# How many grams of sugar would you need to add to water to make 235 grams of a 7% solution? using this formula: (Please Help!)

##### 1 Answer

#### Explanation:

A solution's **percent concentration by mass**, **per** **of solution**.

In your case, sugar is the *solute* and water is the *solvent*. A *solution* is formed when you dissolve a solute in a solvent.

Here's how to solve this problem *without* using the formula for percent concentration by mass, which is given to you as

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

You know that your target sugar solution must be **every**

This ratio between sugar and water is the same **regardless** of the mass of solution. In your case, you want the solution to have a mass of

#235 color(red)(cancel(color(black)("g solution"))) * overbrace("7 g sugar"/(100color(red)(cancel(color(black)("g solution")))))^(color(purple)("= 7% w/w")) = "16.45 g sugar"#

You should round this off to one **sig fig**, since that's how many sig figs you have for the percent by mass, but I'll leave it rounded to two sig figs, just for good measure

#m_"sugar" = color(green)("16 g")#

This is what the formula for percent concentration by mass actually means. If you start with

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

you can rearrange to solve for

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

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

Now plug in your values to get

#m_"solute" = (7 * "235 g")/100 = color(green)("16 g")#