Question

An aqueous solution which is `10^-3` `M` absorbs `10 %` of incident light in a path length of `1` `cm`. Calculate concentration of the solution that will absorb `90 %` of the incident light in the same cell?

Answer 1

`0.022"M"`

Explanation:

The absorbance is given by:

`A=log((I_0)/(I))`

`I` is the intensity of the light as measured by the spectrometer. `I_0` is set at 100 for a solution that absorbs no light at that particular wavelength.

In the first case `10%` of the light is absorbed so `90%` is transmitted and `I=90`.

So in the second case `I=10`.

The Beer - Lambert Law gives us:

`A=epsilon_(@)cl`

`epsilon_(@)` is the molar absorption coefficient.

`c` is the concentration in `"mol/l"`

`l` is the path length of the cell.

Putting in the numbers:

`log(100/90)=epsilon_(@)xx10^(-3)xx1" "color(red)((1))`

`log(100/10)=1=epsilon_(@)xxcxx1" "color(red)((2))`

Dividing `color(red)((1))` by `color(red)((2))rArr`

`log(1.11)=10^(-3)/c`

`:.c=10^(-3)/0.0457=0.0218"mol/l"`