David Robertson works as a chemical engineer for U.S. peroxide Corporation. David has 2500 gallons of commercial-grade hydrogen peroxide solution that is 60% pure hydrogen peroxide. How much distilled water(which is 0% hydrogen peroxide) will David need to add to the solution to create a new solution that is 25% hydrogen peroxide?
amount of water added ---- x gallons
.6(2500) + 0.0x = .25(2500 + x)
solve for x
To solve this problem, we need to calculate the quantity of distilled water that David should add to the solution. Let's break down the problem into smaller parts:
1. Let's determine the quantity of hydrogen peroxide in the original solution:
- The original solution has 2500 gallons.
- The solution is 60% pure hydrogen peroxide.
- So, the quantity of hydrogen peroxide in the original solution is (2500 gallons) * (60/100) = 1500 gallons.
2. Now, let's determine the quantity of hydrogen peroxide in the final solution:
- The final solution should have a hydrogen peroxide concentration of 25%.
- This means that the quantity of hydrogen peroxide in the final solution should be (2500 gallons + X) * (25/100), where X represents the gallons of distilled water added.
3. The next step is to find the quantity of distilled water that David needs to add:
- Given that the original solution has 1500 gallons of hydrogen peroxide, the quantity of hydrogen peroxide in the final solution should also be 1500 gallons.
- Set up the equation: (2500 + X) * (25/100) = 1500. We set the two quantities of hydrogen peroxide equal to each other.
- Simplifying the equation: (X + 2500) * 0.25 = 1500.
- Expanding the equation: 0.25*X + 625 = 1500.
- Subtracting 625 from both sides: 0.25*X = 875.
- Dividing both sides by 0.25 to isolate X: X = 875 / 0.25 = 3500.
Therefore, David needs to add 3500 gallons of distilled water to the solution to create a new solution that is 25% hydrogen peroxide.