A chemistry laboratory has supplies of two sulfuric acid solutions only. One is 10% concentrated and the other is 50% concentrated. How much of each solution should be mixed to make a 40 mL 25% sulfuric acid solution?
To find the amount of each solution to be mixed, we can set up a mathematical equation based on the given information.
Let's assume x mL of the 10% sulfuric acid solution needs to be mixed. Therefore, the amount of the 50% sulfuric acid solution that needs to be mixed would be (40 - x) mL, as the total volume of the final solution is 40 mL.
Now, let's calculate the amount of sulfuric acid present in each solution:
Amount of sulfuric acid in the 10% solution = 10% of x mL
Amount of sulfuric acid in the 50% solution = 50% of (40 - x) mL
To find the total amount of sulfuric acid in the final mixture, we need to add the amounts of acid from the two solutions:
Total amount of sulfuric acid in the final mixture = Amount of sulfuric acid in the 10% solution + Amount of sulfuric acid in the 50% solution
Since we want a 25% sulfuric acid solution, the total amount of sulfuric acid in the final mixture should be 25% of 40 mL.
Therefore, we can set up the equation:
0.10x + 0.50(40 - x) = 0.25(40)
Now, let's solve the equation to find the value of x:
0.10x + 20 - 0.50x = 10
-0.40x = 10 - 20
-0.40x = -10
x = (-10) / (-0.40)
x = 25
Hence, 25 mL of the 10% sulfuric acid solution and (40 - 25) mL (i.e., 15 mL) of the 50% sulfuric acid solution should be mixed to make a 40 mL 25% sulfuric acid solution.