How much of a solution that is 45% sulfuric acid needs to be mixed with a solution that is 90% sulfuric acid to produce 120 liters of a solution that is 60% sulfuric acid?
.45V1+.90(120-V1)=.6*120
solve for V1, then 120-V1
To solve this problem, we can use the concept of mixtures and apply the following equation:
(amount of pure acid in the first solution + amount of pure acid in the second solution) = amount of pure acid in the final solution
Let's assume x liters of the 45% sulfuric acid solution are needed.
1. Calculate the amount of pure acid in the first solution:
In a 45% sulfuric acid solution, 45% of the solution is sulfuric acid.
So, the amount of pure acid in x liters of the 45% solution is 0.45x.
2. Calculate the amount of pure acid in the second solution:
In a 90% sulfuric acid solution, 90% of the solution is sulfuric acid.
As we need 120 liters of the final solution and x liters of the first solution, the amount of the second solution needed is (120 - x) liters.
So, the amount of pure acid in (120 - x) liters of the 90% solution is 0.9(120 - x).
3. Calculate the amount of pure acid in the final solution:
In the final 60% sulfuric acid solution, 60% of the solution is sulfuric acid.
So, the amount of pure acid in 120 liters of the 60% solution is 0.6(120) = 72.
Using the equation mentioned above, we can now set up the equation:
0.45x + 0.9(120 - x) = 72
Solving this equation will give us the value of x, which represents the amount of the 45% sulfuric acid solution needed.
To determine the amount of each solution needed, we can set up a system of equations.
Let's assume that x liters of the 45% sulfuric acid solution is needed, and y liters of the 90% sulfuric acid solution is needed to yield 120 liters of a 60% sulfuric acid solution.
The first equation focuses on the total volume of the mixture:
x + y = 120
The second equation corresponds to the amount of sulfuric acid in the mixture:
(0.45x + 0.9y) / 120 = 0.6
Solving this system of equations will lead us to the values of x and y, which represent the amounts of each solution required. Here's how we can solve it:
1. From the first equation, we can express one of the variables in terms of the other. Let's express y in terms of x:
y = 120 - x
2. Substitute the expression for y in the second equation:
(0.45x + 0.9(120 - x)) / 120 = 0.6
3. Simplify and solve for x:
0.45x + 108 - 0.9x = 72
-0.45x = -36
x = -36 / -0.45
x = 80
4. Plug the value of x back into the first equation to find y:
80 + y = 120
y = 120 - 80
y = 40
Therefore, you would need 80 liters of the 45% sulfuric acid solution and 40 liters of the 90% sulfuric acid solution to produce 120 liters of a 60% sulfuric acid solution.