Question

If the absorbance of a solution of copper(ii) ion decreases by 26.0% upon dilution, what volume of water was added to 20.0 ml of a 1.20 m solution of cu2+(aq)?

Answer 1

Answer: 7.02 mL of water was added in the solution.

Explanation: There is a direct relation of absorbance and concentration which is given by Beer-Lambert's Law.

Mathematically, this law is written as:

$A=\varepsilon lC$

where, A = absorbance

$\varepsilon$ = Molar extinction coefficient

l = Path length

C =  concentration (in terms Molarity)

We are given a copper solution whose absorbance is decreased by 26%.

Assuming that the absorbance of original solution was 100%.

New absorbance will be (100-26)% = 74%

For Original absorbance,

$1=\varepsilon l(1.20)$      ....(1)

For new absorbance,

$0.74=\varepsilon l(M_2)$      ....(2)

As Molar extinction coefficient and path length would be same for both the solutions, dividing equation 2 by 1, we get

$\frac{0.74}{1}=\frac{1.20}{M_2}$

$M_2=0.888M$

Now, to calculate the volume needed to reduce the abosrbance by 26%, we use the relation:

$M_1V_1=M_2V_2$

Where, $M_1\text{ and }V_1$ are the molarity and volume of the original solution.

$M_2\text{ and }V_2$ are the molarity and volume of the diluted solution.

Putting the values, we get

$(1.20)(20)=(0.888)(V_2)$

$V_2=27.02mL$

This is the volume of the diluted solution.

To make the original volume of 20 ml to 27.02 ml,  water need to be added , $(x)mL=(27.02-20)mL$

$x=7.02mL$