Question

The formation of \(\mathrm{O}^{2-}\) (g) starting from \(\mathrm{O}\) (g) is endothermic by \(603 \mathrm{~kJ} \mathrm{~mol}^{-1} .\) If electron affinity of \(\mathrm{O}(\mathrm{g})\) is \(-141 \mathrm{~kJ} \mathrm{~mol}^{-1}\), the second electron affinity of oxygen would be: (a) \(+744 \mathrm{~kJ} \mathrm{~mol}^{-1}\) (b) \(-744 \mathrm{~kJ} \mathrm{~mol}^{-1}\) (c) \(+462 \mathrm{~kJ} \mathrm{~mol}^{-1}\) (d) \(-462 \mathrm{~kJ} \mathrm{~mol}^{-1}\)

Short answer

The second electron affinity of oxygen is \(+744\, \mathrm{kJ}\, \mathrm{mol}^{-1}\), option (a).

Step-by-step solution

Understand Electron Affinity and Process

The exercise involves calculating the second electron affinity of oxygen when forming \( \mathrm{O}^{2-} \) from \( \mathrm{O} \) gas. The first electron affinity is given as \(-141 \mathrm{~kJ} \mathrm{~mol}^{-1}\). The total process of forming \( \mathrm{O}^{2-} \) from \( \mathrm{O} \) is endothermic by \(603 \mathrm{~kJ} \mathrm{~mol}^{-1}\).

Recall Electron Affinity Concept

Electron affinity is the energy change when an electron is added to a gaseous atom. A negative value indicates an energy release (exothermic), while a positive value indicates energy absorption (endothermic).

Calculate Total Energy Change

We know the total energy required to form \( \mathrm{O}^{2-} \) from \( \mathrm{O} \) is \(603 \mathrm{~kJ} \mathrm{~mol}^{-1}\). This is the sum of the first and second electron affinities, as it covers the addition of two electrons to oxygen.

Set Up Equation for Second Electron Affinity

Let the second electron affinity be \( E_2 \). The equation is: \(-141 + E_2 = 603\) because the first electron affinity is \(-141 \mathrm{~kJ} \mathrm{~mol}^{-1}\) and we solve for \( E_2 \).

Solve for Second Electron Affinity

Rearrange the equation to solve for \( E_2 \): \[ E_2 = 603 + 141 = 744 \mathrm{~kJ} \mathrm{~mol}^{-1} \] This result is positive, indicating the second electron addition is endothermic.

Select Correct Answer

The calculated second electron affinity is \(+744 \mathrm{~kJ} \mathrm{~mol}^{-1}\). Thus, the correct answer is \( (a) +744 \mathrm{~kJ} \mathrm{~mol}^{-1} \).

Key concepts

Endothermic Process

An endothermic process is a chemical reaction or physical change that absorbs energy from its surroundings. When you hear that a process is endothermic, think about it taking in energy rather than giving it off. For example, in the context of chemistry, this energy is usually in the form of heat.
In the formation of an oxygen ion \( \mathrm{O}^{2-} \), an endothermic process means energy must be supplied to the system. This contrasts with an exothermic process, where energy is released.

• In our case, to form \( \mathrm{O}^{2-} \) from \( \mathrm{O} \), we require energy to overcome the repulsion as we add the second electron.
• This is why the total energy change here is positive, indicating the process needs energy input.

The concept is important because it helps us understand why some reactions need energy to proceed, such as in breaking bonds or adding electrons against repulsive forces within atoms.

Energy Change

Energy change is an important concept in chemistry that refers to the difference in energy between reactants and products during a reaction. It gives insights into whether a reaction is exothermic (releases energy) or endothermic (requires energy).
For oxygen ion formation, the energy change involves two steps:

• First, adding an electron to \( \mathrm{O} \) to form \( \mathrm{O}^{-} \), which has an electron affinity of \(-141 \mathrm{~kJ} \mathrm{~mol}^{-1}\).
• The second is adding another electron to \( \mathrm{O}^{-} \) to form \( \mathrm{O}^{2-} \).

The total energy change for this entire process is characterized as endothermic, summed up to be \(603 \mathrm{~kJ} \mathrm{~mol}^{-1}\). The calculation for the second electron affinity consists of finding out how much more energy is needed in addition to the first electron affinity. Thus, understanding this energy change explains why it takes significant energy to form the \( \mathrm{O}^{2-} \) ion.

Oxygen Ion Formation

Oxygen ion formation is a chemical process where oxygen atoms become ions by gaining electrons. This usually happens in two steps because oxygen needs to gain two electrons to become \( \mathrm{O}^{2-} \).
The first electron affinity reflects oxygen converting from \( \mathrm{O} \) to \( \mathrm{O}^{-} \), releasing energy. The \(-141 \mathrm{~kJ} \mathrm{~mol}^{-1}\) value indicates this as an exothermic step.

• Forming the \( \mathrm{O}^{2-} \) ion by adding a second electron is more challenging due to repulsion. Thus, it becomes an endothermic process requiring \( +744 \mathrm{~kJ} \mathrm{~mol}^{-1}\).
• This larger energy requirement shows that the negative ion now resists the addition of another electron because of increased electron-electron repulsion.

Understanding oxygen ion formation helps explain why some ions are unstable or require high energy to form, shedding light on chemical stability and reactivity.