How to Figure out the Time Taken when a Reaction Mixture Was Optically Inactive – Part 1

Optical rotation aka polarization rotation or circular birefringence is the rotation of the orientation of the plane of polarization about the optical axis of linearly polarized light as it travels through certain materials.


Circular birefringence and circular dichroism (CD) are the manifestations of optical activity in stereochemistry.

CD is dichroism involving circularly polarized light, i.e., the differential absorption of left- and right-hand circular (LHC & RHC respectively) polarized light. Dichroism is a phenomenon in which light rays having different polarization directions in a material are absorbed in the material differently. Circular polarization of an electromagnetic wave is a polarization state in which, at each point, the electromagnetic field of the wave has a constant magnitude and is rotating at a constant rate in a plane normal to the direction of the wave.

Unlike other sources of birefringence that change a beam's polarization state, optical activity can be observed in fluids, i.e., gases/solutions of chiral molecules (lacking microscopic mirror symmetry), viz., sugars, molecules with helical secondary structure, viz., some proteins, chiral liquid crystals, chiral solids, viz., certain crystals with a rotation between adjacent crystal planes (say, quartz) or metamaterials.

Optical rotation typically follows first-order kinetics.

Question:

The hydrolysis of Sucrose was studied with the help of a polarimeter and the following data were obtained:

Collected time (min)

0

70

∞

Observed rotation (0)

44

16.5

─11

What was the time taken when the reaction mixture was optically inactive?

Solution:



Click/tap to enlarge the image

k = Rate constant, t = Time, r = Rotation

Optimistic about optical rotation❓ Let Chemaficionado know in the comments below or at mychemistryhomework@gmail.com❗

References:

(1)    Wikipedia Contributors. Rate equation. Wikipedia. https://en.wikipedia.org/wiki/Rate_equation.

(2)    Brown, C.; Ford, M. Higher Level Chemistry, 2nd ed.; Pearson Education: Harlow, Essex, 2014.

(3)    Ncert. Chemistry : Textbook for Class XII - Part.I; National Council Of Educational Research And Training: New Delhi.

(4)    Optical Rotation; 2019. https://en.wikipedia.org/wiki/Optical_rotation.
(5)    Wikipedia Contributors. Circular Dichroism; Wikimedia Foundation, 2019. https://en.wikipedia.org/wiki/Circular_dichroism.

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