Question

For the gaseous reaction, \(\mathrm{K}+\mathrm{F} \rightarrow \mathrm{K}^{+}+\mathrm{F}, \Delta \mathrm{H}\) was calculated to be 19 kcal under conditions where the cations and anions were prevented by electrostatic separation from combining with each other. The ionization potential of \(\mathrm{K}\) is \(4.3 \mathrm{eV}\). What is the electron affinity of \(\mathrm{F} ?\) (a) \(3.21\) (b) \(4.28\) (c) \(3.48\) (d) \(1.48\)

Short answer

The electron affinity of fluorine is 3.48 eV, corresponding to option (c).

Step-by-step solution

Question Analysis

We need to find the electron affinity of Fluorine ( F) given the enthalpy change (19 kcal) for the reaction between Potassium ( K) and Fluorine. The ionization potential of Potassium is also provided as 4.3 eV.

Conversion of Units

Convert the given ionization potential from eV to kcal for consistency with the enthalpy change. Use the conversion factor: 1 eV = 23.06 kcal/mol. Thus, \[4.3 \, \text{eV} = 4.3 \, \text{eV} \times 23.06 \, \text{kcal/mol eV} = 99.158 \, \text{kcal/mol}.\]

Establish Relation for Enthalpy Change

The reaction's enthalpy change (\Delta H\u000B) in kcal is calculated using:\[\Delta H = \text{Ionization Potential of } \mathrm{K} - \text{Electron Affinity of } \mathrm{F}.\]Given \(\Delta H = 19 \, \text{kcal/mol} \), substitute into the equation:\[19 = 99.158 - \text{Electron Affinity of } \mathrm{F}.\]

Solve for Electron Affinity

Rearrange the equation to solve for the electron affinity of Fluorine (F):\[\text{Electron Affinity of } \mathrm{F} = 99.158 - 19 = 80.158 \, \text{kcal/mol}.\]

Convert Electron Affinity to eV

Convert the calculated electron affinity from kcal back to eV using the inverse of the previous conversion, knowing that 1 eV = 23.06 kcal/mol:\[\text{Electron Affinity of } \mathrm{F} = \frac{80.158}{23.06} = 3.48 \, \text{eV}.\]

Choose the Correct Option

The calculated electron affinity of Fluorine is 3.48 eV, matching option c in the question.

Key concepts

Ionization Potential

The ionization potential, also known as ionization energy, is a crucial concept in chemistry. It refers to the energy required to remove an electron from a neutral atom in the gaseous state to form a cation. For potassium (K), as given in the exercise, the ionization potential is 4.3 eV. This means that 4.3 eV is needed to remove one electron from each atom of potassium, converting it into a positively charged potassium ion (K⁺).

• The ionization potential is often measured in electron volts (eV).
• Higher ionization potential indicates a stronger attraction between the nucleus and the electrons.
• Elements that are more metallic typically have lower ionization potentials.

Understanding ionization potential helps predict how easily an element can form positive ions, which plays a significant role in chemical reactivity and bonding.

Thermochemistry

Thermochemistry is a branch of chemistry that deals with the heat changes associated with chemical reactions. It helps us understand the energy changes that occur, particularly the enthalpy change, denoted as \( \Delta H \).

• It focuses on measuring and analyzing the heat exchanged during reactions.
• Reactions can either absorb heat (endothermic) or release heat (exothermic).
• The enthalpy change is often measured in kilocalories (kcal) or kilojoules (kJ).

In the given exercise, we see a reaction between potassium and fluorine with an enthalpy change of 19 kcal. This value indicates the net energy exchange without taking into account any additional processes such as the combination of ions by electrostatic forces.

Energy Conversion

Energy conversion is essential for providing a consistent understanding of energy values. In chemistry, especially when dealing with ionization potential and enthalpy changes, it often becomes necessary to convert energy units.

• The common units for energy in chemistry are kilocalories (kcal) and electron volts (eV).
• For the exercise, the ionization potential of potassium was converted from eV to kcal using the factor: 1 eV = 23.06 kcal/mol.
• Consistency in energy unit conversion ensures accurate calculations and comparisons.

Particularly in this problem, converting energy values enabled consistent application of concepts to find the electron affinity of fluorine.

Reaction Enthalpy

Reaction enthalpy, represented by \( \Delta H \), is the total heat content change in a reaction at constant pressure. It gives insight into whether energy is absorbed or released during the process.

• Positive \( \Delta H \) implies that the reaction absorbs energy (endothermic).
• Negative \( \Delta H \) indicates an exothermic reaction where energy is released.
• The exercise involves calculating enthalpy in a gaseous reaction setting.

In the context of the exercise, the enthalpy change of 19 kcal for the K + F reaction suggests specific energy dynamics where cations and anions are prevented from recombining due to electrostatic conditions. Using reaction enthalpy, the problem further explores electron affinity, which complements the ionization potential to predict the reaction's thermodynamic favorability.