Question

Question #33e61

Answer 1

`"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")`