Question

Question #fba72

Answer 1

Here's what I got.

Explanation:

The question wants you to figure out how many milligrams of ascorbic acid, also known as Vitamin C, are present in `"100 mL"` of the final solution.

The idea here is that you're diluting the initial solution twice, first when you make its total volume to `"250 mL"` and then when you take the `"25-mL"` sample and make it up to `"250 mL"`.

The initial solution contains `"0.25 g"` of ascorbic acid in `"100 mL"`. You take this solution and add enough water to gets its total volume to `"250 mL"`.

You can now say that the solution contains `"0.25 g"` of ascorbic acid in `"250 mL"` of solution. As you know, solutions are homogeneous mixtures, which implies that they have the same composition throughout.

You can thus use the composition of the solution after the first dilution as a conversion factor to help you determine the mass of ascorbic acid present in the `"25-mL"` sample

`25 color(red)(cancel(color(black)("mL solution"))) * "0.25 g ascorbic acid"/(250 color(red)(cancel(color(black)("mL solution")))) = "0.0120 g ascorbic acid"`

You then take this sample and add enough water to gets its total volume to `"250 mL"`. This means that the final solution will contain `"0.0120 g"` of ascorbic acid in `"250 mL"` of solution.

Consequently, `"100 ML"` of this solution will contain

`100 color(red)(cancel(color(black)("mL solution"))) * "0.0120 g ascorbic acid"/(250 color(red)(cancel(color(black)("mL solution")))) = "0.0048 g ascorbic acid"`

Convert this to milligrams

`0.0048 color(red)(cancel(color(black)("g"))) * (10^3color(white)(.)"mg")/(1color(red)(cancel(color(black)("g")))) = "4.8 mg"`

Therefore, you can say that the final solution contains

`color(darkgreen)(ul(color(black)("5 mg ascorbic acid/100 mL solution")))`

The answer is rounded to one significant figure.