A lab assistant wants to make five liters acid solution. If solutions of 40% and 18% are in stock, how many liters of each must be mixedto prepare the solution
Amount in liters:
40%:
18%:
What is the acid concentration of the solution he is trying to make?
To determine the amount of each solution needed, we can set up a system of equations based on the desired concentration and total volume of the acid solution.
Let's assume the lab assistant needs to make x liters of the 40% solution and y liters of the 18% solution to prepare a total volume of 5 liters.
Based on the concentration of the solutions and the desired concentration of the acid solution, we can write the following equations:
Equation 1: The sum of the volumes must equal 5 liters: x + y = 5
Equation 2: The concentration of the acid in the final solution can be calculated by multiplying the concentration of each solution by its respective volume. The sum of the acid in each solution is equal to the acid in the final solution: (0.40)x + (0.18)y = (0.40)(5)
Now we can solve this system of equations to find the values of x and y.
First, we can use substitution to eliminate one variable from the equations. Solving Equation 1 for x, we get:
x = 5 - y
Substituting this value for x in Equation 2, we have:
(0.40)(5 - y) + (0.18)y = (0.40)(5)
Expanding and simplifying this equation, we get:
2 - 0.40y + 0.18y = 2
Combining like terms, we have:
-0.22y = 0
Dividing both sides by -0.22, we find:
y = 0
Since the value of y is 0, it means that the lab assistant does not require any liters of the 18% solution.
To find the value of x, we can substitute y = 0 in Equation 1:
x + 0 = 5
x = 5
Therefore, the lab assistant needs 5 liters of the 40% solution and 0 liters of the 18% solution to prepare the desired 5-liter acid solution.