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Chapter 7: Problem 18

Prove mathematically that it is more energetically favorable for a fluorine atom to take an electron from a sodium atom than for a fluorine atom to take an electron from another fluorine atom.

Short Answer

Expert verified
The energy change for Na-F electron transfer is -168 kJ/mole, while the energy change for F-F electron transfer is -1,353 kJ/mole. Since the Na-F energy change is less negative, it is more energetically favorable for a fluorine atom to take an electron from a sodium atom than from another fluorine atom.

Step by step solution

01

Determine ionization energy of Sodium

The ionization energy of sodium (Na) is the energy required to remove an electron from a sodium atom, forming a positive ion (Na+). The ionization energy of sodium is 496 kJ/mole.
02

Determine electron affinity of Fluorine

The electron affinity of fluorine (F) is the energy released when an electron is added to a fluorine atom, forming a negative ion (F-). The electron affinity of fluorine is 328 kJ/mole.
03

Calculate the energy change for Na-F electron transfer

To determine the energy change for the electron transfer between a sodium atom and a fluorine atom, subtract the ionization energy of sodium from the electron affinity of fluorine: Energy change = Electron affinity of F - Ionization energy of Na = 328 kJ/mole - 496 kJ/mole = -168 kJ/mole A negative energy change indicates that energy is released during this process, making it energetically favorable.
04

Determine ionization energy of Fluorine

The ionization energy of fluorine is the energy required to remove an electron from a fluorine atom, forming a positive ion (F+). The ionization energy of fluorine is 1,681 kJ/mole.
05

Calculate the energy change for F-F electron transfer

Assuming that the electron affinity for the second fluorine atom is the same as in step 2 (328 kJ/mole), calculate the energy change for transferring an electron between two fluorine atoms: Energy change = Electron affinity of F - Ionization energy of F = 328 kJ/mole - 1,681 kJ/mole = -1,353 kJ/mole This represents a much greater energy release compared to the Na-F electron transfer, which indicates that the F-F electron transfer is much less energetically favorable.
06

Compare energy change of Na-F and F-F electron transfer

Comparing the energy change between the Na-F and F-F electron transfer processes: Na-F energy change: -168 kJ/mole F-F energy change: -1,353 kJ/mole It is clear that transferring an electron from a sodium atom to a fluorine atom is more energetically favorable than transferring an electron between two fluorine atoms, as the energy change is less negative in the Na-F case. This means that a fluorine atom is more likely to take an electron from a sodium atom than from another fluorine atom.

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