Name: predicting ionic stability with lattice energy
Uploaded: 2020-09-03T13:38:28.000Z
Duration: 2 min 44 s
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North Carolina K-12 Science Standard Course of Study

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Chemistry

Matter and its Interactions

PS.Chm.3.1

The Born-Haber Cycle

La formazione di legami ionici richiede un trasferimento di elettroni da un metallo ad un atomo non metallico, un processo spesso endotermico. Tuttavia, quando il sodio elementare e il cloro reagiscono per formare un cristallo di cloruro di sodio solido, il processo é altamente esotermico. Ma da dove proviene l'energia?

Secondo la legge di Coulomb, cationi e anioni sono attratti l'uno all'altro da forti forze elettrostatiche, in una matrice solida, o reticolo. La struttura reticolare risultante viene stabilizzata diminuendo l'energia potenziale, che viene rilasciata sotto forma di calore, in una reazione esotermica. L'energia totale associata alla formazione o alla scomposizione di un reticolo cristallino nei suoi costituenti gassosi è detta energia reticolare.

In un composto ionico solido, un gran numero di particelle cariche interagiscono fra di loro, rendendo difficile determinare sperimentalmente il valore esatto dell'energia del reticolo. Tuttavia, tale valore può essere calcolato utilizzando la legge di Hess in una serie ipotetica di passaggi, detta ciclo di Born-Haber, che rappresenta la formazione di un composto ionico dai suoi elementi costitutivi. Per esempio, il ciclo di Born-Haber per la formazione del cloruro di sodio considera due percorsi alternativi, uno diretto e l'altro indiretto.

Il percorso diretto rappresenta l'entalpia standard di formazione di NaCl, da sodio elementare e cloro. Il percorso indiretto è composto da cinque passaggi. Nella prima fase, il sodio allo stato solido viene convertito nella sua forma gassosa.

Successivamente, le molecole di cloro biatomico si dissociano in atomi di cloro gassoso. La terza e la quarta fase tengono conto del trasferimento di elettroni per formare gli ioni. Un elettrone viene rimosso dal sodio gassoso per formare un catione di sodio.

L'elettrone viene quindi assorbito dal cloro gassoso per formare un anione cloruro. Nella fase finale, l'attrazione elettrostatica fra gli ioni gassosi, porta alla formazione della struttura reticolare. La legge di Hess afferma che la variazione dell'entalpia complessiva di un processo graduale è la somma delle variazioni entalpiche di ciascuna fase.

Quindi il valore dell'entalpia del percorso diretto è uguale alla somma delle entalpie delle cinque fasi. Risolvendo l'equazione per l'energia reticolare viene determinato un valore fortemente negativo, il che indica una reazione esotermica.

il ciclo born-haber

Energia del reticolo

Un composto ionico è stabile a causa dell'attrazione elettrostatica tra i suoi ioni positivi e negativi. L'energia reticolare di un composto è una misura della forza di questa attrazione. L'energia reticolare (ΔHlattice) di un composto ionico è definita come l'energia richiesta per separare una mole del solido nei suoi ioni gassosi che lo compongono.

Qui viene utilizzata la convenzione secondo cui il solido ionico viene separato in ioni, il che significa che le energie reticolari saranno endotermiche (valori positivi). Un altro modo è utilizzare una convenzione equivalente, ma opposta, in cui l'energia del reticolo è esotermica (valori negativi) e descritta come l'energia rilasciata quando gli ioni si combinano per formare un reticolo. Pertanto, bisogna assicurarsi di confermare quale definizione viene utilizzata quando si cercano le energie reticolari in un altro riferimento.

In entrambi i casi, una grandezza maggiore dell'energia reticolare indica un composto ionico più stabile. Per il cloruro di sodio, ΔHlattice = 769 kJ. Pertanto, sono necessari 769 kJ per separare una mole di NaCl solido negli ioni Na^+ e Cl^– gassosi. Quando una mole di ioni gassosi Na+ e Cl– forma NaCl solido, vengono rilasciati 769 kJ di calore.

