Todd has 1 liter of a 20% sulfuric acid solution. How much of a 12% sulfuric acid solution must he mix with the 1 liter of 20% solution to make a 15% sulfuric acid solution?
SO simple, use ur sense!!
To solve this problem, we need to determine the amount of a 12% sulfuric acid solution that needs to be mixed with a 1 liter of a 20% sulfuric acid solution to obtain a 15% sulfuric acid solution.
Let's assume that Todd needs to mix x liters of the 12% solution.
The amount of sulfuric acid in the 20% solution is 20% of 1 liter, which is (20/100) * 1 = 0.2 liters.
The amount of sulfuric acid in the 12% solution is 12% of x liters, which is (12/100) * x = 0.12x liters.
After mixing the two solutions, the total amount of sulfuric acid in the mixture is 0.2 liters + 0.12x liters.
We want to create a 15% sulfuric acid solution, which means that the total amount of sulfuric acid in the mixture (0.2 + 0.12x) liters, should be 15% of the total volume of the mixture, which is (1 + x) liters.
Setting up the equation:
0.2 + 0.12x = (15/100) * (1 + x)
Simplifying this equation:
0.2 + 0.12x = 0.15(1 + x)
0.2 + 0.12x = 0.15 + 0.15x
0.03x = 0.15 - 0.2
0.03x = -0.05
Dividing both sides by 0.03:
x = -0.05 / 0.03
x = -1.67 (approximately)
Since we cannot have a negative volume of solution, it is not possible to mix a 12% sulfuric acid solution with a 20% sulfuric acid solution to obtain a 15% sulfuric acid solution.