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?
Let X be the volume of weak acid and Y be the volume of pure acid
X + Y = 100 (ml)
0.2X + Y = 0.4*100 ml (amount of pure acid in the mixture)
0.8X = 60
X = 75 ml
Y = 25 ml
To solve this problem, let's break it down step by step.
Step 1: Determine the unknown quantities
Let's represent the amount of pure acid to be added as x milliliters, and the amount of 20% acid solution as y milliliters.
Step 2: Set up equations based on the given information
We know that the total volume of the resulting solution is 100 milliliters. Therefore, we can write the equation: x + y = 100.
We also know that the acid concentration in the final solution is 40%. The acid content from the pure acid added (x milliliters) is 100% in concentration, while the acid content from the 20% acid solution (y milliliters) is 20% in concentration. We can write the equation: (x * 100% + y * 20%) / 100 = 40%.
Step 3: Solve the system of equations
Now, we can solve the system of equations. Let's first rearrange the equation (x * 100% + y * 20%) / 100 = 40% to get rid of the percentages:
(x + 0.2y) / 100 = 0.4
Multiply both sides by 100 to eliminate the denominator:
x + 0.2y = 40
Now, we have a system of two equations:
x + y = 100
x + 0.2y = 40
We can solve this system by substitution or elimination. Let's use the elimination method.
Multiply the second equation by 5 to get the same coefficient for y:
5(x + 0.2y) = 5(40)
5x + y = 200
Now, subtract the first equation from the above equation to eliminate x:
(5x + y) - (x + y) = 200 - 100
4x = 100
Divide both sides by 4 to solve for x:
x = 25
Substitute the value of x into the first equation to find y:
25 + y = 100
y = 100 - 25
y = 75
So, in order to form 100 milliliters of 40% acid solution, the chemist needs to mix 25 milliliters of pure acid with 75 milliliters of the 20% acid solution.