Determinazione dell'energia reticolare di un composto ionico

Non è possibile misurare direttamente le energie reticolari. Tuttavia, l'energia reticolare può essere calcolata utilizzando un ciclo termochimico. Il ciclo di Born-Haber è un’applicazione della legge di Hess che scompone la formazione di un solido ionico in una serie di passaggi individuali:

<table style="margin-left: auto; margin-right: auto;">
	<tbody style="border: 1px solid black;">
		<tr>
			<td style="color: black; border: 1px solid black; text-align: center;">Entalpia di sublimazione di Cs (s)</td>
			<td colspan="2" style="color: black; border: 1px solid black; text-align: center;">Cs (s) → Cs (g)</td>
			<td style="color: black; border: 1px solid black; text-align: center;">ΔH = ΔHs° = 76,5 kJ/mol</td>
		</tr>
		<tr>
			<td style="color: black; border: 1px solid black; text-align: center;">Metà dell'energia di legame di F2</td>
			<td colspan="2" style="color: black; border: 1px solid black; text-align: center;">½ F2 (g) → F (g)</td>
			<td style="color: black; border: 1px solid black; text-align: center;">ΔH = ½ D = 79.4 kJ/mol</td>
		</tr>
		<tr>
			<td style="color: black; border: 1px solid black; text-align: center;">Energia di ionizzazione di Cs (g)</td>
			<td colspan="2" style="color: black; border: 1px solid black; text-align: center;">Cs (g)  → Cs+ (g) + e−</td>
			<td style="color: black; border: 1px solid black; text-align: center;">ΔH = IE = 375.7 kJ/mol</td>
		</tr>
		<tr>
			<td style="color: black; border: 1px solid black; text-align: center;">Affinità elettronica di F</td>
			<td colspan="2" style="color: black; border: 1px solid black; text-align: center;">F (g) + e− → F− (g)</td>
			<td style="color: black; border: 1px solid black; text-align: center;">ΔH = EA = −328.2 kJ/mol</td>
		</tr>
		<tr>
			<td style="color: black; border: 1px solid black; text-align: center;">Negativo dell'energia reticolare di CsF (s)</td>
			<td colspan="2" style="color: black; border: 1px solid black; text-align: center;">Cs+ (g) + F− (g) → CsF (s)</td>
			<td style="color: black; border: 1px solid black; text-align: center;">ΔH = −ΔHlattice = ?</td>
		</tr>
		<tr>
			<td style="color: black; border: 1px solid black; text-align: center;">Entalpia di formazione di CsF (s), add steps 1–5</td>
			<td colspan="2" style="color: black; border: 1px solid black; text-align: center;">ΔH = ΔHf° = ΔHs°+ ½ D + IE + (EA) + (−ΔHlattice) 
			Cs (s) + ½ F2 (g) → CsF (s)</td>
			<td style="color: black; border: 1px solid black; text-align: center;">ΔH = −553.5 kJ/mol</td>
		</tr>
	</tbody>
</table>

<ol>
	<li>Considera gli elementi nei loro stati più comuni, Cs (s) e F_2 (g).</li>
	<li>Il ΔHs° rappresenta la conversione del cesio solido in un gas (sublimazione), quindi l'energia di ionizzazione converte gli atomi di cesio gassoso in cationi.</li>
	<li>Nella fase successiva, è necessario tenere conto dell'energia richiesta per rompere il legame F – F per produrre atomi di fluoro.</li>
	<li>La conversione di una mole di atomi di fluoro in ioni fluoruro è un processo esotermico, quindi questo passaggio emette energia (l'affinità elettronica)</li>
	<li>Ora sono presenti una mole di cationi Cs e una mole di anioni F. Questi ioni si combinano per produrre fluoruro di cesio solido. La variazione di entalpia in questa fase è negativa dell'energia reticolare, quindi è anche una quantità esotermica.</li>
	<li>L'energia totale coinvolta in questa conversione è pari all'entalpia di formazione determinata sperimentalmente, ΔHf°, del composto dai suoi elementi. In questo caso, il cambiamento complessivo è esotermico.</li>
</ol>

