Question #d80bb

1 Answer
Nov 8, 2016

Answer:

Here's how you can do that.

Explanation:

The idea here is that you need to work with the solution's percent concentration by mass, #"%m/m"#, to figure out how much solute you have in your sample.

So, the solution's percent concentration by mass is a measure of how many grams of solute you get in #"100 g"# of solution. Indirectly, this can help you figure out how many grams of solvent you have in #"100 g"# of solution, since

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

In your case, a #"17.3% m/m"# solution will contain #"17.3 g"# of solute for every #"100 g"# of solution. This is, of course, equivalent to saying that #"100 g"# of this solution contains

#m_"solvent" = overbrace("100 g")^(color(blue)("mass of solution")) - overbrace("17.3 g")^(color(darkgreen)("mass of solute")) = "82.7 g solvent"#

Now all you have to do is scale up this proportion to figure out how many grams of solution would contain #"355.2 g"# of solvent

#355.2 color(red)(cancel(color(black)("g solvent"))) * "100 g solution"/(82.7 color(red)(cancel(color(black)("g solvent")))) = color(green)(bar(ul(|color(white)(a/a)color(black)("429.5 g solution")color(white)(a/a)|)))#

Therefore, the mass of solute must be

#m_"solute" = "429.5 g" - "355.2 g" = color(green)(bar(ul(|color(white)(a/a)color(black)("74.3 g solute")color(white)(a/a)|)))#