Name: lattice energy patterns in ionic solids
Uploaded: 2020-09-03T13:38:28.000Z
Duration: 2 min 54 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

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Trends in Lattice Energy: Ion Size and Charge

Energia sieci jest związana z powstawaniem lub oddzielaniem się sieci jonowej. Jednak gdy powstaje chlorek sodu lub tlenek magnezu, ich energia sieci znacznie się różni. Dlaczego każdy związek jonowy ma inną energię sieci i od jakich czynników to zależy?

Związek jonowy składa się z uporządkowanego układu dużej liczby naładowanych jonów przyciąganych do siebie przez oddziaływania elektrostatyczne. 

Zgodnie z prawem Coulomba energia potencjalna dwóch jonów jest odwrotnie proporcjonalna do odległości między jonami, która z kolei zależy od promienia jonowego. 

W układzie okresowym pierwiastków promień jonowy metali alkalicznych i ziem alkalicznych wzrasta w dół kolumny. Wraz ze wzrostem wielkości jonu metalu zwiększa się również odległość między jonami, czyli długość wiązania. Na przykład długość wiązania bromku litu i bromku potasu różni się odpowiednio między 217 pm i 282 pm.

Ze względu na zwiększoną odległość międzyjądrową przyciąganie między jonami zmniejsza się i znacznie łatwiej jest oddzielić jony. Zatem energia sieci do oddzielenia stałego bromku litu jest większa niż w przypadku bromku potasu i wynosi odpowiednio +807 kJ/mol i +682 kJ/mol. 

Oprócz promienia jonowego, wielkość energii sieci zależy również od ładunków jonowych. Zgodnie z prawem Coulomba energia potencjalna jonów jest wprost proporcjonalna do iloczynu ich ładunków.

Weźmy pod uwagę dwa związki jonowe: fluorek sodu i tlenek wapnia. Odległość jonowa w obu związkach jest podobna, ale energia sieci tlenku wapnia jest prawie czterokrotnie większa niż fluorku sodu.

Zarówno sód, jak i fluorek są jonami jednowartościowymi; iloczyn ich ładunku wynosi 1. Jednak jony wapnia i tlenku są dwuwartościowe,  a iloczyn ich ładunku wynosi 4, czyli czterokrotnie więcej niż fluorku sodu.

Dlatego do rozdzielenia tlenku wapnia na jony gazowe potrzeba prawie cztery razy więcej energii w porównaniu z fluorkiem sodu. 

Zatem wielkość energii sieci jest wprost proporcjonalna do iloczynu ładunków jonowych i jest odwrotnie proporcjonalna do odległości między jonami.

tendencje w energii sieci: wielkość jonów i ładunek

Związek jonowy jest stabilny ze względu na przyciąganie elektrostatyczne pomiędzy jonami dodatnimi i ujemnymi. Energia sieci związku jest miarą siły tego rodzaju przyciągania. Energię sieci (ΔHlattice) związku jonowego definiuje się jako energię potrzebną do rozdzielenia jednego mola ciała stałego na składowe jony gazowe. W przypadku jonowego stałego chlorku sodu energia sieci jest zmianą entalpii procesu:

<img alt="Eq1" src="https://www.jove.com/files/core/CDNSource/lessons/1058/1058_Equations-01.png" style="height: 40px;">

<h4>Konwencje</h4>

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. W związku z tym należy upewnić się, jaka definicja jest wykorzystywana podczas analizy energii sieci w różnych źródłach. 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>Prawo Coulomba i energia sieci</h4>

Energię sieci ΔHsieci kryształu jonowego można wyrazić za pomocą następującego równania (wyprowadzonego z prawa Coulomba, rządzącego siłami pomiędzy ładunkami elektrycznymi):

ΔHkrata = C(Z +)(Z-)/Ro

w którym C jest stałą zależną od rodzaju struktury krystalicznej; Z+ i Z– to ładunki jonów, a Ro to odległość międzyjonowa (suma promieni jonów dodatnich i ujemnych). Zatem energia sieci kryształu jonowego szybko rośnie wraz ze wzrostem ładunków jonów i zmniejszaniem się rozmiarów jonów. Gdy wszystkie inne parametry pozostają stałe, podwojenie ładunku zarówno kationu, jak i anionu czterokrotnie zwiększa energię sieci.

