a chemist wants to create a solution that is 36% acid. How many liters of a 60% acid solution must be added to 30 liters of a 15% acid solution to obtain this 36% acid mixture?
.15(30) +.60x = .36(x+30)
solve for x
To solve this problem, we can use the concept of mixture problems. Let's break down the given information:
Let's assume that x liters of the 60% acid solution need to be added to obtain the desired mixture.
Step 1: Calculate the amount of acid in the initial 15% solution.
The amount of acid in the 15% solution can be calculated using the formula:
Amount of acid = (Percentage of acid / 100) * volume of solution
For the initial 15% acid solution:
Amount of acid in the 15% solution = (15 / 100) * 30 liters
Step 2: Calculate the amount of acid in the 60% acid solution.
For the 60% acid solution:
Amount of acid in the 60% solution = (60 / 100) * x liters
Step 3: Calculate the total amount of acid in the final mixture.
The total amount of acid in the final mixture is the sum of the amounts of acid in the initial 15% solution and the additional 60% solution:
Total amount of acid = Amount of acid in the 15% solution + Amount of acid in the 60% solution
Step 4: Determine the concentration of the final mixture.
The concentration of the final mixture is the ratio of the total amount of acid to the total volume of the mixture:
Concentration of final mixture = (Total amount of acid / Total volume of mixture) * 100
We need to solve for x, the number of liters of the 60% acid solution that must be added to obtain the desired 36% acid mixture.
Using the equation, we can set up the equation:
(15/100)*30 + (60/100)*x = (36/100)*(30 + x)
Simplifying the equation:
(15/100)*30 + (60/100)*x = (36/100)*30 + (36/100)*x
Multiply both sides by 100 to eliminate the fractions:
15*30 + 60x = 36*30 + 36x
Step 5: Finally, solve the equation for x to find the number of liters of the 60% acid solution needed.
450 + 60x = 1080 + 36x
Simplify the equation:
24x = 630
Divide both sides by 24:
x = 26.25
Therefore, to obtain a 36% acid solution, the chemist needs to add 26.25 liters of the 60% acid solution to 30 liters of the 15% acid solution.