Born Haber Cycle - Online Tutor, Practice Problems & Exam Prep

The Born-Haber cycle is a systematic approach to understanding the formation of an ionic compound from its constituent elements in their standard states. It involves several key steps: sublimation, ionization energy, bond dissociation (entropy of dissociation), electron affinity, and lattice energy. These steps collectively lead to the calculation of the standard enthalpy of formation (ΔH_f°) for the compound. For example, the formation of sodium chloride (NaCl) requires converting sodium from solid to gas (sublimation), ionizing sodium to form a cation (ionization energy), dissociating chlorine molecules into atoms (bond dissociation), adding an electron to chlorine to form an anion (electron affinity), and finally, the combination of these gaseous ions to form the solid ionic compound (lattice energy). Understanding the Born-Haber cycle is crucial for grasping the thermochemical processes involved in the formation of ionic solids.

Born Haber Cycle

Now the Borne Haber cycle is a reaction outline that gives the steps for the formation of an ionic compound from the standard states of its elements. So I know that's a mouthful. The Born Heber cycle is an extensive process. We're going to go piece by piece, step by step to figure it out.

Now recall first a formation equation shows the standard states of elements combining to form 1 mole of product. Now remember, associated with the formation equation is our enthalpy or heat of formation which is ΔHf. Here standard heat of formation has that little circle there. It's telling me here that the formation of 1 mole of sodium chloride is accomplished by combining 1 mole of sodium solid with half a mole of chlorine gas. Remember in formation equations we can have fractions and decimals as coefficients.

Now in order to calculate the enthalpy of formation, both elements must first be converted into their ionic gaseous forms. So we're starting out here with sodium solid. We're starting out here with Cl2 gas. What we need to do first is realize that we need to get sodium to its ionic form as a gas, and we need to get chlorine to its ionic form as a gas as well. To do that, I first have to convert sodium solid into a gas. Going from a solid to a gas is called sublimation. So we're dealing with enthalpy of sublimation.

Once I have it in its gaseous state, I need to change it from a neutral metal to a positively charged metal. That means I'm removing electrons. Removing electrons has to do with ionization energy, and since I'm only removing one electron, its ionization energy one. If I needed to remove more than one electron, then I'd have to add an ionization 2, ionization 3, and so on. Remember we talked about this under successive ionization energy's.

Next Here I need to separate Cl2 into two separate chlorines, so I have to break the bond. This is called enthalpy of dissociation. Here, once we break the bond between the two chlorines, I just have one chlorine now as a gas, and then I have to add an electron to it. Adding an electron is an electron affinity, and since I'm only adding one electron, it's EA one. If I had to add more than one electron, there would be EA2EA3 and so on.

Now that I have both of them in their ionic forms, they're going to combine together to give me my solid. Remember combining gaseous ions to form a solid ionic product? This is connected to lattice energy, so it's a whole process. We have to do all of this just to get the enthalpy of formation. So I need to do step one which is enthalpy of sublimation. Step 2 would be ionization energy which could be in more than one step. Step three I have to do enthalpy of dissociation to break a bond so I can get a single chlorine. Then I need to make it negative. So what I have to do? Electron affinity, which also could be more than one step. Once I get them into their ionic gas form, then I have lattice energy to complete it.

O. You can say that enthalpy of formation is composed of these five fundamental steps. So like I told you, the Born Haber cycle has a lot of parts to it. But just remember the method we used here to justify how sodium combines with chlorine to give us sodium chloride.

Born Haber Cycle Example 1

Here it says when setting up the steps of the Bornhaber cycle for potassium oxide, how many ionization energies IE and how many electron affinities EA do you need? Remember we have to get them into their ionic forms right? And we need two potassium ions as gas to combine with one oxide ion as a gas. Then they will combine to give me potassium oxide solid.

Realize here that we need oxygen to get a 2 minus charge. So we're not adding one electron, we're adding two electrons. That means that we're going to need to do 2 electron affinities O we need 2 electron affinities, which means this is out, this is out, and this is out. And then finally, what else do we need?

