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

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Chemistry

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The Born-Haber Cycle

イオン結合の形成には 金属原子から 非金属原子への 電子移動が必要です しかし 元素のナトリウムと 塩素が反応して 固体の塩化ナトリウム結晶を 形成するとき それは非常に 発熱性のプロセスです しかし そのエネルギーは どこから来るのでしょうか？クーロンの法則によれば 陽イオンと陰イオンは 強い静電気力によって 互いに引きつけられて 固体の配列 つまり格子になります 結果として得られる 格子構造は ポテンシャルエネルギーを 減少させることで安定化され 発熱反応である 熱として放出されます 結晶性格子の形成または その気体成分への分解に 関連する総エネルギーは 格子エネルギーと呼ばれています 固体イオン性化合物では 多数の荷電粒子が 相互作用するため 格子エネルギーの 正確な値を実験的に 決定することは困難です しかし ヘスの法則を用いて ボルン・ハーバー サイクルと呼ばれる 仮想的な一連のステップで 計算することができ これは構成元素からの イオン性化合物の形成を表します 例えば 塩化ナトリウム生成の ボルン・ハーバーサイクルでは 直接経路と間接経路の 2つの経路が考えられます 直接経路は 元素であるナトリウムと 塩素からのNaClの生成の 標準エンタルピーを表します 間接経路は 5つのステップからなる 最初のステップでは 固体状態のナトリウムが 気体に変換されます 次に 二原子塩素分子が解離して 気体の塩素原子になります 3番目と4番目のステップでは イオンを形成するための 電子移動が行われます 気体のナトリウムから 電子が取り除かれ ナトリウムカチオンが 形成されます 次に 電子はガス状の 塩素に取り込まれ 塩化物アニオンを形成します 最後のステップでは ガス状イオン間の静電引力が 格子構造の 形成につながります ヘスの法則は段階的なプロセスの 全体的なエンタルピーの変化は 各段階のエンタルピーの 変化の総和であることを 示しています 直接経路のエンタルピー値は 5つのステップの エンタルピーの総和に 等しいことを意味します 格子エネルギーの 方程式を解くことで 大きな負の値が算出されますが これは発熱反応を意味します

ボルン・ハーバーサイクル

<h4>格子エネルギー</h4>
 
 イオン化合物が安定しているのは、正イオンと負イオンの間に静電的な引力が働いているからです。化合物の格子エネルギーは、この引力の強さの尺度です。イオン性化合物の格子エネルギー(ΔHlattice)は、1モルの固体を気体のイオンに分離するのに必要なエネルギーと定義されます。
 
 ここでは、イオン性固体がイオンに分離されるという慣例を用いており、格子エネルギーは吸熱（正の値）となります。もう一つの方法は、同等の、しかし反対の慣例を用いることで、格子エネルギーは発熱性（負の値）であり、イオンが結合して格子を形成する際に放出されるエネルギーとして説明されます。このように、他の文献で格子エネルギーを調べる際には、どちらの定義が使われているかを確認する必要があります。
 
 いずれの場合も、格子エネルギーの大きさが大きいほど、より安定したイオン化合物であることを示しています。塩化ナトリウムの場合、ΔHlatticeは769kJです。したがって、1モルの固体NaClを気体のNa+とCl–イオンに分離するには769kJが必要となります。気体のNa+とCl–イオンがそれぞれ1モルずつ固体のNaClになるとき、769kJの熱が放出されます。 
 
 <h4>イオン化合物の格子エネルギーの測定 </h4>
 
 格子エネルギーを直接測定することはできません。しかし、熱化学サイクルを用いることで、格子エネルギーを計算することができます。ボーン-ハーバーサイクルは、ヘスの法則を応用したもので、イオン性固体の形成を一連の個別ステップに分解したものです。 
 
