From the following data, find the energy required to dissociate a KCl molecule into a K atom and

From the following data, find the energy required to...

From the following data, find the energy required to dissociate a $\mathrm{KCl}$ molecule into a $\mathrm{K}$ atom and a $\mathrm{Cl}$ atom. The first ionization potential of $\mathrm{K}$ is $4.34 \mathrm{eV}$; the electron affinity of $\mathrm{Cl}$ is $3.82 \mathrm{eV}$; the equilibrium separation of $\mathrm{KCl}$ is $2.79 \AA$. (Hint: Show that the mutual potential energy of $\mathrm{K}^{+}$and $\mathrm{Cl}^{-}$is $-(14.40 / R) \mathrm{eV}$ if $R$ is given in Angstroms).

Key Concepts

Ionization Potential

This is the energy needed to remove an electron from a neutral atom in its gaseous state, forming a cation. It plays a key role in chemical reactions where an electron is detached from an atom, thereby setting the stage for subsequent interactions between ions.

Electron Affinity

This is the energy change that occurs when an electron is added to a neutral atom, resulting in the formation of an anion. It quantifies the tendency of an atom to accept an electron and is essential in understanding the energetics of ionic bond formation.

Coulombic Interaction

This concept refers to the force of attraction or repulsion between charged particles and is governed by Coulomb's law. In ionic systems, the potential energy of interaction between oppositely charged ions is inversely proportional to their separation distance, and correctly calculating this interaction is crucial when determining the stability and energy of ionic compounds.

Dissociation Energy

Dissociation energy is the energy required to break a compound into its constituent parts. In the context of ionic compounds, it involves accounting for both the energy changes associated with forming ions (captured by ionization potential and electron affinity) and the energy changes due to the electrostatic interactions between the ions.

Transcript

00:01 Hi there.

00:02 So for this problem, we are told that from the following data, we need to find the energy required to dissociate potassium chloride molecule into potassium atom and a chloride atom.

00:17 The first ionization potential for potassium is equal to 4 .34 electron bulbs.

00:31 Of chlorine is equal to 3 .82 electron volts.

00:40 The equilibrium separation between these two, between this molecule, is equal to 2 .79 armstrongs.

00:59 So for this problem, we start with the potential energy of the ion of potassium.

01:09 Potassium and the ion of chloride and that are separated by a distance r.

01:21 So for that we have that the potential, it has the following form.

01:25 That is that the potential is 1 divided by 4 times pi times epsilon sub 0.

01:32 And this times the charge of the potassium times the charge of chlorine.

01:36 And this separated by the distance r.

01:39 Now we substitute the charges.

01:42 We know that the potassium ion, it has a positive charge.

01:48 That is the positive charge of an electron.

01:50 In 4 chlorine, we have a negative charge of an electron, and this divided by the separation distance are.

01:58 Now, we substitute all of the values that we have from this.

02:09 We will have 9 times 10 to the 9.

02:14 And this times 1 .6 times 10 to the minus 19.

02:24 And that to the square, of course.

02:28 And this divided by the separation distance that we are going to say that this is in nanometers.

02:39 So that will be times 10 to the minus 9...

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