The standard heat of formation of CaBr 2 is -675 kJ / mol . The first ionization energy of Ca is

The standard heat of formation of CaBr 2 is -675 kJ / mol ....

The standard heat of formation of CaBr_ $_{2}$ is $-675 \mathrm{kJ} / \mathrm{mol}$ . The first ionization energy of Ca is 590 $\mathrm{kJ} / \mathrm{mol}$ , and its second ionization energy is 1145 $\mathrm{kJ} / \mathrm{mol}$ . The heat of sublimation of $\operatorname{Ca}[\mathrm{Ca}(s) \longrightarrow \mathrm{Ca}(g)]$ is 178 $\mathrm{kJ} / \mathrm{mol} .$ The bond energy of $\mathrm{Br}_{2}$ is $193 \mathrm{kJ} / \mathrm{mol},$ the heat of vaporization of $\mathrm{Br}_{2}(l)$ is $31 \mathrm{kJ} / \mathrm{mol},$ and the electron affinity of $\mathrm{Br}$ is $-325 \mathrm{kJ} / \mathrm{mol} .$ Calculate the lattice energy of $\mathrm{CaBr}_{2} .$

Key Concepts

Phase Change Energies

Phase change energies, such as sublimation and vaporization energies, refer to the energy required to change a substance from one phase to another (for example, from solid to gas or liquid to gas) without changing its chemical composition. These energies are important in thermochemical cycles because they allow elements to be brought into the gaseous state where ionization and electron gain processes occur.

Bond Energy

Bond energy is the energy required to break a chemical bond in a molecule, typically expressed per mole of bonds. In thermochemical calculations, knowing the bond energy of diatomic molecules enables the determination of the energy needed to dissociate the molecule into individual atoms, an important step in the process of forming ions.

Electron Affinity

Electron affinity is the energy change that occurs when an electron is added to a neutral atom in the gaseous state to form a negative ion. It is a measure of an atom’s ability to accept an electron and contributes significantly to the energetics of forming an ionic bond.

Born?Haber Cycle

The Born?Haber cycle is a thermochemical cycle that breaks down the formation of an ionic compound into a series of steps, including atomization, ionization, electron affinity, and lattice formation. It allows the calculation of lattice energy by applying Hess’s law, showing that the overall enthalpy change for the formation of the compound is the sum of these individual energetic steps.

Lattice Energy

Lattice energy is the energy released when gaseous ions combine to form an ionic solid, or equivalently, the energy required to separate one mole of an ionic compound into its gaseous ions. It reflects the strength of the electrostatic forces between oppositely charged ions in the crystal lattice.

Ionization Energy

Ionization energy is the amount of energy needed to remove electrons from a neutral atom in the gaseous state, forming a positive ion. In the context of ionic compound formation, it accounts for the energy cost of converting a metal atom into a metal cation, a critical step in the overall energy balance.

Transcript

00:01 So for questions like these which are born hayber cycle questions, it's really important to be specific about what reactions are happening and be organized.

00:08 And so what we always do is we start with the standard heat of formation, which, as we know, is the two components, sorry, the two components going from their state at room temperature to the final product.

00:27 And so in this case, we have calcium solid and br2 as a liquid becoming calcium bromide.

00:43 And so this is the final reaction that all the other reactions have to build up to.

00:48 And we're told that the delta h for this reaction is negative 675 kilojoules per mole.

00:55 And so all the other reactions are going to add up to this one, and their delta hs are going to add up to that.

01:00 And so let's keep that in mind as we go about this.

01:03 So the first thing that we're going to have is we're going to have calcium having to become the calcium 2 plus ion.

01:11 And so first it has to go through losing or pardon me.

01:18 I'm jumping ahead.

01:19 Remember, ionization energies are for gases and so we have to go from calcium as a solid to calcium as a gas.

01:27 And this is given to us as the heat of sublimation.

01:32 And this is a 178 plus 178 kilojoules per mole.

01:37 It's going to require energy to go from a solid to a gas.

01:41 Now, we have this calcium gas, and now it's going to lose an electron.

01:48 So it's going to become calcium plus as a gas plus an electron.

01:54 And this is the first ionization energy, which is 590...

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