Final answer:
To create an 80% acid solution from 4 gallons of a 60% solution, 3.2 gallons of pure acid should be added. This calculation is based on setting up an equation using the mass balance concept and solving for the volume of pure acid needed.
Step-by-step explanation:
Calculating the Amount of Pure Acid for a Solution:
To determine how much pure acid should be mixed with 4 gallons of a 60% acid solution to obtain an 80% acid solution, we use the concept of mass balance. The mass of acid in the final solution is equal to the mass of acid in the original solution plus the mass of the pure acid added.
Let x represent the volume of pure acid to be added. The amount of acid in the 4 gallons of 60% solution is 0.60 × 4 gallons. The final solution will be x + 4 gallons with 80% of this mixture being acid.
Setting up the equation, we have:
0.60 × 4 + x = 0.80 × (x + 4)
Solving for x gives us:
x = (0.80 × 4) / (1 - 0.80)
x = 3.2 gallons of pure acid should be added.