Question #a9870
1 Answer
Explanation:
All you have to do here is keep track of the number of moles of solute as you progress towards the target solution.
For instance, the initial solution contains
#51.0 color(red)(cancel(color(black)("mL"))) * (1color(red)(cancel(color(black)("L"))))/(10^3color(red)(cancel(color(black)("mL")))) * "1.30 moles solute"/(1color(red)(cancel(color(black)("L")))) = "0.0663 moles solute"#
When you dilute this solution to a total volume of
#"0.0663 moles solute " -># in a total volume of#"288 mL"#
Next, you take
#"144 mL" = "288 mL"/2#
This tells you that the
#"0.0663 moles solute"/2 = "0.03315 moles solute " -># in a volume of#"144 mL"#
When you're diluting this sample by adding
#"144 mL " + " 161 mL" = "305 mL"#
This solution will contain the same number of moles of solute as you had in the
#"0.03315 moles solute"/(305 * 10^(-3)"L") = color(green)(bar(ul(|color(white)(a/a)color(black)("0.109 M")color(white)(a/a)|)))#
The answer is rounded to three sig figs.
ALTERNATIVE APPROACH
You can solve this problem by using the dilution factor
#color(blue)(bar(ul(|color(white)(a/a)"DF" = V_"final"/V_"initial"color(white)(a/a)|)))#
Here
In essence, the dilution factor tells you how concentrated the initial solution was compared with the diluted solution.
So, for the first dilution, you have
#"DF"_1 = (288 color(red)(cancel(color(black)("mL"))))/(51.0color(red)(cancel(color(black)("mL")))) = 5.647#
This means that the
Now look at the second dilution -- this time, the starting volume is
#"DF"_2 = (305color(red)(cancel(color(black)("mL"))))/(144color(red)(cancel(color(black)("mL")))) = 2.118#
This means that the sample we took from the
We've thus performed a serial dilution. The overall dilution factor,
#color(blue)(bar(ul(|color(white)(a/a)"DF"_ "serial" = "DF"_ 1 xx "DF"_ 2color(white)(a/a)|)))#
You will have
#"DF"_"serial" = 5.647 * 2.118 = 11.96#
This means that the initial
Therefore, the concentration of the target solution is
#c_"target" = c_"initial"/"DF"_"serial"#
#c_"target" = "1.30 M"/11.96 = color(green)(bar(ul(|color(white)(a/a)color(black)("0.109 M")color(white)(a/a)|)))#