# Question #a6a3b

##### 1 Answer

#### Explanation:

Your answer is a little off because the *total mass of the solution* **includes** the mass of the added sugar.

You start with

When you add the sugar, the mass of the solution will *increase*

#m_"solution" = m_"water" + m_"sigar"#

#m_"solution" = 100 + 4 = "104 g"#

A solution's percent cocnetration by mass is calculated by dividing the mass of the solute, in your case sugar, by the **total mass of the solution**, then multiplying the result by 100.

#"% w/w" = m_"solute"/m_"solution" * 100#

In your case, this means

#m_"sugar"/m_"solution" * 100 = "% w/w"#

#(4color(red)(cancel(color(black)("g"))))/(104color(red)(cancel(color(black)("g")))) * 100 = color(green)(3.85%)#

Now, an important thing to look out for is the number of sig figs. As it is written, the information you provide justifies an answer rounded to one sig fig - this is because you only gave one sig fig for the volume of water.

In this case, the answer would indeed by

#"% w/w" = 4#

However, I assume that you are supposed to use three sig figs for the answer, which implies that the volume of water is actually

Anyway, the important thing to remember is that for percent concetrations by mass you need the mass of the solute and the **mass of the solution**, i.e. solute + solvent.