Question

A chemistry professor has a solution that is 60% base and another solution that is 20% base. How much of each solution should be used to make 120L of solution that is 52% base?

Answer 1

To create a 120L solution with 52% base, the professor needs to mix 96L of the 60% solution and 24L of the 20% solution by solving a system of equations involving the total volume and the concentration of the base.

Step-by-step explanation:

How to Mix Solutions with Different Concentrations

To make 120L of a solution that is 52% base from solutions that are 60% and 20% base respectively, we can use a system of equations. Let x represent the amount of the 60% solution and y represent the amount of the 20% solution. The two equations to solve are:

1. x + y = 120 (the total volume of the solution needed)
2. 0.60x + 0.20y = 0.52 × 120 (the total percentage of the base in the final solution)

To solve this system, we can multiply the second equation by 100 to get rid of the decimals:

• 60x + 20y = 6240

Reducing the second equation by dividing by 20 gives:

• 3x + y = 312

Subtracting the first equation from this equation gives:

• 2x = 192

So, x = 96L (the amount of the 60% solution)

We can then substitute x back into the first equation to find y:

• y = 120 - 96
• y = 24L (the amount of the 20% solution)

Therefore, to make a 120L solution of 52% base, the chemistry professor should mix 96L of the 60% solution with 24L of the 20% solution.