Question

What is the relative error in concentration from 1% stray light for a sample with a molar absorptivity of 5.0x104 M-1cm-1 and a concentration of 2 x10-5 M held in a 1.00 cm cell? What is the relative error if the concentration is five times higher, 1.0x10-4 M?

Answer 1

ε =A/lc

where ε = molar absorptivity = 5.0x10⁴ M^-1cm^-1

A = absorbance of light

l=length of cell = 1 cm

c= concentration = 2 x10^-5 M

A = 5.0x10⁴ X 2 x10^-5

A = 1

Stray light is any light that has a different wavelength from that supplied by the monochromator. It may also be light, which reaches the detector without having passed through the sample.

Sample beam contains 1% stray light then the light, which reaches the detector, will contain 1% of the light plus the 1% of the stray light. The transmittance will therefore be 1 + 1 = 2%.

A= log 100/T

A= log 100 - log T

A = 2 - log (2) = 2 - 0.301 =1.699

As the nominal absorbance should 1 then the error will be 1 -1.699 = 0.699 Abs.

The relative error caused by the stray light will greater than 0.699/1x 100 = 69%.

b. A = 5.0x10⁴ X 1 x10^-4

A = 5

As the nominal absorbance should 5 then the error will be 5 -1.699 = 3.301 Abs.

The relative error caused by the stray light will greater than 0.699/5x 100 = 13.3%.