10.2: Ionic Bonding
- Page ID
- 371621
- To describe the characteristics of ionic bonding.
- To quantitatively describe the energetic factors involved in the formation of an ionic bond.
Ions are atoms or molecules which are electrically charged. Cations are positively charged and anions carry a negative charge. Ions form when atoms gain or lose electrons. Since electrons are negatively charged, an atom that loses one or more electrons will become positively charged; an atom that gains one or more electrons becomes negatively charged. Ionic bonding is the attraction between positively- and negatively-charged ions. These oppositely charged ions attract each other to form ionic networks (or lattices). Electrostatics explains why this happens: opposite charges attract and like charges repel. When many ions attract each other, they form large, ordered, crystal lattices in which each ion is surrounded by ions of the opposite charge. Generally, when metals react with non-metals, electrons are transferred from the metals to the non-metals. The metals form positively-charged ions and the non-metals form negatively-charged ions.
Lewis symbols can be used to illustrate the formation of cations from atoms, as shown here for sodium and calcium:
Likewise, they can be used to show the formation of anions from atoms, as shown here for chlorine and sulfur:
Lewis Structures of Ionic Compounds: https://youtu.be/oJ9975tmjc0
Energetics of Ionic Bond Formation
Ionic bonds are formed when positively and negatively charged ions are held together by electrostatic forces. Consider a single pair of ions, one cation and one anion. How strong will the force of their attraction be? According to Coulomb's Law, the energy of the electrostatic attraction (\(E\)) between two charged particles is proportional to the magnitude of the charges and inversely proportional to the internuclear distance between the particles (\(r\)):
\[E \propto \dfrac{Q_{1}Q_{2}}{r} \label{Eq1a} \]
\[ E = k\dfrac{Q_{1}Q_{2}}{r} \label{Eq1b} \]
where each ion’s charge is represented by the symbol Q. The proportionality constant k is equal to 2.31 × 10−28 J·m. This value of k includes the charge of a single electron (1.6022 × 10−19 C) for each ion. The equation can also be written using the charge of each ion, expressed in coulombs (C), incorporated in the constant. In this case, the proportionality constant, k, equals 8.999 × 109 J·m/C2. In the example given, Q1 = +1(1.6022 × 10−19 C) and Q2 = −1(1.6022 × 10−19 C). If Q1 and Q2 have opposite signs (as in NaCl, for example, where Q1 is +1 for Na+ and Q2 is −1 for Cl−), then E is negative, which means that energy is released when oppositely charged ions are brought together from an infinite distance to form an isolated ion pair.
Energy is always released when a bond is formed and correspondingly, it always requires energy to break a bond.
As shown by the green curve in the lower half of Figure \(\PageIndex{3}\), the maximum energy would be released when the ions are infinitely close to each other, at r = 0. Because ions occupy space and have a structure with the positive nucleus being surrounded by electrons, however, they cannot be infinitely close together. At very short distances, repulsive electron–electron interactions between electrons on adjacent ions become stronger than the attractive interactions between ions with opposite charges, as shown by the red curve in the upper half of Figure \(\PageIndex{3}\). The total energy of the system is a balance between the attractive and repulsive interactions. The purple curve in Figure \(\PageIndex{3}\) shows that the total energy of the system reaches a minimum at r0, the point where the electrostatic repulsions and attractions are exactly balanced. This distance is the same as the experimentally measured bond distance.
