Question

Question #48318

Answer 1

For part (1)

`m_"solution" = "160. g"`

`m_"solvent" = "138 g"`

Explanation:

I'll show you how to solve part (1), and leave part (2) to you as practice.

A solution's percent concentration by mass, `"% m/m"`, essentially tells you how many grams of solute you get for every `"100 g"` of solution.

In this case, your solution is said to have a `14.0%` concentration by mass, which means that you get `"14.0 g"` of solute for every `"100 g"` of solution.

As you know, the total mass of a solution is given by the mass of solute and the mass of solvent. This means that a solution's percent concentration by mass tells you how many grams of solute you have in `"100 g"` of solute + solvent mixture.

Implicitly, a `14.0%` concentration by mass also tells you that you get `"86.0 g"` of solvent for every `"100 g"` of solute + solvent mixture.

So, you know that this first solution contains `"22.4 g"` of solute. Use the percent concentration by mass to find the mass of the solution

`22.4 color(red)(cancel(color(black)("g solute"))) * overbrace("100 g solution"/(14.0color(red)(cancel(color(black)("g solute")))))^(color(purple)("14.0% by mass")) = color(green)(|bar(ul(color(white)(a/a)"160. g solution"color(white)(a/a)|)))`

This means that the mass of the solvent will be

`color(purple)(|bar(ul(color(white)(a/a)color(black)(m_"solution" = m_"solute" + m_"solvent")color(white)(a/a)|)))`

`m_"solvent" = "160. g" - "22.4 g" = color(green)(|bar(ul(color(white)(a/a)"138 g solvent"color(white)(a/a)|)))`

Both answers are rounded to three sig figs.