Question #fba72

1 Answer
Apr 8, 2017

Answer:

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.