Given the lattice energy of kcl = 699 kj/mol, the ionization energy of k = 419 kj/mol and the electron affinity of cl = −349 kj/mol, calculate the δh o for the reaction: k(g) + cl(g) → kcl(s)

K ---> K⁺ = Ionization energy

Cl ---> Cl⁻ = Electron affinity

delta H = Lattice energy + Ionization energy of K + Electron affinity of Cl

Lattice energy is taken as negative here

delta H = -699 + 419 - 349 = - 629 KJ

ΔH for the reaction K(g) + Cl(g) → KCl(s) is -629 kj.

Explanation:

The Born-Haber cycle describes from the energy point of view the formation of an ionic solid from the elements that constitute it in its most stable thermodynamic state, which is that of minimum energy.

Within this cycle the decisive step is the formation of the ionic compound that is carried out by electrostatic attraction between the ions in the gaseous state to form the crystalline network. At this stage a large amount of energy is released that is called reticular energy or grid energy. Then the reticular energy is defined as the energy released in the process of ionic bond formation from ions in the gaseous state. The more stable the network and the greater the force of attraction between the ions that form the compound, the greater the energy released in the process.

Then it is first necessary that the ions that will then form the solid ionic compound be formed.

The electrons are attracted to the nucleus and it is necessary to provide energy to start them. Ionization energy is the energy needed to start an electron to a gaseous atom, isolated and in a fundamental state. The electrons of the last layer are always lost, which are the weakest attracted to the nucleus. In this way the neutral atom becomes a cation (positively charged ion) gas. This is what happens in this case with potassium K, thus forming the cation K⁺.

Then you have the cation available. The anion (negatively charged ion) necessary for the formation of KCl (s) will be formed from Cl by electronic affinity. Electric affinity is the energy exchanged when a neutral, gaseous atom, and in its fundamental state, picks up an electron to form the anion. As mentioned, this is what happens in this case with the chlorine Cl, thus forming the anion Cl⁻.

Then, once the K + cation and the Cl- anion have been formed, the ionic solid KCl (s) will be formed by means of the lattice energy.

Hess's Law indicates that the enthalpy variation in a chemical reaction will be the same if it occurs in a single stage or in several stages. That is, the sum of the ∆H of each stage of the reaction will give us a value equal to the ∆H of the reaction when verified in a single stage. Then:

ΔH=ionization energy of K+electron affinity of Cl+lattice energy of KCl

When the ions bind to form the crystalline network, heat is released, that is, it is an exothermic process. So the reticular energy is negative. So:

ΔH= 419 kj - 349 kj - 699 kj

ΔH= -629 kj

Finally ΔH for the reaction K(g) + Cl(g) → KCl(s) is -629 kj.

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