Question #47267

1 Answer
Jun 1, 2016

Answer:

Here's what I got.

Explanation:

The key to this problem is the density of the solution.

The density of a substance essentially tells you the mass of one unit of volume of that substance. In your case, the density of the solution is said to be #2.5# grams per milliliter, which means that one unit of volume will be #"1 mL"#.

So, the density of the solution tells you that every #"1 mL"# of this solution has a mass of #"2.5 g"#.

You can thus use density as a conversion factor to help you convert between the mass of the solution and the volume it occupies.

Now, the problem tries to put you off track a little by telling you that

1000 mL of an extremely viscous solution has a density of #2.5# grams/milliliter...

It doesn't matter how much of this solution you have, its density will always be the same.

This means that you can ignore the given #"1000 mL"# altogether, that information is not important in this context.

A fluid ounce is approximately equal to

#color(purple)(|bar(ul(color(white)(a/a)color(black)("1 fl oz " = " 29.57 mL")color(white)(a/a)|)))#

Use this conversion factor to go from fluid ounces to milliliters

#2 color(red)(cancel(color(black)("fl oz"))) * "29.57 mL"/(1color(red)(cancel(color(black)("fl oz")))) = "59.14 mL"#

Now, if #"1 mL"# of this solution has a mass of #"2.5 g"#, it follows that #"59.14 mL"# will have a mass of

#59.14 color(red)(cancel(color(black)("mL"))) * overbrace("2.5 g"/(1color(red)(cancel(color(black)("mL")))))^(color(blue)("the density of the solution")) = "147.85 g"#

You should round this off to one sig fig, the number of sig figs you have for the volume of the solution, i.e. #2# fluid ounces, but I'll leave it rounded to two sig figs

#"mass of 2 fl oz" = color(green)(|bar(ul(color(white)(a/a)color(black)("150 g")color(white)(a/a)|)))#

Finally, to convert this to ounces, use the conversion factor

#color(purple)(|bar(ul(color(white)(a/a)color(black)("1 oz " = " 28.35 g")color(white)(a/a)|)))#

You will have

#150 color(red)(cancel(color(black)("g"))) * "1 oz"/(28.35color(red)(cancel(color(black)("g")))) = color(green)(|bar(ul(color(white)(a/a)color(black)("5.3 oz")color(white)(a/a)|)))#