A lab assistant wants to make FIVE LITERS of 31.2% acid solution. If solutions of 40% and 18% are in stock, how many liters of each must be mixed to prepare the solution.
i don't even know what equation to use or anything, please help me, thank you.
the amount of acid in a solution is the % times the volume.
For example 5L of 50% solution has 2.5L of acid.
So, if you add up all the acid in the parts of your solution, they must add up to the total acid at the end.
If x is the amount of 18% solution, then there must be 5-x liters of 40% solution, since the total volume is 5 liters.
Now, adding up the amount of acid, we need
.18x + .40(5-x) = .312(5)
.18x + 2 - .4x = 1.56
.22x = .44
x = 2
so, 2L of 18% and 3L of 40% will produce 5L of 31.2%
.18*2 + .40*3 = .36+1.2 = 1.56 = .312*5
To solve this problem, we can set up a system of equations based on the following information:
Let x represent the number of liters of the 40% acid solution.
Let y represent the number of liters of the 18% acid solution.
Since the lab assistant wants to make 5 liters of a 31.2% acid solution, we can set up the following equation:
x + y = 5 -- equation (1)
We can also set up an equation based on the percentage concentration of acid in the solution:
(0.4x + 0.18y) / (x + y) = 0.312 -- equation (2)
Now, we have a system of two equations with two variables. We can solve this system to find the values of x and y.
We can start by solving equation (1) for y:
y = 5 - x
Now substitute this expression for y in equation (2):
(0.4x + 0.18(5 - x)) / (x + 5 - x) = 0.312
Simplifying the equation further:
(0.4x + 0.9 - 0.18x) / 5 = 0.312
Combine like terms:
0.22x + 0.9 = 0.312 * 5
0.22x + 0.9 = 1.56
Subtract 0.9 from both sides:
0.22x = 1.56 - 0.9
0.22x = 0.66
Divide both sides by 0.22:
x = 0.66 / 0.22
x = 3
Now, substitute the value of x back into equation (1) to solve for y:
3 + y = 5
y = 5 - 3
y = 2
Therefore, the lab assistant must mix 3 liters of the 40% acid solution and 2 liters of the 18% acid solution to prepare the 5 liter solution with a concentration of 31.2%.