Final answer:
The chemist needs to drain approximately 77.78 mL of the 25% acid solution and replace it with 70% acid solution to obtain 100 mL of a 60% acid solution.
Step-by-step explanation:
To solve the problem of finding how much of the 25% acid solution must be drained and replaced with a 70% acid solution to obtain 100ml of 60% acid solution, we can use a system of equations based on the concentrations before and after the replacement.
Let's denote the amount of solution to be replaced as 'x' mL. We start with 100 mL of a 25% acid solution and want to end up with a 60% acid solution. The total volume of the solution does not change, so it remains 100 mL throughout the procedure.
The equation representing the initial amount of acid in the solution is:
(25/100) * 100 = 25 mL of acid.
After draining 'x' mL, we are left with (100-x) mL of the original solution. We then add 'x' mL of the 70% acid solution.
The final amount of acid in the solution comes from the remaining original solution and the added 70% solution, which we can represent with the equation:
(25/100)*(100-x) + (70/100)*x = 60 mL of acid (since we want a final concentration of 60%).
Now, we solve for 'x' by setting the final concentration equation equal to 60 mL:
(25/100)*(100-x) + (70/100)*x = 60.
Simplify and solve the equation:
25 - (25/100)*x + (70/100)*x = 60
25 + (45/100)*x = 60
(45/100)*x = 35
x = 35 / (45/100)
x = 77.78 mL
The chemist needs to drain and replace approximately 77.78 mL of the 25% acid solution with the 70% acid solution to achieve a 60% concentration in the final 100 mL solution.