Question #ff032
1 Answer
Explanation:
The thing to remember about serial dilutions is that the total dilution factor is the product of the individual dilution factors that you use for each dilution.
For a serial dilution that consists of
#color(blue)(ul(color(black)("DF"_ "total" = "DF"_ 1 xx "DF"_ 2 xx ... xx "DF"_ n)))#
Now, the dilution factor is simply the ratio that exists between
- the volume of the diluted solution and the volume of the concentrated solution
- the concentration of the concentrated solution and the concentration of the diluted solution
Mathematically, this is written as
#"DF" = V_"diluted"/V_"concentrated" = c_"concentrated"/c_"diluted"#
In your case, you're working with a
#{(V_"diluted" = "100.00 mL"), (V_"concentrated" = "5.00 mL") :}#
This means that the dilution factor for one dilution will be
#"DF"_ 1 = (100.00 color(red)(cancel(color(black)("mL"))))/(5.00color(red)(cancel(color(black)("mL")))) = color(blue)(20)#
You can thus say that the concentration of the solution after the first dilution will be equal to
#c_"diluted 1" = c_"concentrated 1"/"DF"_ 1 #
#c_"diluted 1" = "5.00 M"/color(blue)(20) = "0.25 M"#
Now, you're doing
#"DF"_ "total" = "DF"_ 1 xx "DF"_ 1 xx "DF"_ 1#
#"DF"_ "total" = color(blue)(20) xx color(blue)(20) xx color(blue)(20) = color(blue)(8000)#
You can thus say that the concentration of the diluted solution after the third and final dilution will be
#c_"diluted 3" = c_"concentrated 1"/"DF"_ "total"#
#c_"diluted 3" = "5.00 M"/color(blue)(8000) = "0.000625 M" -># rounded to three sig figs
As you can see, the dilution factor for an individual dilution tells how concentrated the concentrated solution was compared with the diluted solution.
For a dilution factor of
After