What is the formal definition of lattice energy of formation?

It is the enthalpy change when one mole of a solid ionic compound is formed from its constituent gaseous ions under standard conditions. It is always an exothermic process.

How does increasing the ionic radius of the constituent ions affect the lattice energy?

Increasing the ionic radius makes the lattice energy less exothermic (less negative). This is because the centers of the ions are further apart, which weakens the electrostatic forces of attraction between them.

Why is the lattice energy of Magnesium Oxide ($MgO$) much more exothermic than that of Sodium Chloride ($NaCl$)?

Magnesium and oxide ions both have higher charges ($+2$ and $-2$) compared to sodium and chloride ($+1$ and $-1$). Additionally, $Mg^{2+}$ is smaller than $Na^+$, leading to much stronger electrostatic attractions in the $MgO$ lattice.

What does a significant difference between the theoretical and experimental lattice energy of a compound suggest?

It suggests that the bonding is not purely ionic and has some 'covalent character.' This occurs when the cation polarizes the anion, distorting its electron cloud and creating a stronger bond than predicted by the purely electrostatic model.

What is the difference between 'polarising power' and 'polarisability'?

Polarising power refers to the ability of a cation to distort the electron cloud of a neighboring anion. Polarisability refers to the ease with which an anion's electron cloud can be distorted by a cation.

Which type of cation has the highest polarising power?

Cations that are small and have a high positive charge (high charge density) have the highest polarising power. For example, $Li^+$ has more polarising power than $K^+$ because it is smaller.

What is a common error when writing the chemical equation for the lattice energy of $MgCl_2$?

A common error is forgetting the state symbols or the stoichiometry. The correct equation is $Mg^{2+}(g) + 2Cl^-(g) \\rightarrow MgCl_2(s)$. Note that the ions must be gaseous and there must be two chloride ions.

Why is lattice energy always a negative value in the context of formation?

Lattice formation involves the creation of bonds between oppositely charged ions, which releases energy. Since energy is given out to the surroundings, the process is exothermic and the enthalpy change is negative.

How does the Born-Haber cycle relate to Hess's Law?

A Born-Haber cycle is an application of Hess's Law, stating that the total enthalpy change for a reaction is the same regardless of the route taken. It allows the calculation of lattice energy by using an alternative route of measurable enthalpy changes.

What error occurs if you use the enthalpy of atomisation of $Cl_2$ instead of $Cl$ in a $MgCl_2$ cycle?

The enthalpy of atomisation is defined per mole of gaseous atoms formed. Since $MgCl_2$ requires two moles of $Cl$ atoms, you must double the atomisation value; failing to do so results in an incorrect lattice energy calculation.

Lattice Energy | Pearson Edexcel A-Level Chemistry

1. Definition & Core Concepts

Lattice Energy ( $\\Delta H_{latt}^{\\ominus}$ ) is formally defined as the enthalpy change that occurs when one mole of an ionic solid is formed from its constituent gaseous ions under standard conditions.
This process is always exothermic, meaning energy is released as the gaseous ions move from an infinite separation to their fixed positions in a highly ordered crystalline structure. Consequently, the value of lattice energy is always negative.
The magnitude of this energy release indicates the stability of the ionic compound; a more negative (more exothermic) value signifies a more stable lattice with stronger ionic bonds.
It is important to distinguish this from the enthalpy of formation, which involves elements in their standard states, whereas lattice energy specifically requires the starting materials to be gaseous ions.

Energy level diagram showing the transition from high-energy gaseous ions to a low-energy solid ionic lattice, illustrating the exothermic nature of lattice energy.

2. Underlying Principles: Factors Affecting Magnitude

The magnitude of lattice energy is governed by Coulomb's Law, which states that the force of attraction between two charged particles is proportional to the product of their charges and inversely proportional to the square of the distance between them.
Ionic Charge: As the charge on the ions increases (e.g., from $+1$ to $+2$ ), the electrostatic attraction becomes significantly stronger. This results in a much more exothermic lattice energy because more energy is released when these highly charged ions bond.
Ionic Radius: Smaller ions can pack more closely together in the lattice, reducing the distance between the centers of the oppositely charged nuclei. This proximity increases the strength of the attraction, making the lattice energy more exothermic.
Consequently, the most exothermic lattice energies are found in compounds containing small, highly charged ions, such as magnesium oxide ( $MgO$ ).

