Question #21437

1 Answer
Oct 31, 2017

Answer:

Here's what I got.

Explanation:

By definition, a #27%# aqueous sugar solution will contain #"27 g"# of sugar for every #"100 g"# of the solution. This means that your #"100-g"# sample contains exactly #"27 g"# of sugar.

Now, when you take #1/3"rd"# of this sample, you end up with a solution that contains

#"27 g sugar"/3 = "9 g sugar"#

in about

#"100 g solution"/3 = "33.33 g solution"#

You then add #"10 g"# of sugar to this second sample. At this point, the mass of sugar will be equal to

#"9 g + 10 g = 19 g"#

and the mass of the solution will be

#"33.33 g + 10 g = 43.33 g"#

In order to find the solution's percent concentration by mass, you need to figure out the number of grams of sugar present in exactly #"100 g"# of this solution.

To do that, use the known composition of the solution as a conversion factor

#100 color(red)(cancel(color(black)("g solution"))) * "19 g sugar"/(43.33 color(red)(cancel(color(black)("g solution")))) = "43.85 g sugar"#

You can thus say that this solution has

#color(darkgreen)(ul(color(black)("% m/m = 43.85% sugar")))#

I'll leave the answer rounded to four sig figs because it comes very close to one of the options given to you, i.e. (4) #43.84%#.