What is the new concentration of a #10%# solution if we dilute a sample from #"25.0 mL"# to #"500 mL"# ?

Question

Naomi Aronson · Accepted Answer

#0.5%#

The idea here is that when you're performing a dilution, the concentration of the solution decreases by the same factor (known as the dilution factor) as the volume increases.

#"volume" uarr "by a factor"color(white)(.)color(blue)("DF") implies "concentration" darr "by the same factor"color(white)(.)color(blue)("DF")#

In your case, the volume of the solution increases from #"25.0 mL"# to #"500 mL"#, which means that the dilution factor is equal to

#"DF" = (500 color(red)(cancel(color(black)("mL"))))/(25.0color(red)(cancel(color(black)("mL")))) = color(blue)(20)#

Now remember, the same dilution factor is applied to the concentration of the solution, i.e. the concentration of the diluted solution must be #color(blue)(20# times lower than the concentration of the stock solution.

This means that the concentration of the diluted solution will be

#"% diluted" = (10%)/color(blue)(20) = color(darkgreen)(ul(color(black)(0.5%)))#

The answer is rounded to one significant figure.

Peyton Adams · Answer

undefined The new concentration of the solution is 0.5%.