 <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;"">Cs 昇華のエンタルピー (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;"">F2の結合エネルギーの1/2</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;"">Cs (g)のイオン化エネルギー</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;"">Fの電子親和力</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;"">CsF (s)の負の格子エネルギー</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;"">CsF (s)形成のエンタルピー, ステップ1-5を加えたもの</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>最も一般的な状態である Cs (s) とF2 (g)の元素について考えます。</li>
 <li>Δ Hs ° は固体セシウムの気体への変換（昇華）を表し、イオン化エネルギーはガス状セシウム原子を陽イオンに変換します。</li>
 <li>次のステップでは、 F – F 結合を分解してフッ素原子を生成するために必要なエネルギーを考慮する必要があります。</li>
 <li>フッ素原子の 1 モルをフッ素イオンに変換するプロセスは発熱プロセスであるため、このステップでエネルギー（電子親和力）を放出します。  </li>
 <li>次に、 Cs イオンの 1 モルと F イオンの 1 モルが存在します。 これらのイオンを組み合わせることで、フッ化固体セシウムが生成されます。 このステップでのエンタルピー変化は格子エネルギーの負であるため、発熱量でもあります。</li>
 <li>この変換に関係する総エネルギーは、その元素から得られた化合物の生成値 Δ Hf ° の実験的に決定されたエンタルピーと等しくなります。 この場合、全体的な変化は発熱となります。 </li>
 </ol>
 
 イオン性化合物の計算で得られる格子エネルギーは、共有結合で測定される結合解離エネルギーよりもはるかに高いのが一般的です。格子エネルギーが通常600～4000kJ/molの範囲にあるのに対し、共有結合の解離エネルギーは単結合で150～400kJ/molの範囲にあります。しかし、これらは直接比較できる値ではないことに注意してください。イオン性化合物では、陽イオンと陰イオンが格子状に広がっているため、格子エネルギーには多くの相互作用が含まれます。共有結合の場合、結合解離エネルギーは、たった2つの原子の相互作用に関連しています。 
 
 <h4>格子エネルギーは、イオン半径と電荷の関数</h4>
 
 イオン性結晶の格子エネルギーは、イオンの電荷が大きく、イオンの大きさが小さくなると急激に増大します。他のパラメータがすべて一定の場合、陽イオンと陰イオンの電荷を2倍にすると格子エネルギーは4倍になります。例えば、LiF (Z+ and Z– = 1)の格子エネルギーは1023kJ/molであるのに対し、MgO (Z+ and Z– = 2) の格子エネルギーは3900kJ/molです（Ro＝正イオンと負イオンの半径の和であるイオン間距離は、両化合物ともほぼ同じ200pmです）。 
 
 原子間距離が異なると、格子エネルギーも異なります。例えば、MgF2の格子エネルギー（2957kJ/mol）とMgI2の格子エネルギー（2327kJ/mol）を比較すると、F-のイオンサイズがI-に比べて小さいことによる格子エネルギーへの影響が示されています。 
 
 <h4>その他のボルン・ハーバーサイクルの適用 </h4>
 
 ボルン・ハーバーサイクルは、残りの部分が既知であれば、格子エネルギーの方程式の他の量のいずれかを計算するためにも使用することができます。例えば、昇華エンタルピーΔHs°、イオン化エネルギー（IE）、結合解離エンタルピー（D）、格子エネルギーΔHlattice、標準生成エンタルピーΔHf°が既知であれば、ボルン-ハーバーサイクルを用いて原子の電子親和力を求めることができます。

Lattice Energy&#160;

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

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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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The periodic table arranges atoms based on increasing atomic number so that elements with the same chemical properties recur periodically. When their ...

The Periodic Table

As early chemists discovered more elements, they realized that various elements could be grouped by their similar chemical behaviors. One such grouping ...

Atomic Mass

Atoms &mdash; and the protons, neutrons, and electrons that compose them &mdash; are extremely small. For example, a carbon atom weighs less than 2 ...

Molar Mass

The identity of a substance is defined not only by the types of atoms or ions it contains but by the quantity of each type of atom or ion. For example, ...

Use the Periodic Table as a model to predict the relative properties of elements based on the pattern of valence electrons in the outermost energy levels of atoms.

PS.Chm.2.1

atomic-radii-and-effective-nuclear-charge

Atomic Radii and Effective Nuclear Charge

The elements in groups of the periodic table exhibit similar chemical behavior. This similarity occurs because the members of a group have the same number ...

Ionic Radii

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:


	...

Bond Energies and Bond Lengths

Stable molecules exist because covalent bonds hold the atoms together. The strength of a covalent bond is measured by the energy required to break it, ...

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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