How much pure acid must be added to 2 liters of a 10% solution of acid to obtain a mixture that is 20% acid?
amount of pure acid added ---- x litres
.1(2) + x = .2(x+2)
2 + 10x = 2(x+2)
2+10x = 2x + 4
8x = 2
x = 1/4 L
To solve this problem, we need to find out how much pure acid should be added to a given 2-liter solution of 10% acid concentration in order to create a final mixture with a 20% acid concentration. Here's how we can calculate it:
Let's start by understanding the information we have:
- We have a 2-liter solution of acid with a concentration of 10%.
- We want to know the amount of pure acid we need to add to this solution to achieve a 20% concentration.
To solve this, we can follow these steps:
Step 1: Calculate the amount of acid in the initial solution:
The initial solution has a volume of 2 liters and a concentration of 10%. Therefore, the amount of acid in this solution is given by:
Amount of acid = Volume of solution × Concentration of acid
= 2 liters × 10%
= 0.2 liters (or 200 ml)
Step 2: Calculate the total volume of the final mixture:
Since we are adding some pure acid to the initial solution, the total volume of the final mixture will be the sum of the initial solution volume and the amount of pure acid added, which is 2 liters + X (where X is the amount of pure acid to be added).
Step 3: Set up the equation for acid concentration:
We know that the final concentration we want to achieve is 20%. The equation for concentration is:
Final concentration = (Amount of acid in the final mixture) / (Total volume of the final mixture)
Step 4: Substitute the values into the equation and solve for X:
20% = (Amount of acid in the initial solution + X) / (2 liters + X)
Now, we can solve for X by cross-multiplying:
0.2(2 liters + X) = (0.2 liters + X)
0.4 liters + 0.2X = 0.2 liters + X
0.2X - X = 0.2 liters - 0.4 liters
-0.8X = -0.2 liters
X = (-0.2 liters) / (-0.8)
X = 0.25 liters (or 250 ml)
So, in order to obtain a mixture that is 20% acid, we need to add 0.25 liters (or 250 ml) of pure acid to the initial 2-liter solution of 10% acid.