Calculate the energy in kJ mol^-1 required to separate a positive and negative charge from 0.3 n

step 1 Estimate the binding energy of a k -cell molecule by calculating the electrostatic potential ene

Calculate the energy in kJ mol^-1 required to separate a...

Calculate the energy in $\mathrm{kJ} \mathrm{mol}^{-1}$ required to separate a positive and negative charge from $0.3 \mathrm{nm}$ to infinity in $(a)$ a vacuum, (b) a solvent of dielectric constant $10,$ and (c) water at $25^{\circ} \mathrm{C},$ which has a dielectric constant of approximately 80

Calculate the energy in $\mathrm{kJ} \mathrm{mol}^{-1}$ required to separate a positive and negative charge from $0.3 \mathrm{nm}$ to infinity in $(a)$ a vacuum,
(b) a solvent of dielectric constant $10,$ and
(c) water at $25^{\circ} \mathrm{C},$ which has a dielectric constant of approximately 80

Key Concepts

Molar Energy Conversion

This concept involves converting the energy calculated for a single pair of charges into energy per mole using Avogadro's number. It bridges the microscopic calculations with macroscopic quantities, allowing chemists and physicists to express energy changes and work in units such as kilojoules per mole, which are more practical for laboratory and industrial applications.

Dielectric Constant

The dielectric constant, or relative permittivity, is a measure of a material's ability to reduce the effective electric field between charges compared to a vacuum. It modifies the interaction between charges by scaling the electrostatic potential energy, making it fundamental when analyzing how different solvents (such as water or other media) influence the energy required to separate charges.

Electrostatic Potential Energy

Electrostatic potential energy refers to the energy stored in a system of charges due to their positions relative to each other. It is calculated using a formula derived from Coulomb's law, which shows that the energy is inversely proportional to the distance between the charges. This concept is essential for calculating the work required to separate charges from a given distance to infinity.

Coulomb's Law

This fundamental principle of electrostatics quantifies the force between two point charges. It states that the force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them, with the proportionality constant depending on the medium. This law is critical for understanding how charged particles interact in both vacuum and various dielectric environments.

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