By measurement in an ion cyclotron resonance mass...

By measurement in an ion cyclotron resonance mass spectrometer, it is possible to measure the proton affinity (PA) of free radicals. These data can be combined with ionization potential (IP) data according to the scheme below to determine the bond dissociation energy (BDE) of the corresponding C-H bond. The ionization potential of the $\mathrm{H}$ atom is $313.6 \mathrm{kcal} / \mathrm{mol}$. Use the data given below to determine the relative stabilization of the various radicals relative to methyl, for which the BDE is $104 \mathrm{kcal} / \mathrm{mol}$. Compare the BDE determined in this way with the comparable values given in Table $3.20$.

Key Concepts

Thermodynamic Cycles

Thermodynamic cycles are analytical tools that involve a series of hypothetical steps connecting initial and final states to calculate unknown thermochemical quantities. By combining measured values such as proton affinities and ionization potentials, these cycles allow for the indirect determination of bond dissociation energies and the evaluation of radical stabilization effects relative to reference species.

Bond Dissociation Energy

Bond dissociation energy refers to the amount of energy needed to break a specific bond in a molecule, separating it into its constituent fragments. It is a fundamental thermodynamic quantity that provides insight into bond strength and molecular stability, and it is derived from measurements including ionization potentials and proton affinities in related experimental schemes.

Proton Affinity

Proton affinity is a measure of the energy change when a proton is added to a molecule or radical in the gas phase. It quantifies the tendency of a species to accept a proton and is intrinsically linked to the stability and basicity of the species, playing a critical role in understanding reaction energetics involving proton transfers.

Ion Cyclotron Resonance Mass Spectrometry

This technique is a form of mass spectrometry that uses a high magnetic field to trap ions and provides very high resolution measurements of their mass?to?charge ratios. It is particularly useful for determining thermodynamic quantities of ions by monitoring their behavior under controlled conditions, enabling precise measurement of properties such as proton affinities.

Ionization Potential

Ionization potential, or ionization energy, is defined as the energy required to remove an electron from a neutral atom or molecule in the gas phase. This property is important for evaluating the electronic structure and reactivity of species, and it is used in combination with other thermodynamic data to derive bond dissociation energies.

Transcript

0:00 Hi there.

00:01 So for this problem, we are told that the dissociation energy is sometimes expressed in kilo calories per mole.

00:12 So for part a of this problem, we need to transform one electron balls per molecule to kilo calories per mold.

00:30 Now, we start with one electron balls per molecule, and we multiply this by a factor of conversion from electron bolts to joules.

00:47 So we note that one electron balls corresponds to 1 .609 times 10 to minus 19 joules.

01:00 And as you can see, we can cancel electron balls from here.

01:07 And now we pass from molecules to moles.

01:12 So we know that in one mole of substance, there are 6 .022 times 10 to the 23 molecules.

01:25 Now the result that we obtain from here is 96 ,472 joules per mold.

01:45 Now we need to pass this value to calories.

01:55 We know that one calorie is equal to 1 .184 ,000.

02:04 Joules.

02:06 So we pass from joules to calories.

02:09 So from here we obtain a value of 23 ,057 calories per mold.

02:23 Finally, we need to transform this from calories to kilo calories.

02:29 We know that one kilo calories is equal to to 1 ,000 calories.

02:41 So from here we obtain that one electron balls per molecule is equal to 23 .06 kilo calories per mold.

03:00 So that's the solution for part a of this problem...

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