Question #682c7
1 Answer
Here's how you could do that.
Explanation:
For starters, you can only dilute the original solution by adding water, the solvent. In any dilution, the amount of solute remains constant.
So, your starting solution is
Let's say that the starting solution has a volume
#V color(red)(cancel(color(black)("mL solution"))) * "83 mL alcohol"/(100color(red)(cancel(color(black)("mL solution")))) = (83/100V)color(white)(.)"mL alcohol"#
The diluted solution must have a
The volume of the diluted solution needed to account for this concentration is
#(83/color(blue)(cancel(color(black)(100)))V) color(red)(cancel(color(black)("mL alcohol"))) * (color(blue)(cancel(color(black)(100))) "mL solution")/(42color(red)(cancel(color(black)("mL alcohol")))) = (83/42V)color(white)(.)"mL solution"#
Now, your goal here is to figure out how much water must be added to the starting solution to increase its volume from
If you take
#Vcolor(white)(.)"mL" + x = (83/42V)color(white)(.)"mL"#
This gets you
#x = 83/42Vcolor(white)(.)"mL" - Vcolor(white)(.)"mL" = color(darkgreen)(ul(color(black)((41/42)Vcolor(white)(.)"mL")))#
Therefore, you can say that in order to dilute a solution from