Le energie reticolari calcolate per i composti ionici sono tipicamente molto più elevate delle energie di dissociazione dei legami misurate per i legami covalenti. Mentre le energie reticolari rientrano tipicamente nell’intervallo 600 – 4000 kJ/mol (alcune anche superiori), le energie di dissociazione dei legami covalenti sono tipicamente comprese tra 150 – 400 kJ/mol per i legami singoli. Tieni presente, tuttavia, che questi non sono valori direttamente confrontabili. Per i composti ionici, le energie reticolari sono associate a molte interazioni, poiché cationi e anioni si impacchettano insieme in un reticolo esteso. Per i legami covalenti, l'energia di dissociazione del legame è correlata all'interazione di soli due atomi.

Energia reticolare in funzione del raggio ionico e della carica

L'energia reticolare di un cristallo ionico aumenta rapidamente all'aumentare delle cariche degli ioni e alla diminuzione delle dimensioni degli ioni. Quando tutti gli altri parametri sono mantenuti costanti, raddoppiando la carica sia del catione che dell'anione si quadruplica l'energia reticolare. Ad esempio, l'energia reticolare di LiF (Z+ e Z– = 1) è 1023 kJ/mol, mentre quella di MgO (Z+ e Z– = 2) è 3900 kJ/mol (R_o = la distanza interionica definita come la somma di il raggio degli ioni positivi e negativi è quasi lo stesso (circa 200 µm per entrambi i composti).

Diverse distanze interatomiche producono differenti energie reticolari. Ad esempio, confrontare l'energia reticolare di MgF_2 (2957 kJ/mol) con quella di MgI_2 (2327 kJ/mol), che dimostra l'effetto sull'energia reticolare della dimensione ionica più piccola di F– rispetto a I–.

Altre applicazioni del ciclo Born-Haber

Il ciclo di Born-Haber può anche essere utilizzato per calcolare una qualsiasi delle altre quantità nell'equazione dell'energia reticolare, a condizione che sia noto il resto. Ad esempio, se si conoscono l'entalpia di sublimazione ΔHs°, l'energia di ionizzazione (IE), l'entalpia di dissociazione del legame (D), l'energia reticolare ΔHlattice e l'entalpia standard di formazione ΔHf°, il ciclo di Born-Haber può essere utilizzato per determinare la affinità elettronica di un atomo.

Questo testo è adattato da <a href="https://openstax.org/books/chemistry-2e/pages/7-5-strengths-of-ionic-and-covalent-bonds">Openstax, Chemistry 2e, Section 7.5: Strengths of Ionic and Covalent Bonds.</a>

Il ciclo Born-Haber

Energia reticolare

Un composto ionico è stabile a causa dell'attrazione elettrostatica tra i suoi ioni positivi e negativi. L'energia reticolare di un ...

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predicting ionic stability with lattice energy

Lattice energy helps explain why ionic compounds are stable. It measures the strength of attraction between positive and negative ions in a crystal. In one common definition, lattice energy is the energy required to separate one mole of an ionic solid into gaseous ions, so it has a positive value. Another definition uses the opposite sign and describes the energy released when gaseous ions form a lattice. When checking data, it is important to confirm which convention is being used. In either case, a larger lattice energy magnitude means a more stable ionic compound.

Sodium chloride gives a simple example. Its lattice energy is 769 kJ/mol, which means 769 kJ is needed to pull one mole of solid NaCl apart into Na+ and Cl- ions in the gas phase. The same amount of heat is released when those ions come together to form solid NaCl. This value shows how strongly the ions attract each other in the crystal.

