Question

If the absorbance of a solution of copper(II) ion decreases by 41.00% upon dilution, what volume of water was added to 20.0 mL of a 1.20 M solution of Cu2+(aq)?

Answer 1

According to a so-called Beer-Lambert law, the absorbance is linearly proportional to the concentration of the solution:

$A=eCl;$

, where e - absorbance coefficient, C - molar concentration in mol/L and l is a width of the liquid layer.

Thus, we shall try to modify the formula to get the right expression for the concentration of the diluted solution:

$A_1=eC_1l ;$

$A_2=eC_2l;$

$\eta=\frac{A_1-A_2}{A_1}=\frac{el(C_1-C_2)}{elC_1}=\frac{C_1-C_2}{C_1};$

$\eta C_1=C_1-C_2,$

$C_2=C_1(1-\eta),$

$n=C_1V_1,$

$С_2=\frac{n}{V_1+V}=\frac{C_1V_1}{V_1+V}=C_1(1-\eta),$

$\frac{V_1}{V_1+V}=1-\eta,$

Now, we can find a volume of water added:

$V=V_1(\frac{\eta}{1-\eta}),$

Thus, $V=20.0mL(\frac{0.41}{1-0.41})=13.9mL.$

There was 13.9 mL of water added.