Question

If the absorbance of a solution of copper(II) ion decreases by 32.0% upon dilution, what volume of water was added to 20.0 mL of a 1.20 M solution of Cu2+(aq)?

Answer 1

Answer : The volume of water added = 9.411 ml

Solution : Given,

Absorbance decreases by 32% upon dilution means,

Let, initial absorbance = 100
`Lmol^(-1)Cm^(-1)`

then final absorbance = 100 - 32 = 68
`Lmol^(-1)Cm^(-1)`

initial concentration = 1.2 M

initial volume = 20 ml = 0.02 L ( 1 L = 1000 ml )

According to Beer-Lambert law, the absorbance is directly proportional to the concentration of an absorbing species.

A ∝ C

`(A_(inital))/(A_(final))=(C_(initial))/(C_(final))`

Now put all the given values in this formula, we get

`(100)/(68)=(1.2)/(C_(final))`

`C_(final)` = 0.816 M

Now, calculating the number of moles,

Moles = concentration × volume

Moles = 1.2 × 0.02 = 0.024 moles

Now, Calculating the final volume by this formula.

`C_(final)=(moles)/(V_(final))`

`V_(final)` =
`(0.024)/(0.816)` = 0.0294 L = 29.411 ml

The inital volume is 20 ml and final volume is 29.411 ml.

Volume of water added = final volume - initial volume = 29.411 - 20 = 9.411 ml