In this section, we will delve into the Born–Haber cycle, a vital concept in thermodynamics used to analyse the formation of ionic compounds. We'll explore its components, interpret the cycle, and understand factors influencing lattice enthalpy.
Introduction to the Born–Haber Cycle
The Born–Haber cycle is a series of hypothetical steps that represent the formation of an ionic compound from its constituent elements. It connects various thermodynamic properties such as ionisation energy, electron affinity, and lattice enthalpy to calculate the overall enthalpy change for the formation of the compound.
Components of the Born–Haber Cycle
1. Ionisation Energies
- First Ionisation Energy: The energy required to remove one mole of electrons from one mole of gaseous atoms to form one mole of +1 ions.
- Second Ionisation Energy: Required when removing a second electron to form +2 ions, and so on.
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2. Enthalpy of Atomisation
- This is the energy required to convert one mole of a substance into its gaseous atoms.
- For metals, it's the enthalpy change when one mole of solid metal is vaporised to form gaseous atoms.
- For non-metals, it might involve breaking covalent bonds to form gaseous atoms.
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3. Electron Affinities
- First Electron Affinity: The energy change when one mole of electrons is added to one mole of gaseous atoms to form one mole of -1 ions.
- Second Electron Affinity: Energy change when adding a second electron to form -2 ions.
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4. Lattice Enthalpy
- The energy required to separate one mole of an ionic compound into its gaseous ions.
- It is always exothermic for ionic compounds, as energy is released when the gaseous ions come together to form a solid lattice.
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5. Enthalpy of Formation
- The enthalpy change when one mole of the compound is formed from its elements in their standard states.
Interpreting the Born–Haber Cycle
- The cycle helps visualise the energy changes involved in the formation of an ionic compound.
- It starts with the elements in their standard states and progresses through various stages, including atomisation, ionisation, and electron gain, until the ionic compound is formed.
- The energy levels in the cycle represent the potential energy of the system, and the arrows show the energy changes for each step.
Calculating Values from the Born–Haber Cycle
- To find the lattice enthalpy of an ionic compound:
- Sum the energies of all the steps in the cycle.
- The sum of the energies of the steps equals the enthalpy change of formation of the ionic compound.
- Rearrange the equation to solve for the unknown.
- Example: For NaCl,
- Enthalpy of atomisation (Na) + First ionisation energy (Na) + Enthalpy of atomisation (Cl) + First electron affinity (Cl) + Lattice enthalpy (NaCl) = Enthalpy of formation (NaCl)
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Factors Influencing Lattice Enthalpy
- Ionic Size: Smaller ions have stronger attraction and higher lattice enthalpy.
- Ionic Charge: Ions with higher charges attract each other more strongly, leading to a higher lattice enthalpy.
- Polarisability: Larger anions are more easily distorted, reducing the lattice enthalpy.
Practical Implications and Applications
- Understanding lattice enthalpy helps predict the stability of ionic compounds.
- It also provides insights into the physical properties of ionic substances, such as melting and boiling points.
By thoroughly understanding the Born–Haber cycle and its components, students can gain a comprehensive insight into the energetics of ionic compounds, equipping them with the knowledge to tackle related IB Chemistry problems and appreciate the practical implications in real-world contexts.
FAQ
The Born–Haber cycle is a theoretical construct used to analyse and predict the formation of ionic compounds. While the steps in the Born–Haber cycle do not directly represent the actual processes that occur during the formation of an ionic solid from its elements, they provide a useful model for understanding and calculating the energetics involved. In reality, ionic compounds form in a more complex manner, often involving gaseous ions coming together to form a solid. Despite this complexity, the Born–Haber cycle accurately reflects the overall change in enthalpy and helps chemists understand and quantify the forces at play in the formation of ionic compounds.
