25 mL of a #"10% m/v"# #NH_4Cl# solution is diluted to 250 mL. What is the final concentration of the #NH_4Cl#?
You can actually solve this problem without using any formulas, provided that you have a clear understanding of what it means to dilute a solution.
The underlying principle behind a dilution is that the number of moles of solute, i.e. the mass of solute, remains constant.
The concentration of the original solution decreases following a dilution because the volume of the solution is increased by adding more solvent.
Now, your original solution is
In other words, you get one part solute for every
Notice that you dilute this solution to a volume that is ten times bigger than the initial volume.
Since the mass of solute remained constant, you can say that the diluted solution contains one part solute for every
This means that the concentration of the solution decreased by a factor of
#"% m/v" = 1/10 * "10%" = color(green)(|bar(ul(color(white)(a/a)1%color(white)(a/a)|)))#
The ratio that exists between the final volume and the initial volume of the solution is called the dilution factor.
#color(blue)(|bar(ul(color(white)(a/a)"D.F." = V_"final"/V_"initial"color(white)(a/a)|)))#
As you can see, the dilution factor allows you to calculate the concentration of the diluted solution by simply looking at the two two volumes.