# How many grams of acetic acid should be dissolved in 100.0 g of water to make a 4.0 percent (by mass) solution of vinegar?

##### 1 Answer

#### Explanation:

As you know, percent concentration by mass is defined as mass of solute, which in your case will be acetic acid, divided by mass of solution, and multiplied by

#color(blue)("% m/m" = "mass of solute"/"mass of solution" xx 100)#

Now, the trick here is to realize that adding the acetic acid will **Increase** the mass of the solution.

If the mass of glacial acetic acid, which is *pure* acetic acid, is equal to *mass of the solution* to

#m_"sol" = (100.0 + x)" g"#

You need this solution to be

#"4.0%" = (xcolor(red)(cancel(color(black)("g"))))/((100.0+x)color(red)(cancel(color(black)("g")))) xx 100#

This is equivalent to

#4.0 * (100.0+x) = 100x#

#400 = 96x implies x = 400/96 = 4.1667#

Rounded to two sig figs, the number of sig figs you have for the percent concentration of the target solution, the answer will be

#m_"acetic acid" = color(green)("4.2 g")#

So, if you add *vinegar*.