Name: predicting ionic stability with lattice energy
Uploaded: 2020-09-03T13:38:28.000Z
Duration: 2 min 44 s
Channel: JoVE

K12 Standards

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North Carolina K-12 Science Standard Course of Study

9-12

Chemistry

Matter and its Interactions

PS.Chm.3.1

The Born-Haber Cycle

Tworzenie wiązań jonowych wymaga przeniesienia elektronu z atomu metalu na atom niemetalu - proces, który często jest endotermiczny. Jednak gdy pierwiastkowy sód i chlor reagują, tworząc stały kryształ chlorku sodu, jest to proces wysoce egzotermiczny. Ale skąd pochodzi ta energia?

Zgodnie z prawem Coulomba kationy i aniony są przyciągane do siebie przez silne siły elektrostatyczne do stałego układu lub sieci. Powstała struktura sieciowa jest stabilizowana poprzez zmniejszenie energii potencjalnej, która jest uwalniana w postaci ciepła, reakcji egzotermicznej. 

Całkowita energia związana z powstawaniem lub rozpadem sieci krystalicznej na jej składniki gazowe nazywana jest energią sieci.

W stałym związku jonowym duża liczba naładowanych cząstek oddziałuje ze sobą, co utrudnia eksperymentalne określenie dokładnej wartości energii sieci. Można go jednak obliczyć za pomocą prawa Hessa w hipotetycznej serii kroków zwanych cyklem Borna-Habera, który reprezentuje tworzenie związku jonowego z jego elementów składowych.

Na przykład cykl Borna-Habera dla tworzenia chlorku sodu uwzględnia dwie alternatywne drogi, jedną bezpośrednią, a drugą pośrednią. Bezpośrednia droga reprezentuje standardową entalpię tworzenia NaCl z pierwiastkowego sodu i chloru. 

Trasa pośrednia składa się z pięciu etapów. W pierwszym etapie sód w stanie stałym jest przekształcany w postać gazową. Następnie dwuatomowe cząsteczki chloru dysocjują na gazowe atomy chloru. 

Trzeci i czwarty krok uwzględniają transfer elektronów w celu utworzenia jonów. Elektron jest usuwany z gazowego sodu, tworząc kation sodu. Elektron jest następnie pobierany przez gazowy chlor, tworząc anion chlorkowy. 

W końcowym etapie przyciąganie elektrostatyczne między jonami gazowymi prowadzi do powstania struktury sieciowej.

Prawo Hessa mówi, że zmiana ogólnej entalpii procesu krokowego jest sumą zmian entalpii każdego kroku. Oznacza to, że wartość entalpii trasy bezpośredniej jest równa sumie entalpii pięciu kroków.

Rozwiązując równanie energii sieci, określa się dużą wartość ujemną, która oznacza reakcję egzotermiczną.

cykl borna-habera

<h4>Energia sieci</h4>

Związek jonowy jest stabilny ze względu na przyciąganie elektrostatyczne pomiędzy jonami dodatnimi i ujemnymi. Energia sieci związku jest miarą siły tego przyciągania. Energię sieci (ΔHlattice) związku jonowego definiuje się jako energię potrzebną do rozdzielenia jednego mola ciała stałego na składowe jony gazowe.

Tutaj stosowana jest konwencja, w której ciało stałe jonowe jest rozdzielane na jony, co oznacza, że energie sieci będą endotermiczne (wartości dodatnie). Innym sposobem jest zastosowanie równoważnej, ale odwrotnej konwencji, w której energia sieci jest egzotermiczna (wartości ujemne) i opisywana jako energia uwalniana, gdy jony łączą się, tworząc sieć. Dlatego pamiętaj, aby potwierdzić, która definicja jest używana podczas wyszukiwania energii sieci w innym dokumencie.

W obu przypadkach większa wielkość energii sieci wskazuje na bardziej stabilny związek jonowy. Dla chlorku sodu ΔHlattice = 769 kJ. Zatem potrzeba 769 kJ, aby rozdzielić jeden mol stałego NaCl na gazowe jony Na+ i Cl–. Kiedy jeden mol gazowych jonów Na+ i Cl– tworzy stały NaCl, uwalnia się 769 kJ ciepła.

