Question

What is the concentration of a cobalt (II) nitrate solution whose absorbance was measured at 0.55 in a 1.1 cm cuvette with a molar extinction coefficient of 1.5M/cm?
Option
(A) 0.3 M
(B) 0.6 M
(C) 0.9 M
(D) 1.2 M

Answer 1

Hint: In optics, absorbance, also known as decadic absorbance, is the standard logarithm of the ratio of incident to transmitted radiant power through a material, while spectral absorbance, also known as spectral decadic absorbance, is the common logarithm of the ratio of incident to transmitted spectral radiant power through a material.
$A = \varepsilon \ell c$
A is the absorbance
$\varepsilon $is the molar attenuation coefficient or absorptivity of the attenuating species
l is the optical path length in cm
c is the concentration of the attenuating species

Complete answer:
The Beer–Lambert law, also known as Beer's law, Lambert–Beer law, or Beer–Lambert–Bouguer law, is a relationship between light attenuation and the properties of the medium by which it travels. The law is widely used in chemical research calculations and in physical optics to explain attenuation for electrons, neutrons, and rarefied gases. The optical attenuation of a physical medium comprising a single attenuating species of uniform concentration is related to the optical path length through the sample and the species' absorptivity, according to a standard and functional expression of the Beer–Lambert law. This is the phrase:
$A = \varepsilon \ell c$
A is the absorbance
$\varepsilon $is the molar attenuation coefficient or absorptivity of the attenuating species
l is the optical path length in cm
c is the concentration of the attenuating species
Given values:
$\varepsilon $= 1.5 M/cm
l= 1.1 cm
A =0.55
$A = \varepsilon \ell c$becomes
$ \Rightarrow 0.55 = (1.5)(1.1)C$
$ \Rightarrow {\mathbf{C}} = {\mathbf{0}}.{\mathbf{33M}}$.

Note:
At very high concentrations, the rule appears to break down, particularly if the substance is strongly scattering. Maintaining linearity in the Beer–Lambert law needs an absorbance range of 0.2 to 0.5. Nonlinear optical mechanisms will also induce variations if the radiation is very strong. However, the key explanation is that concentration dependency is non-linear in general, and Beer's law is only true under such conditions, as seen in the derivation below. The variations are greater for solid oscillators and at high concentrations. As molecules are in near proximity to one another, interactions may occur. Physical and chemical interactions can be loosely separated into these interactions.