# Question 6a5d8

Nov 29, 2015

$\text{364 g " -> " lactose}$
$\text{196 g " -> " water}$

#### Explanation:

So, you know that your target solution has a total mass of $\text{560 g}$, and that its percent concentration by mass is equal to 65%.

What that means is that every $\text{100 g}$ of solution must contain $\text{65 g}$ of solute. In your case, the target solution needs to contain $\text{65 g}$ of lactose per $\text{100 g}$.

So, you know that

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

If $x$ represents the mass of lactose needed to make this solution, you can say that you have

 ( x )/"560 g" xx 100 = 65%

The value of $x$ will come out to be

x = (65 * "560 g")/100 = "364 g"#

Since the total mas of the solution is equal to $\text{560 g}$, it follows that the mass of water needed to make this solution will be

${m}_{\text{sol" = m_"solute" + m_"solvent}}$

${m}_{\text{water" = "560 g" - "364 g" = "196 g}}$

Therefore, if you mix $\text{196 g}$ of water with $\text{364 g}$ of lactose, you will get a final solution that is $\text{65% w/w}$ lactose.