How many centiliters of pure acid must be added to 6 centiliters of a 50% acid solution to obtain a 70% solution?
To solve this problem, we can use the concept of the mixture equation. The mixture equation states that the amount of pure substance in a solution is equal to the sum of the amounts of that substance in each component of the solution.
Let "x" represent the number of centiliters of pure acid that needs to be added.
First, let's calculate the amount of acid in the original 50% solution. The 50% solution means that 50% of the solution is acid. Therefore, we have 6 centiliters * 0.50 = 3 centiliters of acid in the original solution.
Next, let's write the mixture equation based on the total amount of acid in the final solution:
3 centiliters (from the original solution) + x centiliters (to be added) = (6 + x) centiliters (total final solution)
Now, let's set up the equation to solve for "x":
3 + x = 0.70 * (6 + x)
Simplifying the equation:
3 + x = 4.2 + 0.70x
Combining "x" terms:
x - 0.70x = 4.2 - 3
0.30x = 1.2
Dividing both sides by 0.30:
x = 1.2 / 0.30
x = 4 centiliters
Therefore, you would need to add 4 centiliters of pure acid to obtain a 70% solution.