<h4>Wyznaczanie energii sieci jonowej związku</h4>

Nie można bezpośrednio zmierzyć energii sieci. Jednakże energię sieci można obliczyć za pomocą cyklu termochemicznego. Cykl Borna-Habera jest zastosowaniem prawa Hessa, które dzieli proces powstawania ciała stałego jonowego na serię pojedynczych etapów:

<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 sublimacji 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;">Połowa energii wiązania 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 jonizacji 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;">Powinowactwo elektronowe 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;">Ujemna energia sieci 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 tworzenia CsF (s), dodaj kroki 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 style="display: flex; flex-direction: column; gap: 10px;">
	<li> Rozważmy elementy w ich najczęstszych stanach, Cs (s) i F2 (g).</li>
	<li>ΔHs° oznacza przemianę stałego cezu w gaz (sublimacja), po której ma miejsce przekształcenie gazowych atomów cezu w kationy przez energię jonizacji.</li>
	<li>W następnym kroku należy uwzględnić energię wymaganą do rozerwania wiązania F – F w celu wytworzenia atomów fluoru.</li>
	<li>Przekształcenie jednego mola atomów fluoru w jony fluorkowe jest procesem egzotermicznym, więc na tym etapie wydziela się energia (powinowactwo elektronowe)</li>
	<li>Teraz obecny jest jeden mol kationów Cs i jeden mol anionów F. Jony te łączą się, tworząc stały fluorek cezu. Zmiana entalpii na tym etapie jest ujemną energią sieci, a więc jest to również wielkość egzotermiczna.</li>
	<li>Całkowita energia zaangażowana w tę konwersję jest równa doświadczalnie określonej entalpii tworzenia się związku, ΔHf°, z jego pierwiastków. W tym przypadku ogólna zmiana jest egzotermiczna.</li>
</ol>

Energie sieci obliczone dla związków jonowych są zazwyczaj znacznie wyższe niż energie dysocjacji wiązań mierzone dla wiązań kowalencyjnych. Podczas gdy energie sieci zwykle mieszczą się w zakresie 600–4000 kJ/mol (niektóre nawet są wyższe), energie dysocjacji wiązań kowalencyjnych wynoszą zazwyczaj 150–400 kJ/mol dla wiązań pojedynczych. Należy jednak pamiętać, że nie są to wartości bezpośrednio porównywalne. W przypadku związków jonowych energie sieci są powiązane z wieloma interakcjami, ponieważ kationy i aniony łączą się w wydłużoną sieć. W przypadku wiązań kowalencyjnych energia dysocjacji wiązania jest związana z oddziaływaniem tylko dwóch atomów.

<h4>Energia sieci jako funkcja promienia jonu i ładunku</h4>

Energia sieci kryształu jonowego szybko rośnie wraz ze wzrostem ładunku jonów i zmniejszaniem się rozmiarów jonów. Gdy wszystkie inne parametry pozostają stałe, podwojenie ładunku zarówno kationu, jak i anionu czterokrotnie zwiększa energię sieci. Na przykład energia sieci LiF (Z+ i Z– = 1) wynosi 1023 kJ/mol, natomiast MgO (Z+ i Z– = 2) wynosi 3900 kJ/mol (Ro = odległość międzyjonowa zdefiniowana jako suma promienie jonów dodatnich i ujemnych są prawie takie same — około 200 µm dla obu związków).

Różne odległości międzyatomowe wytwarzają różne energie sieci. Na przykład porównaj energię sieci MgF2 (2957 kJ/mol) z energią MgI2 (2327 kJ/mol), co pokazuje wpływ mniejszego rozmiaru jonowego F– w porównaniu z I– na energię sieci.

<h4>Inne zastosowania cyklu Borna-Habera</h4>

Cykl Borna-Habera można również zastosować do obliczenia dowolnej innej wielkości w równaniu energii sieci, pod warunkiem, że znana jest reszta. Na przykład, jeśli znana jest odpowiednia entalpia sublimacji ΔHs°, energia jonizacji (IE), entalpia dysocjacji wiązania (D), energia sieci ΔHsieć i standardowa entalpia tworzenia ΔHf°, cykl Borna-Habera można zastosować do określenia powinowactwo elektronowe atomu.

Cykl Borna-Habera

Energia sieci

Związek jonowy jest stabilny ze względu na przyciąganie elektrostatyczne między jego jonami dodatnimi i ujemnymi. Energia sieci ...

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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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Ionic radius is the measure used to describe the size of an ion. A cation always has fewer electrons and the same number of protons as the parent atom; it ...

Ionization Energy

The amount of energy required to remove the most loosely bound electron from a gaseous atom in its ground state is called its first ionization energy ...

Electron Affinity

The electron affinity (EA) is the energy change for adding an electron to a gaseous atom to form an anion (negative ion).



This process can be either ...

Construct an explanation to infer the atomic size, reactivity, electronegativity, and ionization energy of an element based on its position in the Periodic Table.

PS.Chm.2.2

Types of Chemical Bonds

Chemical bonding theories were pioneered by American chemist Gilbert&#xA0;N. Lewis. He developed a model called the Lewis model to explain the type and ...

Lewis Symbols and the Octet Rule

Chemical bonds are complex interactions between two or more atoms or ions, which reduce the potential energy of the molecule. Gilbert N. Lewis developed a ...

Ionic Bonding and Electron Transfer

Ions are atoms or molecules bearing an electrical charge. A cation (a positive ion) forms when a neutral atom loses one or more electrons from its valence ...

Lattice Energy&#xA0;

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

Trends in Lattice Energy: Ion Size and Charge

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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