To determine the net energy released or absorbed when converting 1 gram of oxygen atoms into [tex]\( O^{2-} \)[/tex] ions, we need to follow several steps. Below is a detailed, step-by-step explanation:
1. Atomic Mass of Oxygen:
- The atomic mass of an oxygen atom is approximately 16 grams per mole.
2. Energy Required to Add Electrons:
- When adding electrons to an oxygen atom, we have specific energies associated with each electron added, known as the electron affinity.
- The energy required to add the first electron to an oxygen atom (thus forming [tex]\( O^- \)[/tex]) is approximately [tex]\( -141.0 \)[/tex] kJ/mol.
- The energy required to add the second electron to the [tex]\( O^- \)[/tex] ion (thus forming [tex]\( O^{2-} \)[/tex]) is approximately [tex]\( -744.6 \)[/tex] kJ/mol.
3. Total Electron Affinity:
- To find the total energy change when an oxygen atom gains two electrons to become [tex]\( O^{2-} \)[/tex], we sum the electron affinities for both additions:
[tex]\[
\text{Total Electron Affinity} = -141.0 \, \text{kJ/mol} + (-744.6 \, \text{kJ/mol}) = -885.6 \, \text{kJ/mol}
\][/tex]
4. Energy for 1 Gram of Oxygen:
- We need to determine the energy change per gram of oxygen. We know the atomic mass of oxygen:
[tex]\[
1 \, \text{mol of oxygen} = 16 \, \text{grams}
\][/tex]
- Therefore, the energy change per gram of oxygen can be calculated as:
[tex]\[
\text{Energy per gram} = \frac{\text{Total Electron Affinity}}{\text{Atomic Mass of Oxygen}} = \frac{-885.6 \, \text{kJ/mol}}{16 \, \text{grams/mol}} = -55.35 \, \text{kJ/gram}
\][/tex]
Hence, the net energy released or absorbed in converting 1 gram of oxygen atoms into [tex]\( O^{2-} \)[/tex] ions is [tex]\(-55.35 \, \text{kJ}\)[/tex] per gram. This value is negative, indicating that the process releases energy.
