Final answer:
To obtain a 50% solution, you will need to add 6 gallons of pure hydrochloric acid to 10 gallons of a 20% solution.
Step-by-step explanation:
To find the amount of pure hydrochloric acid needed to obtain a 50% solution, we need to set up an equation using the concept of mass balance.
Let x be the amount of pure hydrochloric acid in gallons.
The total volume of the solution will be 10 + x gallons.
The equation will be: 0.2 * 10 + 1 * x = 0.5 * (10 + x)
Simplifying the equation, we get: 2 + x = 5 + 0.5x
Combining like terms, we get: 0.5x = 3
Dividing both sides of the equation by 0.5, we get: x = 6
Therefore, 6 gallons of pure hydrochloric acid must be added to 10 gallons of a 20% solution to obtain a 50% solution.