# Question 45384

Aug 14, 2017

15.0%

#### Explanation:

I'll assume you mean to say $85.0$ grams of water (units were left off).

We're asked to find the percent by mass of sucrose, given how much is dissolved in a known amount of water.

The formula for mass percentage of a substance $x$ is given by

$\underline{\overline{| \stackrel{\text{ ")(" "%"mass"color(white)(l)x = ("mass of"color(white)(l)x)/("total mass") xx 100%" }}{|}}}$

(Here, $x$ represents sucrose.)

The total mass of the solution is the mass of the *sucrose plus the mass of *water:

$\text{total mass" = overbrace(15.0color(white)(l)"g")^"sucrose" + overbrace(85.0color(white)(l)"g")^"water" = color(red)(ul(100.0color(white)(l)"g}$

The mass percentage of sucrose is therefore

color(blue)(%color(white)(l)"mass sucrose") = (15.0color(white)(l)"g sucrose")/(color(red)(100.0color(white)(l)"g solution")) xx 100% = color(blue)(ulbar(|stackrel(" ")(" "15.0%" ")|)#