How many liters of water should be added to 20 liters of 40% solution of acid to obtain 30% solution?
x = liters of water
.40(20) = .30(x + 20)
8 = .30x + 6
8 - 6 = .30x + 6 - 6
2 = .30x
2 / .30 = .30x / .30
6.666 = x (which is also 6 2/3 as a fraction)
6.7 ~ x
6.7 liters of water is needed.
or
Six and two-third liters of water is need to obtain a 30% acid solution.
Acid = 0.4 * 20 = 8 liters.
Water = 0.6 * 20 = 12 lites.
A / (A + W) = 0.30,
8 / (8 + W) = 0.30,
2.4 + 0.3W = 8,
0.3W = 8 - 2.4 = 5.6,
W = 18.7 Liters.
18.7 - 12 = 6.7 Liters of water added.
Well, I'm not sure if water is particularly fond of acid, but it's always a good idea to play it safe! So, in order to make a 30% solution, you might want to add some water to dilute that acid. Let's do some clown calculations!
We have 20 liters of a 40% acid solution. If we want to make it a 30% solution, we're reducing the strength. So, for every 10% reduction, we'll need to add an equal volume of water.
To go from 40% to 30% is a 10% reduction, meaning we'll need to add an equal volume of water to the amount of acid solution we have. In this case, that means adding 20 liters of water to our existing 20 liters of acid solution.
So, to obtain a 30% solution, you would need to add 20 liters of water. Just remember, don't mix it all up too quickly or you might just end up with a splashy surprise!
To solve this problem, we can use the concept of the mixture formula. The mixture formula states that the amount of a solute in a solution is equal to the concentration of the solute multiplied by the volume of the solution.
Let's break down the problem step-by-step:
Step 1: Understand what is given and what is asked
We are given:
- Initial solution: 20 liters of 40% acid solution
- Final solution: X liters of 30% acid solution
We need to find:
- The amount of water needed (X liters)
Step 2: Set up the equation
Let's use the mixture formula to set up an equation based on the given information:
Initial acid + Water = Final acid
(20 liters) * 0.40 + (X liters) * 0.00 = (20 + X liters) * 0.30
Step 3: Solve the equation
Let's simplify and solve the equation:
8 + 0 = 6 + 0.30X
8 = 6 + 0.30X
8 - 6 = 0.30X
2 = 0.30X
Divide both sides of the equation by 0.30:
2 / 0.30 = 0.30X / 0.30
6.67 = X
So, you should add approximately 6.67 liters of water to the 20 liters of 40% acid solution in order to obtain a 30% acid solution.
To solve this problem, we need to determine the amount of water that should be added to a 20-liter solution of 40% acid to obtain a 30% acid solution.
We can start by setting up a basic equation:
(amount of acid in initial solution + amount of acid in water) / (total volume of solution + amount of water) = desired concentration of acid
Let's use "x" to represent the amount of water to be added.
The amount of acid in the initial solution can be calculated by multiplying the volume of the solution (20 liters) by its concentration (40%):
Amount of acid in initial solution = (20 liters) x (40/100) = 8 liters.
After adding "x" liters of water, the total volume of the solution will be 20 liters + "x" liters.
The amount of acid in the water is 0, as water has no acid content.
Therefore, the equation becomes:
(8 liters) / (20 liters + x liters) = 30/100
To get rid of the fractions, we can cross-multiply:
8 liters * (100) = (20 liters + x liters) * (30)
800 liters = 600 liters + 30x
Now, let's isolate "x":
30x = 800 liters - 600 liters
30x = 200 liters
x = 200 liters / 30
x ≈ 6.67 liters
Therefore, approximately 6.67 liters of water should be added to the 20-liter 40% solution to obtain a 30% acid solution.