The following table displays energy data for selected atoms and diatomics in kJ mol –1 : [VISUAL] *h — Physical Chemistry — Kinetics Chemistry Question
Theoretical Problem 29
The following table displays energy data for selected atoms and diatomics in kJ mol –1 :
[VISUAL]
*hypothetical atom
The interaction energy of two point charges (q1 and q2) separated by a distance R is
E = k * q1 * q2 / R
where k = 8.9910 9 m F –1 . The charge of the electron (e) is 1.60210 –19 C.
Na and Cl atoms are approaching each other in the gas phase. Find the minimal distance at which they still do not react.
Model Answer
At a given Na–Cl distance an electron jumps from Na to Cl. At this point the energy gain arising from the electrostatic attraction and the electron affinity of the Cl atom is exactly equivalent to the energy necessary to ionize the Na atom.
E_I = k * q^2 / R + EA
where EA = 348 kJ mol -1 = 5.7810 –19 J, EI = 496 kJ mol -1 = 8.2410 –19 J.
Rearranging the equation to solve for R we obtain R = 939 pm.
Is this distance smaller or larger if the Na atom is in its first excited state? Show your calculations.
Model Answer
The distance will be larger as the excited Na atom can be ionized easier. In the equation above the ionization energy should be replaced with the value EI – Eex = 445 kJ mol -1 . The distance is: 1432 pm.
Considering all the elements, the electron affinities vary between 4.6 – 348 kJ mol -1 , and the ionization energies vary between 375 – 2374 kJ mol -1 .
Is it possible to make a diatomic molecule dissociate into a stable state containing two ions? Show your calculation.
Model Answer
The formula for R, the distance where the electron jump occurs:
R = k * q^2 / (EI - EA)
This value increases as EI – EA decreases. However it always remains positive as the largest electron affinity of the elements is smaller than the smallest ionization energy. Therefore for all possible (ionic) diatomics there is a well-defined R value beyond which the dissociated ions are less stable than the dissociated atoms.
A neutral Hu atom and a Hu + ion are approaching each other in the gas phase. Will they react? Prove it with calculations.
Model Answer
We postulate the redox reaction:
Hu + + Hu = Hu 2+ + Hu –
For the Coulomb interaction we have q1 = 2 * 1.60210 –19 C,
EA(Hu) = 250 kJ mol -1 = 4.1510 –19 J,
IE = IEII(Hu) = 500 kJ mol -1 = 8.3010 –19 J.
The reacting distance is: 1110 pm.