Answer :
Final answer:
Approximately 5.33 ounces of a 36 Index solution are required to make 3 gallons of a 0.5% solution, after converting gallons to fluid ounces and calculating the volume of the strong solution needed.
Explanation:
To determine the amount of 36 Index solution needed to create 3 gallons of a 0.5% solution, we must first calculate the total volume in ounces of the solution to be made. We start by converting the volume from gallons to ounces, knowing that 1 gallon is equivalent to 128 fluid ounces.
3 gallons × 128 fluid ounces/gallon = 384 fluid ounces
Now, we need to find out how many ounces of the 36 Index are required to get a 0.5% solution. To achieve a 0.5% concentration, we calculate 0.5% of the total volume:
0.005 × 384 fluid ounces = 1.92 fluid ounces
However, this result is in pure form, and we need to convert it to the 36 Index, which implies dilution. A 36 Index is equivalent to 36% solution concentration. If we have 1.92 ounces of pure substance, we can find the amount of a 36% solution that will give us the same amount of the pure substance by dividing the pure amount by the percentage concentration:
1.92 fluid ounces / 0.36 = 5.33 fluid ounces
Therefore, approximately 5.33 ounces of a 36 Index is needed to make 3 gallons of a 0.5% solution.