Well, we have one potassium solid initially, but at the end we're going to need 2 potassiums. So we're going to have to do ionization energy twice, one for each of the potassium solids, and then both of them would then undergo, oops, we'll have them as gases actually, and then each one will have its electron plucked off. So we need to do 2 ionization energies, 1 for each Potassium as a neutral gas.

So we need to do 2 electron affinities and two ionization energies, giving us E as our final answer.

Using the Born-Haber Cycle, demonstrate the formation of cesium chloride, CsCl, and calculate its enthalpy of formation.

• A. -433 kJ/mol
• B. -354 kJ/mol
• C. 589 kJ/mol
• D. 498 kJ/mol

Calculate the lattice energy for the following formation equation:

• A. -891 kJ/mol
• B. -598 kJ/mol
• C. -1049 kJ/mol
• D. -2098 kJ/mol

Here’s what students ask on this topic:

What is the Born-Haber cycle?

The Born-Haber cycle is a theoretical model used in chemistry to help understand the formation of ionic compounds from their constituent elements. It's a way of applying Hess's Law, which states that the total enthalpy change in a chemical reaction is the same, regardless of the number of steps the reaction is carried out in.

In the Born-Haber cycle, the formation of an ionic compound is considered as a series of steps that include sublimation, ionization, and electron affinity, leading up to the final lattice energy of the compound. The cycle begins with the elements in their standard states and ends with the formation of ionic crystals.

The purpose of the Born-Haber cycle is to analyze the different energy changes that occur during the formation process. By doing so, chemists can calculate the lattice energy of an ionic solid - a measure of the strength of the ionic bonds within the solid - which cannot be measured directly. Understanding these energy changes is crucial for predicting the stability and properties of ionic compounds.

How can lattice energy be calculated from the Born-Haber cycle?

To calculate lattice energy using the Born-Haber cycle, you need to consider the various energy changes that occur when forming an ionic compound from its elements. The Born-Haber cycle is a thermochemical cycle that relates the lattice energy of an ionic solid to the enthalpy changes of several other steps that include:

1. Sublimation of the solid metal to gaseous atoms.
2. Ionization of the gaseous metal atoms to metal cations.
3. Dissociation of the non-metal molecule into gaseous atoms (if the non-metal is diatomic or polyatomic).
4. Ionization of the non-metal atoms to anions (electron affinity).
5. Formation of the ionic solid from gaseous ions (lattice energy).

The lattice energy can be calculated using Hess's Law, which states that the total enthalpy change for a reaction is the same regardless of the number of steps it takes. By combining the enthalpy changes for the steps mentioned above, and knowing the overall enthalpy change of the formation of the ionic compound (which can be found in tables or measured experimentally), you can solve for the lattice energy. Essentially, the lattice energy is the difference between the sum of the enthalpies of the individual steps and the overall enthalpy change of formation.

How do you draw a Born-Haber cycle?

To draw a Born-Haber cycle, you'll be constructing an energy diagram that illustrates the steps involved in forming an ionic compound from its constituent elements. Here's a step-by-step guide:

1. Start with the Elements: At the top of the diagram, write down the reactants in their standard states, which are the pure elements in their most stable form at 1 atm and 25°C (298 K).
2. Atomization: Draw a horizontal line to represent the energy of the elements. From this line, draw an arrow upwards for the endothermic atomization process of the metal to form gaseous atoms, and label the energy change (atomization enthalpy).
3. Ionization: From the metal atoms, draw another upward arrow to represent the endothermic ionization of the metal atoms to form cations, labeling the ionization energy.
4. Dissociation and Electron Affinity: For the non-metal, show the endothermic process of dissociation if it's a diatomic molecule, then an arrow downwards for the exothermic addition of an electron(s) to form anions, labeled with the electron affinity.
5. Lattice Energy: Finally, from the gaseous ions, draw a large arrow downwards to represent the exothermic formation of the ionic compound, which