Question #33e61

1 Answer
May 14, 2016

Answer:

#"25 L"#

Explanation:

Molarity is simply a measure of how many moles of solute you get per liter of solution.

In this regard, a #"1 molar"# solution will contain #1# mole of solute for every liter of solution. Right from the start, you should be able to tell that since the #"2 molar"# solution si less concentrated than the #"5 molar"# solution, you're going to need a bigger volume to get the same number of moles of solute.

The #"10 molar"# solution contains #10# moles of solute per liter of solution, which means that #"5 L"# of solution will contain

#5color(red)(cancel(color(black)("L solution"))) * "10 moles solute"/(1color(red)(cancel(color(black)("L solution")))) = "50 moles solute"#

Now, the #"2 molar"# solution contains #2# moles of solute per liter of solution, which means that #50# moles of solute will correspond to

#50 color(red)(cancel(color(black)("moles solute"))) * "1 L solution"/(2color(red)(cancel(color(black)("moles solute")))) = color(green)(|bar(ul(color(white)(a/a)"25 L solution"color(white)(a/a)|)))#

Notice that since the first solution is five times as concentrated as the second solution

#color(blue)("10 molar") color(white)(a)"vs."color(white)(a) color(red)("2 molar")#

the volume of the second solution that will contain the same number of moles as the first solution will be five times bigger than the volume of the first solution

#color(red)("25 L")color(white)(a) "vs." color(white)(a) color(blue)("5 L")#