Problem 51 - A Complete Resource Book in Chemistry for JEE Main

Question

The ionization potential of \(\mathrm{K}^{+}\)is \(2.4 \mathrm{eV}\). The electron affinity of \(\mathrm{K}^{+}\)will be (a) \(1.2 \mathrm{eV}\) (b) \(2.4 \mathrm{eV}\) (c) \(4.2 \mathrm{eV}\) (d) \(8.4 \mathrm{eV}\)

Step-by-Step Solution

Answer

The electron affinity of \(\mathrm{K}^{+}\) is 2.4 eV.

Step 1: Interpret Ionization Potential

The ionization potential, 2.4 eV, represents the energy required to remove the outermost electron from the ion. For \(\mathrm{K}^{+}\), it means removing an electron from a singly charged positive ion to make it a neutral atom.

Step 2: Understand Electron Affinity

Electron affinity is the energy change when an electron is added to an atom or ion. For \(\mathrm{K}^{+}\), electron affinity refers to the energy released when it gains an electron to become a neutral potassium atom.

Step 3: Relate Ionization Potential with Electron Affinity

For a positively charged ion \(\mathrm{K}^{+}\), the energy needed to remove an electron (ionization potential) is essentially the same amount of energy released when an electron is added back (electron affinity)—thus balancing the process.

Step 4: Determine Electron Affinity from Ionization Potential

Since the ionization potential is 2.4 eV, the electron affinity for converting \(\mathrm{K}^{+}\) into a neutral potassium atom is also 2.4 eV, as the processes are the reverse of each other.

Key Concepts

Electron Affinity

Electron affinity is an essential concept in chemistry, particularly when discussing ions. It describes the amount of energy released when an electron is added to a neutral atom or an ion. In simple terms, it measures how much an atom 'wants' an additional electron. When an atom gains an electron, energy might be released, creating a more stable state. This is because atoms tend to strive for a stable electron configuration, often resembling that of noble gases.
Taking potassium (\[\text{K}^+\]) as an example, when it captures an electron, it results in an energy release. This release occurs because the ion morphs into a more stable, neutral potassium atom. To put it in the context of the exercise, the electron affinity for potassium ion \(\text{K}^+\) is equivalent to the energy needed to return to its neutral form, set at 2.4 eV.

• Energy is released when an electron is added, enhancing stability.
• For \(\text{K}^+\), this energy release balances with its ionization potential.

Potassium Ion

The potassium ion, represented as \(\mathrm{K}^{+}\), plays a crucial role in biological systems and various chemical reactions. It forms by losing one electron from a neutral potassium atom, creating a positive charge due to the imbalance between protons and electrons. This ionization process requires energy, known as the ionization potential.
In nature, potassium ions are essential for cellular functions, especially in nerve transmission and muscle contraction. In a chemistry context, when discussing reactions involving \(\mathrm{K}^{+}\), one might consider its tendency to return to a neutral state by gaining an electron. This conversion from an ion back to a neutral atom releases energy, quantified by its electron affinity.

• \(\text{K}^+\) results from an electron loss, becoming a positively charged ion.
• Restoring neutrality by gaining an electron releases energy, known as electron affinity.

Energy Change

Understanding energy change when discussing ionization and electron affinity is pivotal in grasping basic chemistry principles. Energy is neither created nor destroyed; it only changes form. So, when ions transform, energy changes directly correspond to those transformations.
For the potassium ion \(\mathrm{K}^{+}\), an ionization potential of 2.4 eV signifies the energy input required to remove an electron, converting \(\text{K}^+\) into neutral potassium. Conversely, adding an electron to convert back to a neutral atom releases the same amount of energy. This balance illustrates how ionization potential and electron affinity are interlinked.

• Energy change defines the amount of energy invested or released during a chemical change.
• The processes of ionization and gaining an electron are reversible and balance each other energetically.