A chemist has 40 ml of a solution that is 50% acid. How much water should be added to make a solution that is 10% acid?
since you want 1/5 the concentration, the final volume will be 5 times as much.
To solve this problem, we need to determine how much water should be added to the 50% acid solution in order to achieve a 10% acid solution.
Let's break down the problem and create an equation:
- The initial solution contains 40 ml of a 50% acid solution.
- We want to add water to this solution, so let's denote the amount of water added as "x."
- The final volume of the solution will be 40 ml + x ml.
The acid content in the initial solution and the acid content in the final solution should match. In other words, the amount of acid in the initial solution should be the same as the amount in the final solution.
Now, let's set up the equation using the acid content:
Initial acid: 50% of 40 ml = (50/100) * 40 = 20 ml
Final acid: 10% of (40 ml + x ml)
Since the amount of acid in both solutions should be equal, we can set up the equation as follows:
20 ml = (10/100) * (40 ml + x ml)
Now we can solve the equation to find the value of x (the amount of water to be added):
20 ml = (10/100) * (40 ml + x ml)
Multiplying both sides by 100:
2000 = 10 * (40 + x)
Dividing both sides by 10:
200 = 40 + x
Subtracting 40 from both sides:
160 = x
Therefore, 160 ml of water should be added to the 40 ml 50% acid solution to obtain a 10% acid solution.