If there are 400 cubic centimeters of a chemical in 1 liter of solution (1000 cc=1 liter), how many cubic centimeters of water must be added to dilute it to a 25% solution?
If the chemical occupies 400 of the 1000 ml of solution, then it is a 40% solution.
25% is 5/8 as strong, so the volume of solution has to grow by a factor of 8/5, to 1600 ml.
To solve this problem, we can set up a proportion based on the concentration of the solution.
Let's denote the volume of water to be added as "x" cubic centimeters.
The initial concentration of the solution is 400 cc / 1000 cc = 0.4 or 40%.
The desired concentration of the solution is 25% or 0.25.
We can set up the following proportion:
0.4 / 0.25 = 1000 / (1000 + x)
We can cross-multiply to solve for x:
0.4 * (1000 + x) = 0.25 * 1000
400 + 0.4x = 250
0.4x = 250 - 400
0.4x = -150
x = -150 / 0.4
x ≈ -375
Since volume cannot be negative, we ignore the negative value. Therefore, we conclude that 375 cubic centimeters of water must be added to dilute the solution to 25%.
To solve this problem, we need to find out how many cubic centimeters of water should be added to the 400 cubic centimeters of the chemical to make a 25% solution. Let's break it down step by step:
Step 1: Determine the desired volume of the 25% solution
A 25% solution means that 25% of the total volume will be the chemical. In this case, the total volume of the solution is not given directly, but we know that it needs to be diluted. Let's assume that we want to make 1 liter of the 25% solution.
Step 2: Calculate the amount of chemical required in the 25% solution
We know that the desired volume of the solution is 1 liter, and we want 25% of it to be the chemical. So, we need to calculate 25% of 1 liter.
25% of 1 liter = 0.25 * 1 liter = 0.25 liters
Step 3: Calculate the amount of water required in the 25% solution
To find the amount of water required, we need to subtract the volume of the chemical from the desired total volume of the solution.
Volume of water = Total volume - Volume of chemical
Volume of water = 1 liter - 0.25 liters = 0.75 liters
Step 4: Convert the volume of water into cubic centimeters
We know that 1 liter is equal to 1000 cubic centimeters.
Volume of water in cubic centimeters = Volume of water in liters * Conversion factor
Volume of water in cubic centimeters = 0.75 liters * 1000 cubic centimeters/liter = 750 cubic centimeters
So, 750 cubic centimeters of water must be added to dilute the 400 cubic centimeters of the chemical to a 25% solution.