A chemist mixes some 20% acid solution with pure 100% acid to increase the concentration. How much pure acid and acid solution should be mixed to form 100 milliliters of 40% acid solution?
first, represent:
let x = amount of 20% acid used (in mL)
let 100-x = amount of 100% acid used (since the total volume of the 2 acids mixed must be 100)
therefore,
0.2x + 1(100-x) = .4(100)
*note: 0.2 = 20%, 1 = 100%, .4=40%
0.2x + 100-x = 40
-0.8x=-60
x = 75 mL of 20% acid, and
100-x = 25 mL of 100% acid
so there,, i hope i was able to help.. =)
To determine how much pure acid and acid solution should be mixed, we can set up an equation based on the principles of concentrations.
Let's denote the volume of pure acid as x and the volume of the 20% acid solution as y. The sum of these volumes should equal the final volume of the solution, which is 100 milliliters.
We can express the amount of acid in each component of the mixture using the equation:
0% acid * x + 20% acid * y = 40% acid * 100 mL
Since the pure acid component has 100% acid concentration, we have:
100% acid * x = 40% acid * 100 mL
Simplifying this equation, we get:
x = (40/100) * 100 mL
x = 40 mL
Therefore, we need to mix 40 milliliters of pure acid with the acid solution to form a 40% acid solution. The remaining volume will be filled with the 20% acid solution:
100 mL - 40 mL = 60 mL
Hence, 40 milliliters of pure acid and 60 milliliters of the 20% acid solution should be mixed to form 100 milliliters of a 40% acid solution.
To solve this problem, you can use the following steps:
Step 1: Assume that x milliliters of the 20% acid solution will be mixed with y milliliters of pure 100% acid.
Step 2: Write down the equation for the amount of acid in the original solution and the final solution:
In the original solution: 0.20x milliliters of acid
In the pure acid: 1.00y milliliters of acid
In the final solution: 0.40 * 100 = 40 milliliters of acid
Step 3: Write down the equation for the total volume of the final solution:
x + y = 100
Step 4: Write down the equation for the total amount of acid in the final solution:
0.20x + 1.00y = 0.40 * 100
Step 5: Solve the system of equations by substitution or elimination.
From equation 3, we can isolate x:
x = 100 - y
Substitute this value of x into equation 4:
0.20(100 - y) + 1.00y = 40
Step 6: Solve for y:
20 - 0.20y + 1.00y = 40
0.80y = 20
y = 25
Step 7: Substitute the value of y into equation 3 to find x:
x = 100 - y
x = 100 - 25
x = 75
Therefore, to form 100 milliliters of 40% acid solution, you need to mix 75 milliliters of the 20% acid solution with 25 milliliters of pure 100% acid.