Question #48318

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.