Question

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

The energy difference for electron transfer from sodium to fluorine is 167.6 kJ/mol, while that for electron transfer from fluorine to another fluorine atom is 1,352.8 kJ/mol. Since the energy difference is lower (more negative) in the case of sodium to fluorine, it is more energetically favorable for a fluorine atom to take an electron from a sodium atom.

Step-by-step solution

Calculate Ionization energy of sodium (

The ionization energy of sodium (Na) is the energy required to remove an electron from its outermost shell. Sodium has only 1 electron in its outermost shell, which is in the 3s orbital. The ionization energy of sodium is 495.8 kJ/mol.

Calculate Ionization energy of fluorine (

The ionization energy of fluorine (F) is the energy required to remove an electron from its outermost shell. Fluorine has 7 electrons in its outermost shell, which is in the 2p orbital. The ionization energy of fluorine is 1,681 kJ/mol.

Calculate Electron affinity of fluorine (

The electron affinity of fluorine (F) is the energy change when an electron is added to its outermost shell to form a negative ion. Fluorine has 7 electrons in its outermost shell, and it can accommodate an extra electron in the 2p orbital to complete its octet. The electron affinity of fluorine is -328.2 kJ/mol. Notice that the electron affinity is negative, which means that energy is released when an electron is added to fluorine.

Calculate energy difference for electron transfer from sodium to fluorine (

The energy difference in this case involves the sum of the ionization energy of sodium and the electron affinity of fluorine: Energy difference = Ionization energy of Na + Electron affinity of F = 495.8 kJ/mol + (-328.2 kJ/mol) = 167.6 kJ/mol

Calculate energy difference for electron transfer from fluorine to fluorine (

In this case, the energy difference involves the sum of the ionization energy of fluorine and the electron affinity of another fluorine atom: Energy difference = Ionization energy of F + Electron affinity of F = 1,681 kJ/mol + (-328.2 kJ/mol) = 1,352.8 kJ/mol

Compare the energy differences (

Now, let's compare the energy differences between the two processes: Energy difference (Na to F) = 167.6 kJ/mol Energy difference (F to F) = 1,352.8 kJ/mol Since the energy difference for electron transfer from sodium to fluorine (167.6 kJ/mol) is lower (more negative) than the energy difference for electron transfer from fluorine to another fluorine atom (1,352.8 kJ/mol), it is more energetically favorable for a fluorine atom to take an electron from a sodium atom.