A cellulose solution contains 5% cellulose by weight in water. It is to be diluted to 4.0 % using a 1% solution of cellulose in water. Determine the kilograms of 1% solution required to dilute 100 kg of the 5% solution.
To solve this problem, we need to determine the amount of the 1% solution required to dilute 100 kg of the 5% solution.
Let's start by finding the amount of cellulose in the 5% solution. We know that the solution contains 5 kg of cellulose for every 100 kg of the solution.
Now we need to determine how much water is in the 5% solution. Since the solution is 5% cellulose by weight, the remaining 95% must be water. Therefore, there are 95 kg of water in the 5% solution.
Our goal is to dilute the 5% solution to 4% using the 1% solution. To do this, we need to calculate the amount of cellulose in the final diluted solution.
We know that the diluted solution will contain 4 kg of cellulose for every 100 kg of the solution, as it is 4%.
Let's assume we need x kilograms of the 1% solution to dilute the 100 kg of the 5% solution.
So the amount of cellulose in the 1% solution will be 0.01x kg.
Now we can set up an equation to solve for x by equating the amount of cellulose in the original 5% solution to the amount of cellulose in the final diluted solution:
5 kg = 0.01x kg + 4 kg
Simplifying the equation, we subtract 0.01x from both sides:
1 kg = 0.01x
Divide both sides by 0.01:
x = 100 kg
Therefore, you would need 100 kg of the 1% solution to dilute 100 kg of the 5% solution.