3. Theoretical vs. Experimental Values

The Purely Ionic Model: Theoretical calculations of lattice energy assume that ions are perfect, non-polarisable spheres and that the bonding is 100% electrostatic. This is known as the point-charge model.
Covalent Character: In many real-world compounds, the experimental lattice energy (determined via a Born-Haber cycle) is more exothermic than the theoretical value. This discrepancy occurs because the cation distorts the electron cloud of the anion, a process called polarisation.
Polarization introduces a degree of covalent character into the bond. Because covalent bonds involve the sharing of electrons and provide additional stability beyond pure electrostatic attraction, the actual lattice is stronger than predicted by the ionic model.
Polarization is most significant when a small, highly charged cation (high polarising power) is paired with a large anion (high polarisability).

4. Methods & Techniques: Born-Haber Cycles

Lattice energy cannot be measured directly in a single laboratory experiment. Instead, it is calculated indirectly using a Born-Haber cycle, which is a specific application of Hess's Law.
The cycle connects the enthalpy of formation of an ionic compound to a series of measurable steps: atomisation of elements, ionisation energy of the metal, and electron affinity of the non-metal.
By summing these energy changes, the 'indirect route' to the ionic solid is established. The lattice energy is then found by closing the loop between the gaseous ions and the solid product.
This method allows chemists to determine the strength of the lattice by accounting for all the energy required to transform elements in their standard states into gaseous ions.

5. Key Distinctions

Comparison of Factors

Factor	Change	Effect on Lattice Energy
Ionic Charge	Increase (e.g. $+1 \\rightarrow +2$ )	Becomes more exothermic (stronger attraction)
Ionic Radius	Increase (moving down a group)	Becomes less exothermic (ions further apart)
Bonding Type	Pure Ionic vs. Covalent Character	Covalent character makes it more exothermic than theoretical

Lattice Formation vs. Dissociation: While usually defined as the formation of a solid from ions (exothermic), some contexts define it as the energy required to break the lattice into ions (endothermic). Always check the sign convention used in the specific problem.
Polarising Power vs. Polarisability: Polarising power is a property of the cation (ability to distort others), while polarisability is a property of the anion (ease of being distorted).

6. Exam Strategy & Tips

State Symbols are Critical: In any equation representing lattice energy, the reactants MUST be in the gaseous state ( $g$ ) and the product MUST be in the solid state ( $s$ ). Forgetting these symbols is a common way to lose marks.
The 'More Exothermic' Trap: When comparing two compounds, use the phrase 'more exothermic' or 'more negative' rather than 'larger' or 'smaller'. This demonstrates a clear understanding of the thermodynamic sign convention.
Check the Stoichiometry: When calculating lattice energy from a Born-Haber cycle, ensure you multiply the enthalpy of atomisation or electron affinity by the correct coefficient if the formula contains multiple atoms of one type (e.g., $MgCl_2$ requires $2 \\times$ the electron affinity of chlorine).
Reasoning Chains: When asked to explain trends, always follow this logical path: 1. State the change in radius/charge $\\rightarrow$ 2. State the effect on electrostatic attraction $\\rightarrow$ 3. Conclude the effect on the magnitude of lattice energy.

Lattice Energy

Summary

1. Definition & Core Concepts

2. Underlying Principles: Factors Affecting Magnitude

3. Theoretical vs. Experimental Values

4. Methods & Techniques: Born-Haber Cycles

5. Key Distinctions

6. Exam Strategy & Tips

Lattice Energy

Summary

1. Definition & Core Concepts

2. Underlying Principles: Factors Affecting Magnitude

3. Theoretical vs. Experimental Values

4. Methods & Techniques: Born-Haber Cycles

5. Key Distinctions

Comparison of Factors

6. Exam Strategy & Tips

Comparison of Factors