How many liters of water must be added to 8 liters of a 40% acid solution to obtain a 10% acid solution? Please Show All Work!
To solve this problem, we need to determine how much water must be added to 8 liters of a 40% acid solution to obtain a 10% acid solution.
Let's begin by understanding the concept of a solution. In a solution, there is a solute and a solvent. In this case, the acid is the solute, and water is the solvent.
Now, let's consider the acid content in the original solution. We have 8 liters of a 40% acid solution. This means that in those 8 liters, 40% is acid, and the remaining 60% is water.
To obtain a 10% acid solution, we need to add water. Let's assume we need to add x liters of water.
After adding x liters of water, the total volume of the solution will be (8 + x) liters.
Since we are looking for a 10% acid solution, it means that 10% of the total volume should be acid. So, 10% of (8 + x) liters should be acid.
We can set up the equation:
0.10 (8 + x) = 0.40(8)
Let's solve this equation to find x, the amount of water to be added.
0.10 (8 + x) = 0.40(8)
0.80 + 0.10x = 3.20
0.10x = 3.20 - 0.80
0.10x = 2.40
x = 2.40 / 0.10
x = 24
Therefore, 24 liters of water must be added to 8 liters of a 40% acid solution to obtain a 10% acid solution.
8 litres of 40% acid
3.2 litres acid and 4.8 litres of water
lets say you add x litres
3.2 / (8+ x) = 10%
3.2 = 0.8 + 0.1x
x = 24 litres of water needs to be added