A student accidentally poured 2 liters of 20% acid solution into a container having 10 liters of 15% acid solution. What is the concentration of the new solution?

Question

Julia Adams · Accepted Answer

Almost 16%

The formula you have is #(2*0.20)+(10*0.15)=12*x#. The final volume is 12 liters, and your final percentage is x. The result of solving the equation is x:

Isaiah Anthony · Answer

undefined To find the concentration of the new solution, we can use the method of mixture. First, calculate the total amount of acid in both solutions. Then, determine the total volume of the new solution. Finally, divide the total amount of acid by the total volume to find the concentration of the new solution.

1. Calculate the amount of acid in the 2 liters of 20% solution:
   $ \text{Amount of acid} = \text{Volume} \times \text{Concentration} $
   $ \text{Amount of acid} = 2 \, \text{liters} \times 0.20 $

2. Calculate the amount of acid in the 10 liters of 15% solution:
   $ \text{Amount of acid} = \text{Volume} \times \text{Concentration} $
   $ \text{Amount of acid} = 10 \, \text{liters} \times 0.15 $

3. Find the total amount of acid:
   $ \text{Total amount of acid} = \text{Amount of acid from 20% solution} + \text{Amount of acid from 15% solution} $

4. Find the total volume of the new solution:
   $ \text{Total volume} = \text{Volume of 20% solution} + \text{Volume of 15% solution} $

5. Calculate the concentration of the new solution:
   $ \text{Concentration} = \frac{\text{Total amount of acid}}{\text{Total volume}} $