# Question 21437

Oct 31, 2017

Here's what I got.

#### Explanation:

By definition, a 27% aqueous sugar solution will contain $\text{27 g}$ of sugar for every $\text{100 g}$ of the solution. This means that your $\text{100-g}$ sample contains exactly $\text{27 g}$ of sugar.

Now, when you take $\frac{1}{3} \text{rd}$ of this sample, you end up with a solution that contains

$\text{27 g sugar"/3 = "9 g sugar}$

$\text{100 g solution"/3 = "33.33 g solution}$

You then add $\text{10 g}$ of sugar to this second sample. At this point, the mass of sugar will be equal to

$\text{9 g + 10 g = 19 g}$

and the mass of the solution will be

$\text{33.33 g + 10 g = 43.33 g}$

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 $\text{100 g}$ 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

$\textcolor{\mathrm{da} r k g r e e n}{\underline{\textcolor{b l a c k}{\text{% m/m = 43.85% sugar}}}}$

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%#.