Lactic acid 4 g Salicylic acid 5 g Trichloroacetic acid 2 g Flexible collodion qs ad 100 g Sig: wart remover. Use as directed. (a) Flexible collodion contains 20% w/w camphor and 30% w/w castor oil. How many grams of each would be contained in 30 g of the final product? Round to the nearest hundredth. Camphor: of 6 grams Castor Oil: of 6 grams (b) The specific gravity of castor oil is 0.955. How many milliliters of the oil is 3 of 6 mL (c) If the specific gravity of the final product is 0.781, what are the percent w/v concentrations of lactic acid, salicylic acid, and trichloroacetic acid in the final product (Round to the nearest hundredth)? Lactic Acid: Question Blank 4 of 6 % Salicylic Acid Question Blank 5 of 6 % Trichloroacetic Acid Question Blank 6 of 6 %
The correct answer and explanation is:
Here are the calculations and explanations for the wart remover prescription:
First, let’s determine the amount of Flexible Collodion in the original 100 g formula.
Total formula weight = 100 g
Weight of active ingredients = Lactic acid (4 g) + Salicylic acid (5 g) + Trichloroacetic acid (2 g) = 11 g
Weight of Flexible Collodion = Total weight – Weight of active ingredients = 100 g – 11 g = 89 g
So, in 100 g of the final product, there are 89 g of Flexible Collodion. The final product is 89% w/w Flexible Collodion.
(a) Flexible collodion contains 20% w/w camphor and 30% w/w castor oil. How many grams of each would be contained in 30 g of the final product? Round to the nearest hundredth.
In 30 g of the final product, the amount of Flexible Collodion is:
89% of 30 g = 0.89 * 30 g = 26.7 g of Flexible Collodion.
Now, calculate the amount of Camphor and Castor Oil in 26.7 g of Flexible Collodion:
Camphor: 20% of 26.7 g = 0.20 * 26.7 g = 5.34 g
Castor Oil: 30% of 26.7 g = 0.30 * 26.7 g = 8.01 g
Note: The “of 6 grams” in the prompt seems like a placeholder typo.
Camphor: 5.34 grams
Castor Oil: 8.01 grams
(b) The specific gravity of castor oil is 0.955. How many milliliters of the oil is 3 of 6 mL
Specific gravity (SG) is the ratio of the density of a substance to the density of water (approximately 1 g/mL). So, the density of castor oil is 0.955 g/mL.
Density = Mass / Volume. Therefore, Volume = Mass / Density.
Note: The phrasing “3 of 6 mL” is unclear. Assuming it means converting 3 grams (as a likely intended mass value in a calculation involving grams) of castor oil to milliliters.
Assuming the question asks for the volume of 3 grams of castor oil:
Volume = 3 g / 0.955 g/mL = 3.14136… mL
Rounded to two decimal places (consistent with part a): 3.14 mL.
Note: If the question intended something else by “3 of 6 mL”, it is too ambiguous to calculate.
Volume of Castor Oil (assuming 3 g): 3.14 mL
(c) If the specific gravity of the final product is 0.781, what are the percent w/v concentrations of lactic acid, salicylic acid, and trichloroacetic acid in the final product (Round to the nearest hundredth)?
Percent w/v concentration is calculated as (grams of solute / milliliters of solution) * 100%.
The mass of the final product is 100 g.
The specific gravity of the final product is 0.781, meaning its density is 0.781 g/mL.
We need to find the volume of the 100 g final product using its density:
Volume = Mass / Density = 100 g / 0.781 g/mL = 128.0409… mL
Now calculate the w/v concentration for each active ingredient using their mass (from the formula) and the total volume (128.04 mL):
Lactic Acid: (4 g / 128.0409 mL) * 100% = 3.1238… %
Rounded to the nearest hundredth: 3.12 %
Salicylic Acid: (5 g / 128.0409 mL) * 100% = 3.905… %
Rounded to the nearest hundredth: 3.91 %
Trichloroacetic Acid: (2 g / 128.0409 mL) * 100% = 1.5619… %
Rounded to the nearest hundredth: 1.56 %
Lactic Acid: 3.12 %
Salicylic Acid: 3.91 %
Trichloroacetic Acid: 1.56 %
Explanation:
This calculation involves understanding component percentages, specific gravity, and concentration units.
For part (a), we first determined the amount of Flexible Collodion in the total 100 g formula (100 g – 11 g active ingredients = 89 g). This means the final product is 89% Flexible Collodion by weight. To find the amount of Flexible Collodion in 30 g of the final product, we calculated 89% of 30 g, which is 26.7 g. Then, using the specified composition of Flexible Collodion (20% camphor, 30% castor oil by weight), we calculated 20% and 30% of 26.7 g to find the amounts of camphor (5.34 g) and castor oil (8.01 g) present.
For part (b), specific gravity relates the density of a substance to that of water (1 g/mL). A specific gravity of 0.955 means the density of castor oil is 0.955 g/mL. Assuming the prompt intended to ask for the volume of 3 grams of castor oil, we used the formula Volume = Mass / Density (3 g / 0.955 g/mL) to find the volume, rounding the result to 3.14 mL.
For part (c), percent weight-in-volume (w/v) concentration is defined as grams of solute per 100 mL of solution. The formula provides the grams of each active ingredient in 100 g of the final product. To calculate the w/v concentration, we needed the volume of this 100 g batch. We used the specific gravity of the final product (0.781) to determine its density (0.781 g/mL) and then calculated the volume using Volume = Mass / Density (100 g / 0.781 g/mL = 128.04 mL). Finally, we divided the mass of each active ingredient (lactic acid 4g, salicylic acid 5g, trichloroacetic acid 2g) by the total volume (128.04 mL) and multiplied by 100% to get the percent w/v concentration for each, rounding to two decimal places.