Ionisation energy and electron affinity are crucial components of the Born–Haber cycle because they account for the energy changes associated with forming ions from atoms. Ionisation energy represents the energy required to remove an electron from an atom, turning it into a cation. Electron affinity, on the other hand, reflects the energy change when an electron is added to an atom, forming an anion. Since ionic compounds consist of cations and anions, these energy changes are essential for accurately calculating the lattice enthalpy and understanding the overall energetics of ionic compound formation.
The structure of an ionic compound, including the arrangement of ions and their coordination numbers, plays a significant role in determining its lattice enthalpy. In a closely packed structure, where ions are efficiently arranged and have high coordination numbers, the interactions between ions are maximised, leading to a higher lattice enthalpy. Conversely, in a less efficiently packed structure with lower coordination numbers, the interactions between ions are reduced, resulting in a lower lattice enthalpy. The specific geometry and arrangement of ions in the crystal lattice are thus key factors influencing the strength of the ionic bonds and the stability of the ionic compound.
Lattice enthalpy cannot be measured directly because it involves the hypothetical process of forming an ionic compound from its gaseous ions, which is not a practical experimental setup. Instead, the Born–Haber cycle is employed to calculate lattice enthalpy indirectly. This cycle breaks down the formation of an ionic compound into a series of steps, each of which corresponds to a physical process with an associated enthalpy change that can be measured or calculated. By using these known values and applying Hess's law, which states that the total enthalpy change for a reaction is the same, no matter how many steps the reaction is carried out in, the lattice enthalpy can be deduced.
The lattice enthalpy of an ionic compound provides invaluable insight into its physical properties, such as melting and boiling points, solubility, and hardness. A compound with a high lattice enthalpy typically has high melting and boiling points because more energy is required to overcome the strong ionic bonds. Such a compound also tends to be less soluble in water and is usually harder. Conversely, a compound with a lower lattice enthalpy will have lower melting and boiling points, and it is likely to be more soluble in water and softer. Understanding lattice enthalpy is crucial for predicting how an ionic compound will behave under different conditions, aiding in the synthesis and application of these compounds in various fields.
Practice Questions
- First ionisation energy of K: +418.8 kJ/mol
- Second ionisation energy of K: +3051 kJ/mol
- Enthalpy of atomisation of K: +89 kJ/mol
- Enthalpy of atomisation of O: +249 kJ/mol
- First electron affinity of O: -141 kJ/mol
- Second electron affinity of O: +744 kJ/mol
- Enthalpy of formation of K2O: -361 kJ/mol
Calculate the lattice enthalpy of K2O.
To find the lattice enthalpy of K2O, we need to use the Born–Haber cycle and the provided data. First, sum the atomisation energies of potassium and oxygen, which are +89 kJ/mol and +249 kJ/mol respectively. Then, add the ionisation energies of potassium. Since we need two moles of K+ ions, we multiply the first ionisation energy by 2, resulting in +837.6 kJ/mol. However, for the second electron, the ionisation process requires significantly more energy, totaling +6102 kJ/mol. Next, include the electron affinity of oxygen. Since we are forming O2-, we add the first electron affinity and then subtract the second (as it requires energy input), giving a total of -397 kJ/mol. Adding these values together with the enthalpy of formation of K2O (-361 kJ/mol), we can solve for the lattice enthalpy. The lattice enthalpy of K2O is found to be -2247.6 kJ/mol.
The lattice enthalpy of an ionic compound is significantly influenced by the size and charge of the ions. Smaller ions have stronger attraction between the positive and negative charges, leading to a higher lattice enthalpy. This is because the distance between the charges in smaller ions is less, resulting in a stronger electrostatic attraction. On the other hand, larger ions have a weaker attraction due to the increased distance between the charges, resulting in a lower lattice enthalpy. Regarding the charge of the ions, ions with higher charges attract each other more strongly. Therefore, an ionic compound composed of ions with higher charges will have a higher lattice enthalpy compared to a compound with ions of lower charges. This is because the electrostatic force of attraction is directly proportional to the product of the charges of the ions. In summary, smaller, highly charged ions result in a compound with a higher lattice enthalpy due to the stronger electrostatic forces of attraction.
