A particular C-N bond in a protein (polypeptide) of interest has a vibrational f

Question

A particular C-N bond in a protein (polypeptide) of interest has a vibrational frequency of 1250 cm^-1, and the cleavage of this bond is suspected to be the rate-limiting step in a very important biological reaction. Biologists are willing to do the incredible careful experiment of substituting labeling only this particular nitrogen in the protein with N^15 instead of N^14. However, they need your help in estimating the maximum change in the rate of the reaction, which can be expected if the cleavage of the bond is indeed the rate-limiting step. Express your answer as a ratio of the reaction rates for the N^15 and N^14 isotopes respectively.

Explanation / Answer

According to Kinetic Isotopic Effect, the rate of the reaction will be depending upon the slowest step and if we are using the isotope with the higher mass, then the energy required will be reduced depending on the percentage increase of mass

Percentage Increase of Nitrogen Mass = (15 - 14 )/ 14 * 100 = 100/14 = 7.28%

Hence the energy required will be reduced by a factor of 8% approximately

Previous frequency/new frequency = 1/1.08

New frequency = 1250/1.08 = 1157.40

Hence the ratio of reaction rates will be given by 1250/1157.40 = 1.08/1

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