in chemistry class, todd has 1 liter of a 23% sulfuric acid solution, how much of a 15% sulfuric acid solution must he mix with the 1 liter of 23% solution to make a 18% solution?

Algebraic representations of the sulfuric acid solutions would be:

.23A = S
.15B = S
.18C = S

To solve this problem, we need to use the concept of mixing two solutions with different concentrations to obtain a desired concentration.

Let's break down the problem:

1) Let's calculate how much of the 23% sulfuric acid solution Todd has in terms of pure sulfuric acid (H2SO4) content:

1 liter * 0.23 = 0.23 liters of pure H2SO4

2) Now let's calculate how much of the 15% sulfuric acid solution Todd needs to mix in order to obtain a final solution of 18% sulfuric acid:

Let's assume Todd needs x liters of the 15% sulfuric acid solution.

x liters * 0.15 = 0.15x liters of pure H2SO4

3) Now let's set up an equation to represent the problem:

The total volume of the final solution will be the sum of the volumes of the 23% and 15% sulfuric acid solutions:

1 liter + x liters = 1 + x liters

The total amount of pure H2SO4 in the final solution will be the sum of the amounts from both solutions:

0.23 liters + 0.15x liters = 0.23 + 0.15x liters

The final concentration of the solution will be the proportion of pure H2SO4 to the total volume of the solution, expressed as a percentage:

(0.23 + 0.15x) / (1 + x) * 100% = 18%

4) Now, we can solve the equation to find the value of x (the amount of the 15% sulfuric acid solution Todd needs to mix):

First, let's multiply both sides of the equation by (1 + x) to get rid of the denominator:

0.23 + 0.15x = 18/100 * (1 + x)

0.23 + 0.15x = 0.18 + 0.18x

0.15x - 0.18x = 0.18 - 0.23

-0.03x = -0.05

x = (-0.05) / (-0.03)

x ≈ 1.67 liters

Therefore, Todd needs to mix approximately 1.67 liters of the 15% sulfuric acid solution with the 1 liter of the 23% sulfuric acid solution to obtain a 18% sulfuric acid solution.