Lattice Enthalpy, Entropy, and Gibbs Free Energy

Flashcards covering definitions of enthalpy changes, Born-Haber cycles, lattice energy trends, entropy, Gibbs free energy calculations, and enthalpies of solution and hydration.

What is the standard enthalpy change of formation ($\Delta_f H$)?

The energy transferred when $1\text{ mole}$ of a compound is formed from its elements under standard conditions ($298\,K$ and $100\text{ kPa}$), with all reactants and products being in their standard states.

How is the enthalpy of atomisation ($\Delta_{at} H$) defined, and what alternative name applies to solid metals?

It is the enthalpy change when $1\text{ mole}$ of gaseous atoms is formed from the element in its standard state. For a solid metal turning into gaseous atoms, it is also called the enthalpy of sublimation ($\Delta_{sub} H$) and is numerically identical.

What is the difference between first ionisation enthalpy and second ionisation enthalpy?

First ionisation enthalpy is the enthalpy change required to remove $1\text{ mole}$ of electrons from $1\text{ mole}$ of gaseous atoms to form $1\text{ mole}$ of gaseous $1+$ ions ($Mg\,(g) \rightarrow Mg^+\,(g) + e^-$). Second ionisation enthalpy is the enthalpy change to remove $1\text{ mole}$ of electrons from $1\text{ mole}$ of gaseous $1+$ ions to produce $1\text{ mole}$ of gaseous $2+$ ions ($Mg^+\,(g) \rightarrow Mg^{2+}\,(g) + e^-$).

Why is the first electron affinity exothermic while the second electron affinity is endothermic?

The first electron affinity is exothermic because the resulting negative ion is more stable than the neutral atom and an attractive force exists between the nucleus and the incoming electron. The second electron affinity is endothermic because energy is required to overcome the repulsive electrostatic force between the negative ion and the incoming electron.

What is the lattice enthalpy ($\Delta_{LE} H$) of formation?

The standard enthalpy change when $1\text{ mole}$ of an ionic crystal lattice is formed from its constituent ions in gaseous form (e.g., $Na^+\,(g) + Cl^-\,(g) \rightarrow NaCl\,(s)$). It serves as a measure of ionic bond strength.

How is the bond energy of chlorine related to its enthalpy of atomisation?

$E(Cl-Cl) = 2 \times \Delta_{at} H(Cl)$.

What two factors determine the strength of lattice enthalpy?

1. The sizes of the ions: larger ions result in less negative lattice enthalpies (weaker lattices) because the charges are further apart and have weaker attractive forces.
2. The charges on the ions: higher ionic charges result in greater attraction and stronger, more negative lattice enthalpies.

How do lattice enthalpies vary down a group in the periodic table?

Lattice enthalpies become less negative down any group (e.g., from $LiCl$ to $NaCl$, $KCl$, and $RbCl$) because the ionic radius increases, weakening the electrostatic attraction.

What is a spontaneous process?

A process (such as diffusion) that will proceed on its own without any external influence.

What is entropy ($S$) and how does it relate to the number of arrangements ($W$)?

Entropy is a description of the number of ways atoms can share quanta of energy. If the number of ways of arranging the energy ($W$) is high, the system is disordered and entropy ($S$) is high.

Which groups of substances tend to have lower entropies relative to others?

Elements tend to have lower entropies than compounds; simpler compounds tend to have lower entropies than complex compounds; and pure substances tend to have lower entropies than mixtures.

Based on this graph showing entropy versus temperature, why is the jump in entropy for boiling significantly larger than the jump for melting?

Gases have large entropies because particles in the gas phase are much more disordered than in liquids or solids, whereas melting produces a much smaller increase in disorder.

Under what condition does a substance have an entropy of zero?

Only perfect crystals at absolute zero ($T = 0\,K$) have zero entropy. Elements in their standard states do not have zero entropy, and it is impossible for a substance to have a standard entropy less than zero.

What qualitative changes in a chemical reaction indicate a positive entropy change ($\Delta S^\circ > 0$)?

A change of state from solid or liquid to gas, or a significant increase in the total number of gas/product molecules relative to reactants.

Based on this reaction profile, why might a thermodynamically feasible reaction with a negative Gibbs free energy change ($\Delta G < 0$) fail to occur at room temperature?

If the reaction has a high activation energy ($E_A$), the rate of reaction will be so slow that effectively the reaction does not happen.

What is the Gibbs free energy relationship, and what unit conversion is required for $\Delta S$?

$\Delta G = \Delta H - T\Delta S$. Since $\Delta S$ is measured in $J\,K^{-1}\,mol^{-1}$ and $\Delta H$ in $kJ\,mol^{-1}$, $\Delta S$ must be divided by $1000$ to convert to $kJ\,K^{-1}\,mol^{-1}$.

Under what thermodynamic conditions is a reaction always feasible at all temperatures?

When the reaction is exothermic ($\Delta H$ is negative) and involves an increase in entropy ($\Delta S$ is positive), making $\Delta G$ negative at all temperatures.

What is the value of $\Delta G$ during a physical phase change such as melting or boiling, and how can the transition temperature be calculated?

$\Delta G = 0$ during phase equilibria. The transition temperature is calculated using $T = \frac{\Delta H}{\Delta S}$.

In a plot of $\Delta G$ against temperature ($T$), what do the y-intercept and the gradient represent?

Applying $y = mx + c$ to $\Delta G = \Delta H - T\Delta S$, the y-intercept ($c$) equals $\Delta H$ and the gradient ($m$) equals $-\Delta S$.

How is the standard enthalpy of solution ($\Delta_{sol} H$) calculated using lattice formation enthalpy and hydration enthalpies?

$\Delta_{sol} H = -\Delta_{LE} H + \sum \Delta_{hyd} H$.

Based on this diagram of hydrated ions, how do water dipoles orient around cations and anions?

The partially negative oxygen atoms ($\delta^-$) of water molecules are attracted to positive ions (cations), and the partially positive hydrogen atoms ($\delta^+$) of water molecules are attracted to negative ions (anions).

What factors give an ion a more exothermic (more negative) hydration enthalpy?

A higher charge density, which occurs with smaller ionic radii or larger ionic charges, allows the ions to attract polar water molecules more strongly.

Why do salts with an exothermic enthalpy of solution ($\Delta_{sol} H < 0$) dissolve at all temperatures?

Dissolving increases disorder, so $\Delta S$ is positive and $-T\Delta S$ is always negative. When $\Delta H$ is also negative, $\Delta G$ is guaranteed to be negative at any temperature.

Why does increasing temperature increase the likelihood of dissolution for a salt with an endothermic enthalpy of solution ($\Delta_{sol} H > 0$)?

Because $\Delta S$ is positive when solid dissolves into ions, increasing $T$ makes the negative term $-T\Delta S$ more significant. At higher temperatures, $-T\Delta S$ can overcome the positive $\Delta H$, making $\Delta G$ negative and the process feasible.