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

`(0.74)/(1)=(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`