Final answer:
To calculate the strength of hydrocortisone acetate and pramoxide in the mixture, total amounts of each drug are determined from their respective percentages in the original gels, summed up, and then divided by the total mixture volume.
Step-by-step explanation:
To calculate the percentage strength of each of the two drugs, hydrocortisone acetate and pramoxide, in the mixture of gels, we must first determine the total amount of each drug in the mixture and then divide by the total volume of the mixture.
For the first gel, we have 50 mL of a 1% w/w hydrocortisone acetate solution. This means there is 0.5 g of hydrocortisone acetate in the 50 mL of the first gel (1% of 50 g, since density is not provided, we assume the gel's density approximates that of water, which is 1 g/mL).
For the second gel, we have 14.5 mL of a 3.5% w/w hydrocortisone acetate solution. This means there is 0.5075 g of hydrocortisone acetate in the 14.5 mL of the second gel (3.5% of 14.5 g).
Adding both amounts gives us a total of 1.0075 g of hydrocortisone acetate in 64.5 mL of the mixture (50 mL + 14.5 mL).
To find the percentage of hydrocortisone acetate in the mixture, divide the mass of hydrocortisone acetate by the total mass of the mixture and multiply by 100:
Percentage of hydrocortisone acetate = (1.0075 g / 64.5 g) × 100 = 1.56%
Since both gels have the same 1% w/w of pramoxide, the percentage of pramoxide in the mixture remains unchanged at 1%.
The final concentration of hydrocortisone acetate in the mixture is 1.56% and the concentration of pramoxide is 1%.