Heavy/ light isotopes

Question

Is a carbon-hydrogen bond likely to have the biggest difference between heavy and light isotopic pairings in comrpision to a carbon-oxygen bond? Explain using effects on isotopes due to bond stretching frequencies

Answer 1

Bond stretching frequencies in IR spectra are directly proportional to the energy of that particular stretching vibration. The energy of some vibration between two atoms is inversely proportional to the square root of their reduced mass. The reduced mass is a physically convenient way of combining the masses of two oscillating objects, but it should be interpreted as behaving much like simple mass would. This means if one of the two atoms were to be suddenly exchanged for a heavier atom, the reduced mass would increase and the overall energy of the vibration would decrease. An intuitive picture of this idea is that it's harder to make heavier objects move a certain way.

Back to comparisons of carbon-hydrogen and oxygen bonds. If you take normal carbon-12 and hydrogen-1, their reduced mass is ~0.923 amu. If you replace hydrogen-1 with the heaviest known isotope, hydrogen-3 (tritium), and carbon with the heaviest known carbon isotope, carbon-14, the new reduced mass is ~2.47 amu. This new reduced mass is 2.67 times greater! Let's play the same game with a carbon-oxygen bond. The normal carbon-12 and oxygen-16 bond has a reduced mass of ~6.86 amu. Now, substitute in carbon-14 and the heaviest isotope of oxygen, oxygen-18, and the new reduced mass is ~7.88 amu. This is only 1.14 times greater.

The conclusion we can draw is that changing the mass of the smaller atom (hydrogen) is much more impactful than changing the mass of the larger atom (oxygen). It leads to greater differences in reduced mass and, thus, greater differences in bond stretching frequencies.