Final answer:
To prepare 8 fluid ounces of a solution containing 0.12%(w/v) of methyl paraben, 283.872 milligrams of methyl paraben are needed, after converting fluid ounces to milliliters and using the proportion based on the given concentration.
Step-by-step explanation:
To calculate how many milligrams of methyl paraben are needed to prepare an 8 fluid ounce solution containing 0.12%(w/v) of methyl paraben, we need to convert the volume from fluid ounces to milliliters, as the concentration is given in weight/volume. One fluid ounce is equivalent to approximately 29.57 milliliters. Therefore, 8 fluid ounces is equivalent to 8 x 29.57 = 236.56 milliliters.
The 0.12%(w/v) concentration means that there are 0.12 grams of methyl paraben in 100 milliliters of solution. To find out how many grams are in 236.56 milliliters, we can set up a proportion:
(0.12 grams/100 milliliters) = (x grams/236.56 milliliters)
To solve for x, we cross-multiply and divide:
x = (0.12 grams * 236.56 milliliters) / 100 milliliters
x = 0.283872 grams
Since we want to find the amount in milligrams, we convert grams to milligrams (1 gram = 1000 milligrams):
0.283872 grams * 1000 milligrams/gram = 283.872 milligrams
Therefore, 283.872 milligrams of methyl paraben are needed to prepare 8 fluid ounces of a 0.12%(w/v) solution.