A chemist has a solution that is 20% HIC and a solution that is 50% HCI. How much of each solution should be mixed to attain 300ml of a solution that is 30% HCI?
let the amount of the 20% solution used be x ml
then the amount of the 50% solution used is 300-x m.
solve for x ....
.2x + .5(300-x) = .3(300)
times 10
2x + 5(300-x) = 3(300)
take it from there
It may help to set up a table for these kinds of problems:
............Amount.....%....HCl
Solution 1....x......0.2....0.2x
Solution 2...300-x...0.5....0.5(300-x)
Mixture......300.....0.3....0.3(300)
Equation:
0.2x + 0.5(300-x) = 0.3(300)
Solve for x. (Be sure to list the amount of both solutions!)
I hope this helps.
To solve this problem, we can use the concept of mixing two solutions to obtain a desired concentration.
Let's assume that the chemist needs to mix x ml of the 20% HIC solution and y ml of the 50% HIC solution to get a total volume of 300 ml of a 30% HIC solution.
1. First, let's set up the equation for the concentration of HIC in the final mixture:
(Amount of HIC in the 20% solution + Amount of HIC in the 50% solution)/(Total volume of the mixture) = Desired concentration of HIC in the final mixture
Mathematically, it can be written as:
(0.2x + 0.5y)/(x + y) = 0.3
2. We also know that the total volume of the mixture should be 300 ml:
x + y = 300
Now, we have a system of two equations that we can solve simultaneously to find the values of x and y.
There are several methods to solve this system of equations, such as substitution, elimination, or matrix method. I will use the substitution method here.
Rearranging the second equation, we get:
x = 300 - y
Substituting this value of x into the first equation, we have:
(0.2(300 - y) + 0.5y)/(300 - y + y) = 0.3
Simplifying the equation, we get:
(60 - 0.2y + 0.5y)/300 = 0.3
Combining like terms, we have:
(0.3y + 60)/300 = 0.3
Now, cross-multiplying the equation, we get:
0.3y + 60 = 0.3 * 300
Simplifying further, we have:
0.3y + 60 = 90
Subtracting 60 from both sides, we get:
0.3y = 90 - 60
0.3y = 30
Dividing by 0.3, we get:
y = 30/0.3
y = 100
Substituting this value of y into the equation x = 300 - y, we have:
x = 300 - 100
x = 200
Therefore, the chemist will need to mix 200 ml of the 20% HIC solution and 100 ml of the 50% HIC solution to obtain 300 ml of a solution that is 30% HIC.