5 8 The molar absorption coefficient e for ethane is 40 cm b

5. [8] The molar absorption coefficient, e, for ethane is 40 (cm bar)-1 at a wavelength of 12 m. a) Calculate Lo/i in a 1.0-cm long absorption cell if ethane is present at a level of 2.0 ppm in one bar of air b) What cell length is required to make load/in-0.90?

Solution

a)

Expression for Beer Lambert’s law can be written as follows:

I/I_o = e^-(cl)

Where,

I_o = incident intensity

I = transmitted intensity

=absorption coefficient

c = concentration

l = path length

Substitute, = 40 cm^-1bar^-1; c=2.0 x10^-6 bar; l=1.0 cm and calculate Io/I

I/I_o = e^-( 40 cm^-1bar^-1 x 2.0 x10^-6 bar x 1.0 cm)

I/I_o = 0.99992

Therefore, value of (I/I_o) is 0.99992.

b)

Calculate l for (I/I_o) =0.90 by substituting = 40 cm^-1bar^-1 and c=2.0 x10^-6 bar

I/I_o = e^-(cl)

0.90 = e^-( 40 cm^-1bar^-1 x 2.0 x10^-6 bar x l)

ln 0.90 = -( 40 cm^-1bar^-1 x 2.0 x10^-6 bar x l)

-0.10536 = - (80 x 10-6 cm^-1 x l)

l = 1.3 x 10³ cm

Therefore, for (I/I_o) =0.90, path length will be 1.3 x 10³ cm.