# Question fba72

Apr 8, 2017

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 $\text{100 mL}$ of the final solution.

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

The initial solution contains $\text{0.25 g}$ of ascorbic acid in $\text{100 mL}$. You take this solution and add enough water to gets its total volume to $\text{250 mL}$.

You can now say that the solution contains $\text{0.25 g}$ of ascorbic acid in $\text{250 mL}$ 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 $\text{25-mL}$ 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 $\text{250 mL}$. This means that the final solution will contain $\text{0.0120 g}$ of ascorbic acid in $\text{250 mL}$ of solution.

Consequently, $\text{100 ML}$ 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

$\textcolor{\mathrm{da} r k g r e e n}{\underline{\textcolor{b l a c k}{\text{5 mg ascorbic acid/100 mL solution}}}}$

The answer is rounded to one significant figure.