Thermodynamics - AL only (3.1.8)

It is useful to note that, while it is possible to draw Born-Haber cycles to scale, this is not necessary for their use. A rough sketch is sufficient in an exam.

The ionic compound in its standard state will be at the cycle’s lowest point. This can be created from its elements in their standard states () or from its constituent ions in their gaseous states ().

Note that both arrows follow the direction of the reaction described in the enthalpy definitions: towards the ionic compound.

The remaining enthalpies are used to connect the elements in their standard states to the ions in their gaseous states.

To connect the elements in their standard states to the ions in their gaseous states.

• Atomise each element, ​ separately. This is endothermic, so the single gaseous species sits above the element in its standard state.

• Take electrons from the metal atoms to reach their preferred charge, This is endothermic so the gaseous cation will sit above its gaseous atom.

• Ionise the non-metal atoms to their preferred charge, This is exothermic, so the gaseous anion will sit below its gaseous atom.

Born-Haber cycles can be used to calculate missing enthalpies.

Hess’s Law states that the total enthalpy change in a chemical reaction is independent of the route by which the chemical reaction takes place as long as the initial and final conditions are the same.

For a Born-Haber cycle this means, for example, that the formation enthalpy can be equated to the sum of the remaining enthalpies shown.

In this example, all arrows are followed in their forwards direction, so there is no need for sign reversal.

Water molecules, being polar, have a partial negative charge on the oxygen atom and a partial positive charge on the hydrogen atoms.

During hydration, when gaseous ions dissolve in water, the negative ions show intermolecular interactions with the positive sides of water molecules, whilst positive ions interact with the negative side.

This interaction releases energy, making the hydration process exothermic.

The hydration enthalpy depends on the charge and size of the ion. Smaller, highly charged ions have a greater charge density and show higher due to stronger ion-dipole interactions.

The lattice enthalpy, the enthalpy of solution and the enthalpies of hydration can be connected in an enthalpy cycle.

It is useful to know that this enthalpy cycle can be used to calculate a missing value given a subset of the data.

Polarisation of ions is the electron cloud distortion around an anion due to proximity to cation of high charge density.

When an ion is highly polarised, there is a degree of electron sharing, and the bonding becomes partially covalent.

The most polarisable anions are large with a low charge; the charge density is low.

The most polarising cations are small with a high charge; the charge density is high.

A system with high entropy has more ways of arranging particles and hence is more disordered. Conversely, a system with low entropy is more ordered.

In a solid, particles are arranged in a structured, fixed pattern, leading to lower entropy compared to liquids and gases where particles have freedom to move around.

Entropy in solids

Particle arrangement: In a solid, particles are tightly packed in a fixed, orderly structure, such as a crystalline lattice. The particles have limited movement and vibrate about fixed positions.

Energy distribution: Energy is not widely dispersed because the particles have little freedom to move. As a result, solids have low entropy.

Example: A crystal of sodium chloride at room temperature has relatively low entropy due to its highly ordered crystalline structure.

Entropy in liquids

Particle arrangement: In a liquid, particles are still close together but not in a fixed position. They can move around and slide past each other, giving liquids a fluid nature.

Energy distribution: There is more dispersal of energy compared to solids, leading to higher entropy. The particles have more freedom to move, but not as much as in a gas.

Example: Liquid water ( at room temperature has higher entropy than ice because the water molecules can move more freely.

Entropy in gases

Particle arrangement: In a gas, particles are far apart and move independently in all directions. There is no fixed structure, and the particles are in constant, random motion.

Energy distribution: Energy is highly dispersed because the particles have the greatest freedom of movement. As a result, gases have the highest entropy.

Example: Gaseous oxygen ( has very high entropy compared to liquid oxygen or solid oxygen because in the gaseous state the oxygen molecules are free to move throughout the entire volume of the container.

This graph shows how entropy changes as temperature increases across the solid, liquid and gas phases:

The graph shows that as a substance changes state there is a dramatic increase in entropy shown by the vertical lines (boiling and melting). This is linked to the change in particle arrangement.

The entropy increases gradually with temperature within a state. This is linked to increased vibration and/or motion of the particles and its relationship to the degree of disorder and energy dispersal increases.

Consider , the change in entropy, for the decomposition of copper carbonate :

In this reaction, a solid decomposes to produce a solid and a gas ). The number of gaseous molecules increases from zero to one.

The formation of a gaseous molecule from a solid significantly increases the system’s entropy because the gas molecules are much more disordered and have more freedom to move than solid particles.

Consider , the change in entropy, for the synthesis of ammonia from nitrogen and hydrogen in the Haber process:

In this reaction, four moles of gas – one mole of – and three moles of react to produce two moles of ammonia gas.

The total number of gaseous molecules decreases from four to two, which means the entropy of the system decreases.

Fewer gas molecules result in less disorder and a lower entropy state.

Entropy, , measures system disorder; reactions increasing disorder (positive ) are more likely feasible, especially at higher temperatures where becomes more significant.

is the product of entropy and temperature, highlighting entropy’s influence as temperature rises. When the value of is negative, favouring feasibility.

can tell us if a reaction is thermodynamically feasible, but it does not provide any information about the rate of the reaction.

A reaction with a negative might occur so slowly that it is effectively not happening within any practical time frame. This is often due to a high activation energy barrier.

Activation energy, , is the minimum energy required for reactants to form the transition state before converting into products.

Even if , a high activation energy can make the reaction proceed very slowly.

Consider dissolving ammonium nitrate in water.

There is an increase in entropy, as the solid dissolves into ions in solution, creating disorder, which drives the reaction.

This endothermic reaction, absorbs thermal energy, cooling the surroundings.

The increase in entropy makes the reaction feasible despite a positive enthalpy change. It is only spontaneous above a given temperature.

Consider the mixing of solid barium hydroxide with solid ammonium chloride.

This is a highly endothermic reaction, absorbing enough thermal energy from the surroundings to reduce the environmental temperature to below the freezing point of water.

The magnitude of the entropy increase when solid products are fully converted to gases and liquids is so large that the reaction is feasible despite a highly positive .

The reaction is only spontanious above certain temperatures.