# Question 82ae2

Oct 6, 2017

30%

#### Explanation:

The trick here is to realize that a solution's mass by mass percent concentration, $\text{m/m %}$, is defined as the number of grams of solute, which in your case is sugar, present in $\text{100 g}$ of solution.

When you add $\text{40 g}$ of sugar to $\text{100 g}$ of water, the mass of the solution will be

$\text{40 g + 100 g = 140 g}$

Now, you know that this solution contains $\text{40 g}$ of sugar in $\text{140 g}$ of solution, so use the known composition of the solution to find the number of grams of sugar present in $\text{100 g}$ of this solution.

100 color(red)(cancel(color(black)("g solution"))) * "40 g sugar"/(140color(red)(cancel(color(black)("g solution")))) = "28.6 g sugar"

This means that your solution has a mass by mass percent concentration of

$\textcolor{\mathrm{da} r k g r e e n}{\underline{\textcolor{b l a c k}{\text{% m/m = 30% sugar}}}}$

The answer must be rounded to one significant figure, the number of sig figs you have for your values.

So, you can say that dissolving $\text{40 g}$ of sugar in $\text{100 g}$ of water will produce a solution that is 30color(red)(%)# sugar, i.e. it contains $\text{30 g}$ of sugar for every $\textcolor{red}{\text{100 g}}$ of solution.