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The Born-Haber Cycle: Calculating Lattice Energy of Ionic Solids

The Born-Haber cycle is a thermochemical concept used to calculate the lattice energy of ionic solids. It involves steps like sublimation, ionization, and electron affinity, and utilizes Hess's Law to determine the energy changes during the formation of an ionic compound. The cycle provides insights into the stability and physical properties of ionic substances, such as melting points and solubility, by depicting the sequence of enthalpy changes from element to ionic compound.

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1

Define lattice energy in thermochemistry.

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Lattice energy is the energy needed to separate one mole of an ionic solid into gaseous ions.

2

State Hess's Law.

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Hess's Law posits that total enthalpy change of a reaction is constant, irrespective of the reaction pathway.

3

Role of lattice energy in ionic substances.

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Lattice energy determines the stability and properties of ionic compounds.

4

The standard conditions for measuring ______ ______ are a pressure of 1 bar and a temperature of 298 K.

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lattice enthalpy

5

Purpose of Born-Haber cycle

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Calculates lattice enthalpy, reveals energy changes in ionic compound formation.

6

Role of sublimation in Born-Haber cycle

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Converts solid element to gaseous atoms, initial step in cycle.

7

Significance of electron affinity in Born-Haber cycle

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Energy change when electron added to non-metal atom, forms anion.

8

The ______ ______ of formation is the thermal variation when one mole of a compound is created from its elements in their ______ states.

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standard enthalpy standard

9

The standard enthalpy of ______ is the energy needed to generate one mole of ______ atoms from an element in its standard state.

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atomisation gaseous

10

Ionisation Energy Definition

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Energy required to remove an electron from a gaseous atom, forming a cation.

11

Electron Affinity Definition

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Energy change when an electron is added to a gaseous atom, forming an anion.

12

Born-Haber Cycle Importance

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Illustrates energy changes during formation of ionic compounds from neutral atoms.

13

The cycle includes ______ energies for the metal and ______ affinities for the non-metal, with multiple values added ______ if necessary.

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ionisation electron sequentially

14

Purpose of Born-Haber cycle

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Calculates lattice enthalpies; predicts ionic compound formation energy.

15

Sequence of enthalpy changes in Born-Haber cycle

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Shows energy steps in ionic solid formation; aids in understanding chemical bonding energetics.

16

Connection between Born-Haber cycle and physical properties

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Links theoretical calculations to observable properties; enhances understanding of ionic solids.

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Exploring the Born-Haber Cycle

The Born-Haber cycle is an essential concept in thermochemistry, providing a method to calculate the lattice energy of ionic solids. This cycle is a hypothetical series of steps that represents the formation of an ionic compound from its constituent elements in their standard states. It involves the use of Hess's Law, which states that the total enthalpy change for a chemical reaction is the same, regardless of the route by which the chemical reaction takes place. The lattice energy, which can be defined as the energy required to separate one mole of a solid ionic compound into its gaseous ions, is a critical factor in determining the stability and properties of ionic substances.
Cubic crystal structure with blue and red spheres representing cations and anions in an ionic lattice, on gray gradient background.

The Importance of Lattice Enthalpy

Lattice enthalpy is a fundamental property that influences the physical characteristics of ionic compounds, including melting points, boiling points, and solubility. It is an indirect measure of the electrostatic forces between ions in a crystal lattice. While lattice enthalpy itself cannot be measured directly, it can be derived from other measurable thermodynamic quantities using the Born-Haber cycle. The standard conditions for lattice enthalpy are a pressure of 1 bar (slightly different from the historical 1 atm) and a temperature of 298 K (25°C).

Steps in the Born-Haber Cycle

The Born-Haber cycle integrates various thermodynamic processes, such as sublimation, ionization, and electron affinity. It begins with the sublimation of the solid element to form gaseous atoms, followed by the ionization of the metal atoms and the addition of electrons to the non-metal atoms. The cycle also includes the dissociation of diatomic molecules for non-metal elements and the formation of the ionic compound. By summing the enthalpy changes for each step, the lattice enthalpy can be calculated, providing insight into the energy changes during compound formation.

Enthalpy of Formation and Atomisation

The standard enthalpy of formation is the heat change that occurs when one mole of a compound is formed from its elements in their standard states. Conversely, the standard enthalpy of atomisation is the heat change required to produce one mole of gaseous atoms from an element in its standard state. The enthalpy of atomisation is always positive, reflecting the endothermic nature of breaking chemical bonds within an element to form individual atoms.

Ionisation Energy and Electron Affinity in the Cycle

Ionisation energy and electron affinity are pivotal in the Born-Haber cycle, representing the energy changes associated with the formation of ions from atoms. Ionisation energy is the energy required to remove an electron from a gaseous atom, resulting in a cation. Electron affinity is the energy change when an electron is added to a gaseous atom, leading to the formation of an anion. These steps are integral to the cycle as they reflect the transition from neutral atoms to charged ions, which are the building blocks of ionic compounds.

Constructing a Born-Haber Cycle

Constructing a Born-Haber cycle involves a systematic approach to account for all relevant enthalpy changes in the formation of an ionic compound. The cycle starts with the standard enthalpy of formation, followed by the enthalpy of atomisation for each element. Next, the ionisation energies for the metal and the electron affinities for the non-metal are considered. If multiple ionisation energies or electron affinities are involved, they are included sequentially. The cycle is depicted graphically, with exothermic processes shown with downward arrows and endothermic processes with upward arrows, culminating in the determination of the lattice enthalpy.

Insights from Born-Haber Cycles

The Born-Haber cycle is a vital analytical tool in chemistry, enabling the calculation of lattice enthalpies and providing insights into the energy changes during the formation of ionic compounds. Understanding the sequence of enthalpy changes and their application within the cycle allows chemists to predict and explain the properties of ionic substances. This concept is not only fundamental for theoretical calculations but also for connecting these calculations to observable physical properties, enhancing our comprehension of chemical bonding and the energetics of ionic solids.