When using the Born-Haber Cycle for Na2S, do I double the ionization energy of Na since there are two Na ions for every S ion in Na2S?

Also, the problem asked me to find the change in energy for S- (g) + e- => S2- (g). Assuming that you do double the ionization energy, I got an answer of about 550 kJ/mol give or take 50 kJ/mol. Is this value in the ball park or am I totally wrong?

Thanks for the help in advance!

To answer your first question, no, you do not double the ionization energy of Na when using the Born-Haber Cycle for Na2S. The ionization energy is the energy required to remove one electron from an atom in the gas phase, regardless of the compound it is present in. In Na2S, there are indeed two Na ions for every S ion, but each Na ion loses only one electron during the formation of Na2S. Therefore, you should consider the ionization energy of Na as it is, without doubling it.

Now, let's move on to your second question. To find the change in energy for the reaction S- (g) + e- => S2- (g), you need to consider several steps in the Born-Haber Cycle.

1. First, you need to get the ionization energy for S to form S- (g). This is the energy required to remove one electron from a sulfur atom in the gas phase.

2. Next, you need to consider the electron affinity of S to form S2- (g). Electron affinity is the energy change when an atom or ion in the gas phase gains an electron. In this case, S2- (g) is formed by adding an electron to an S ion in the gas phase.

3. Finally, you should consider other relevant energy changes in the cycle, such as lattice energy (energy released when gaseous ions come together to form a solid lattice) and enthalpy of formation (energy change when one mole of a compound is formed from its elements in their standard states).

By summing up these energy changes, you can determine the overall change in energy for the reaction. The value you mentioned, 550 kJ/mol, seems to be within the ballpark considering the complexity of the Born-Haber Cycle calculations. However, it is always recommended to consult your textbook or instructor to verify the correctness of your answer.

Remember, when using the Born-Haber Cycle, it's important to carefully consider each energy change and make sure you're working with the correct values for the substances involved.