Lattice energy cannot be measured directly. Instead, it is found with a thermochemical cycle. The Born-Haber cycle uses Hess’s law to break the formation of an ionic solid into separate steps. For cesium fluoride, these steps include sublimation of Cs(s) to Cs(g), half of the F2 bond energy to make F(g), ionization of Cs(g) to Cs+(g) plus an electron, electron affinity of F(g) to make F-(g), and formation of solid CsF from the gaseous ions. The enthalpy change for forming the lattice is the negative of the lattice energy.

For CsF, the overall reaction Cs(s) + 1/2 F2(g) -&gt; CsF(s) has a standard enthalpy of formation of -553.5 kJ/mol. The cycle combines the sublimation enthalpy of cesium, 76.5 kJ/mol, one-half of the F2 bond energy, 79.4 kJ/mol, the ionization energy of cesium, 375.7 kJ/mol, and the electron affinity of fluorine, -328.2 kJ/mol, with the lattice term. Because the total is exothermic, energy is released overall when the solid forms from the elements in their most common states, Cs(s) and F2(g).

Lattice energies for ionic compounds are usually much larger than bond dissociation energies for covalent bonds. Ionic lattice energies often fall between 600 and 4000 kJ/mol, and some are even higher. Single covalent bond dissociation energies are usually about 150 to 400 kJ/mol. These values are not directly comparable because lattice energy reflects many attractions in an extended crystal, while a covalent bond energy describes the interaction of just two atoms.

Ion charge and ion size strongly affect lattice energy. When all other factors stay the same, larger charges give much larger lattice energies, and smaller ions also increase lattice energy. Doubling the charge on both ions can quadruple the lattice energy. For example, LiF has a lattice energy of 1023 kJ/mol, while MgO is 3900 kJ/mol, even though their interionic distances are nearly the same at about 200 pm. Size also matters in compounds such as MgF2 and MgI2, where the smaller F- ion leads to a higher lattice energy than the larger I- ion.

The Born-Haber cycle can also solve for other unknowns in the lattice energy equation. If the other terms are known, the cycle can be used to find a missing quantity such as electron affinity. This makes the method useful for linking measured enthalpy values to the energy changes inside ionic compounds.

Predicting Ionic Stability with Lattice Energy

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the born-haber cycle

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Learn how lattice energy, ion charge, ion size, and the Born-Haber cycle help explain ionic stability and calculate values for compounds like CsF.

Predicting Ionic Stability with Lattice Energy | JoVE K12

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An ionic compound is stable because of the electrostatic attraction between its positive and negative ions. The lattice energy of a compound is a measure ...

Covalent Bonding and Lewis Structures

Compared to ionic bonds, which results from the transfer of electrons between metallic and nonmetallic atoms, covalent bonds result from the mutual ...

Electronegativity

Whether a bond is nonpolar or polar covalent is determined by a property of the bonding atoms called electronegativity.&#xA0;

Electronegativity values of ...

Bond Polarity, Dipole Moment, and Percent Ionic Character

Bond Polarity

The absolute value of the difference in electronegativity (&Delta;EN) of two bonded atoms provides a rough measure of the polarity to be ...

Lewis Structures of Molecular Compounds and Polyatomic Ions

To draw Lewis structures for complicated molecules and molecular ions, it is helpful to follow a step-by-step procedure as outlined:


	Determine the ...

Resonance

The Lewis structure of a nitrite anion (NO2&minus;) may actually be drawn in two different ways, distinguished by the locations of the N-O and N=O ...

Formal Charges

In some cases, there are seemingly more than one valid Lewis structures for molecules and polyatomic ions. The concept of formal charges can be used to ...

Exceptions to the Octet Rule

Many covalent molecules have central atoms that do not have eight electrons in their Lewis structures. These molecules fall into three categories:


	...

Analyze and interpret data to explain the mechanisms and properties of the two main types of intramolecular (ionic and covalent) bonds.

Analyze the structure of atoms and isotopes.

Predicting Ionic Stability with Lattice Energy

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