Question

Question #6a5d8

Answer 1

`"364 g " -> " lactose"`
`"196 g " -> " water"`

Explanation:

So, you know that your target solution has a total mass of `"560 g"`, and that its percent concentration by mass is equal to `65%`.

What that means is that every `"100 g"` of solution must contain `"65 g"` of solute. In your case, the target solution needs to contain `"65 g"` of lactose per `"100 g"`.

So, you know that

`color(blue)("% w/w" = "mass of solute"/"mass of solution" xx 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 `"560 g"`, it follows that the mass of water needed to make this solution will be

`m_"sol" = m_"solute" + m_"solvent"`

`m_"water" = "560 g" - "364 g" = "196 g"`

Therefore, if you mix `"196 g"` of water with `"364 g"` of lactose, you will get a final solution that is `"65% w/w"` lactose.