Question #48318

1 Answer
Apr 21, 2016

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.