<h4>Przykłady</h4>

<ol style="display: flex; flex-direction: column; gap: 10px;">
	<li>Energia sieci LiF (Z+ i Z– = 1) wynosi 1023 kJ/mol, podczas gdy MgO (Z+ i Z– = 2) wynosi 3900 kJ/mol (Ro jest prawie taki sam — około 200 pm dla obu związków) .</li>
	<li>Różne odległości międzyatomowe wytwarzają różne energie sieci. Na przykład porównaj energię sieci MgF2 (2957 kJ/mol) z energią MgI2 (2327 kJ/mol), aby zaobserwować wpływ mniejszego rozmiaru jonowego F– w porównaniu z I– na energię sieci.</li>
	<li>Cennym klejnotem rubinem jest tlenek glinu Al2O3 zawierający śladowe ilości Cr3+. Związek Al2Se3 jest używany do produkcji niektórych urządzeń półprzewodnikowych. W tych dwóch związkach jonowych ładunki Z+ i Z– są takie same, zatem różnica w energii sieci zależy od Ro. Ponieważ jon O2– jest mniejszy niż jon Se2–, Al2O3 ma krótszą odległość międzyjonową niż Al2Se3 i dlatego ma większą energię sieci.</li>
	<li>Innym przykładem jest tlenek cynku, ZnO, w porównaniu z NaCl. ZnO ma większą energię sieci, ponieważ wartości Z zarówno kationu, jak i anionu w ZnO są większe, a odległość międzyjonowa ZnO jest mniejsza niż NaCl. </li>
</ol>

Tendencje w energii sieci: wielkość jonów i ładunek

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

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lattice energy patterns in ionic solids

Lattice energy shows how strongly ions hold an ionic solid together. It is the energy required to separate one mole of a solid into its gaseous ions. For sodium chloride, this process requires 769 kJ per mole. The opposite convention may also be used, where lattice energy is the energy released when gaseous ions form the solid. In either case, a larger magnitude means a more stable ionic compound.

For ionic crystals, lattice energy follows a pattern based on charge and ion size. The relationship can be written as ΔH lattice = C(Z+)(Z−)/Ro. In this equation, C depends on the crystal structure, Z+ and Z− are the ion charges, and Ro is the distance between the ions. Because of this, lattice energy rises quickly when ion charges increase and when ion sizes decrease. If both ion charges double, the lattice energy becomes four times larger.

Examples show these trends clearly. LiF, with ion charges of 1 and 1, has a lattice energy of 1023 kJ/mol, while MgO, with charges of 2 and 2, has a lattice energy of 3900 kJ/mol. Their interionic distances are nearly the same, at about 200 pm. Ion size also matters. MgF2 has a lattice energy of 2957 kJ/mol, while MgI2 has a lower value of 2327 kJ/mol because F− is smaller than I−.

The same idea explains differences in other compounds. Ruby is aluminum oxide, Al2O3, and it contains traces of Cr3+. Al2Se3 is used in some semiconductor devices. These compounds have the same ion charges, so the difference in lattice energy depends on Ro. O2− is smaller than Se2−, so Al2O3 has the shorter interionic distance and the larger lattice energy. ZnO also has a larger lattice energy than NaCl because the ion charges are greater and the interionic distance is smaller.

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Learn how ion charge and ion size affect lattice energy in ionic solids, with examples like NaCl, LiF, MgO, MgF2, MgI2, Al2O3, and ZnO.

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	...

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Lattice Energy Patterns in Ionic Solids

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