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?

1 Answer
Michael
Feb 14, 2016

#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"#

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