# 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!)

Feb 11, 2016

$\text{16 g}$

#### Explanation:

A solution's percent concentration by mass, $\text{% w/w}$, basically tells you what mass of solute you get per $\text{100 g}$ 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

$\textcolor{b l u e}{\text{% w/w" = "mass of solute"/"mass of solution} \times 100}$

You know that your target sugar solution must be $\text{7% w/w}$. This means that every $\text{100 g}$ of this solution must contain $\text{7 g}$ of sugar.

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 $\text{235 g}$. Since it must contain $\text{7 g}$ of sugar for every $\text{100 g}$ of solution, you can say that

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

$\text{% w/w" = m_"solute"/m_"solution} \times 100$

you can rearrange to solve for ${m}_{\text{solute}}$, which is the mass of sugar

$\text{% w/w" * m_"solution" = m_"solute} \cdot 100$

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

Now plug in your values to get

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