a chemistry lab assistant wants to prepare 10 liters of 48% acid solution. in stock he has 80% and 40% acid solutions. how many liters of each in stock solution should he mix to prepare a 10-liter mixture?
L = no. of liters of 80% solution
.80L = value of 80% solution
10 - L = no. of liters of 40% solution
.40(10 - L) = value of 40% solution
.48(10) = value of mixture
.80L + .40(10 - L) = .48(10)
Solve for L
L = no. of liters of 80% solution
10 - L = no. of liters of 40% solution
To solve this problem, we can use the concept of the amount of acid in the solution.
Let's assume that x liters of the 80% acid solution is mixed with y liters of the 40% acid solution to make a 10-liter mixture.
Now we can set up two equations based on the amount of acid in the solution:
Equation 1: The total amount of acid in the mixture
0.80x + 0.40y = 0.48(10) [since we want a 10-liter mixture with 48% acid]
Equation 2: The total volume of the mixture
x + y = 10 [since we want the total mixture to be 10 liters]
To solve this system of equations, we can use substitution. Rearrange Equation 2 to solve for x:
x = 10 - y
Now substitute this expression for x in Equation 1:
0.80(10-y) + 0.40y = 0.48(10)
Simplify the equation:
8 - 0.80y + 0.40y = 4.8
Combine like terms:
0.40y = 4.8 - 8
0.40y = -3.2
Divide both sides by 0.40:
y = -3.2 / 0.40
y = -8
Since a negative value for y doesn't make sense in this context, we made an error somewhere in our calculations. Please check the problem statement or equations provided.
To solve this problem, we can set up a system of equations using the following information:
Let x be the number of liters of the 80% acid solution.
Let y be the number of liters of the 40% acid solution.
Since the desired mixture is 10 liters, we have the equation:
x + y = 10
We also know that the acid percentage in the 10-liter mixture should be 48%. Therefore, the equation for the acid concentration is:
(80% * x + 40% * y) / 10 = 48%
Now we can solve this system of equations to find the values of x and y.
Let's start by rearranging the first equation to solve for x:
x = 10 - y
Now substitute this value of x in the second equation:
(80% * (10 - y) + 40% * y) / 10 = 48%
Simplifying this equation:
(8 - 0.8y + 0.4y) / 10 = 0.48
(8 - 0.4y) / 10 = 0.48
To eliminate the decimal point, multiply both sides of the equation by 10:
8 - 0.4y = 4.8
Now, isolate the term with y by subtracting 8 from both sides of the equation:
-0.4y = -3.2
Divide both sides of the equation by -0.4 to solve for y:
y = -3.2 / -0.4
y = 8
Now substitute the value of y back into the first equation to solve for x:
x = 10 - 8
x = 2
Therefore, the lab assistant should mix 2 liters of the 80% acid solution with 8 liters of the 40% acid solution to prepare a 10-liter mixture with a 48% acid concentration.