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Coulomb's Law is the foundation for calculating electrostatic potential energy between two charged particles. It describes how the potential energy (often referred to as "electric potential energy") between two point charges depends on the magnitudes of the charges and the distance between them. The formula is expressed as:\[ U = \frac{k_e \cdot q_1 \cdot q_2}{r} \]Here:

• \(U\) is the potential energy,
• \(k_e\) is the Coulomb's constant \((8.99 \times 10^9 \, \text{N m}^2/\text{C}^2)\),
• \(q_1\) and \(q_2\) are the magnitudes of the charges, and
• \(r\) is the separation distance between the two charges.

Coulomb's Law is essential for understanding interactions between ions like \(\text{K}^+\) and \(\text{Cl}^-\) in a KCl molecule. When dealing with molecules, calculating this energy helps determine how strongly the ions attract each other.

Binding energy refers to the energy required to separate two bonded particles or ions. When a potassium ion (\(\text{K}^+\)) and a chloride ion (\(\text{Cl}^-\)) form a bond, energy is released, which is reflected as a negative sign in the calculated potential energy. This is because the system loses energy as the ions come together. The binding energy is equivalent to the potential energy calculated using Coulomb's Law, because it represents the same amount of energy required to break the bond and separate the ions again to the point where they no longer influence each other. High binding energy means a stable and strong interaction between ions.

To calculate the potential energy for a system of ions, like a potassium ion and a chloride ion, you can use Coulomb's Law. Start by inserting the charge values and separation distance into the formula. For this KCl problem:\[ q_1 = q_2 = 1.6 \times 10^{-19} \text{ C} \]and\[r = 0.28 \times 10^{-9} \text{ m}\]These charges are of equal magnitude but opposite signs (one is positive and the other is negative), leading to an attractive force. Substitute these values:\[ U = \frac{(8.99 \times 10^9) \cdot (1.6 \times 10^{-19}) \cdot (-1.6 \times 10^{-19})}{0.28 \times 10^{-9}} \]The result will be a negative value, indicating an attractive (or binding) interaction between the ions.

The separation distance \(r\) between ions plays a crucial role in determining the potential energy of their interaction. According to Coulomb's Law, potential energy is inversely proportional to the distance, which means that as the distance decreases, the potential energy becomes more negative, indicating stronger attraction. In the case of a KCl molecule, the stable separation distance \(r\) of \(0.28 \text{ nm}\) represents the distance at which the forces of attraction and repulsion balance each other, creating a stable ionic bond. At this optimal distance, the energy of interaction is minimized, meaning the system is energetically stable. Understanding the role of ion separation can help explain why certain molecular configurations are more stable than others.