/v stock solution should be used in preparing 1 gallon of a 0.05% w/v solution, we need to use the concept of dilution.
The dilution equation C1V1 = C2V2 (where C1 and V1 are the concentration and volume of the stock solution, and C2 and V2 are the concentration and volume, respectively, of the final diluted solution) can be applied to solve this problem.
First, we need to convert the volume of 1 gallon to milliliters remembering that 1 gallon is equivalent to 3.78541 liters or 3785.41 milliliters (since 1 liter = 1000 milliliters). Using the equation:
(10%)(V1) = (0.05%)(3785.41 mL)
Solving for V1 gives:
V1 = (0.05% * 3785.41 mL) / 10%
V1 = (0.05 / 10) * 3785.41 mL
V1 = 0.005 * 3785.41 mL
V1 = 18.92705 mL
Therefore, to prepare 1 gallon of a 0.05% w/v solution, 18.93 milliliters of the 10% w/v stock solution are required.