Consider the energy released when a gaseous \(Na^+\) ion and a gaseous \(Cl^-\) ion are brought together from r = ∞ to r = r0. Given that the observed gas-phase internuclear distance is 236 pm, the energy change associated with the formation of an ion pair from an \(Na^+_{(g)}\) ion and a \(Cl^-_{(g)}\) ion is as follows:
\[ \begin{align*} E &= k\dfrac{Q_{1}Q_{2}}{r_{0}} \\[4pt] &= (2.31 \times {10^{ - 28}}\rm{J}\cdot \cancel{m} ) \left( \dfrac{( + 1)( - 1)}{236\; \cancel{pm} \times 10^{ - 12} \cancel{m/pm}} \right) \\[4pt] &= - 9.79 \times 10^{ - 19}\; J/ion\; pair \label{Eq2} \end{align*}\]
The negative value indicates that energy is released. Our convention is that if a chemical process provides energy to the outside world, the energy change is negative. If it requires energy, the energy change is positive. To calculate the energy change in the formation of a mole of NaCl pairs, we need to multiply the energy per ion pair by Avogadro’s number:
\[ E=\left ( -9.79 \times 10^{ - 19}\; J/ \cancel{ion pair} \right )\left ( 6.022 \times 10^{ 23}\; \cancel{ion\; pair}/mol\right )=-589\; kJ/mol \label{Eq3} \]
This is the energy released when 1 mol of gaseous ion pairs is formed, not when 1 mol of positive and negative ions condenses to form a crystalline lattice. Because of long-range interactions in the lattice structure, this energy does not correspond directly to the lattice energy of the crystalline solid. However, the large negative value indicates that bringing positive and negative ions together is energetically very favorable, whether an ion pair or a crystalline lattice is formed.
We summarize the important points about ionic bonding:
- At r0, the ions are more stable (have a lower potential energy) than they are at an infinite internuclear distance. When oppositely charged ions are brought together from r = ∞ to r = r0, the energy of the system is lowered (energy is released).
- Because of the low potential energy at r0, energy must be added to the system to separate the ions. The amount of energy needed is the bond energy.
- The energy of the system reaches a minimum at a particular internuclear distance (the bond distance).
Calculate the amount of energy released when 1 mol of gaseous Li+F− ion pairs is formed from the separated ions. The observed internuclear distance in the gas phase is 156 pm.
Given: cation and anion, amount, and internuclear distance
Asked for: energy released from formation of gaseous ion pairs
Strategy:
Substitute the appropriate values into Equation \(\ref{Eq1b}\) to obtain the energy released in the formation of a single ion pair and then multiply this value by Avogadro’s number to obtain the energy released per mole.
Solution:
Inserting the values for Li+F− into Equation \(\ref{Eq1b}\) (where Q1 = +1, Q2 = −1, and r = 156 pm), we find that the energy associated with the formation of a single pair of Li+F− ions is
\[ \begin{align*} E &=k \dfrac{Q_1Q_2}{r_0} \\[4pt] &=\left(2.31 \times 10^{−28} J⋅\cancel{m} \right) \left(\dfrac{\text{(+1)(−1)}}{156\; pm \times 10^{−12} \cancel{m/pm}} \right)\\[4pt] &=−1.48 \times 10^{−18} \end{align*}\]
Then the energy released per mole of Li+F− ion pairs is
\[ \begin{align*} E&= \left(−1.48 \times 10^{−18} J/ \cancel{\text{ion pair}}\right) \left(6.022 \times 10^{23} \cancel{\text{ion pair}}/mol\right)\\[4pt] &−891 \;kJ/mol \end{align*}\]
Because Li+ and F− are smaller than Na+ and Cl− (see Section 7.3), the internuclear distance in LiF is shorter than in NaCl. Consequently, in accordance with Equation \(\ref{Eq1b}\), much more energy is released when 1 mol of gaseous Li+F− ion pairs is formed (−891 kJ/mol) than when 1 mol of gaseous Na+Cl− ion pairs is formed (−589 kJ/mol).
Calculate the amount of energy released when 1 mol of gaseous \(\ce{MgO}\) ion pairs is formed from the separated ions. The internuclear distance in the gas phase is 175 pm.
- Answer
-
−3180 kJ/mol = −3.18 × 103 kJ/mol
Summary
The amount of energy needed to separate a gaseous ion pair is its bond energy. The formation of ionic compounds are usually extremely exothermic. The strength of the electrostatic attraction between ions with opposite charges is directly proportional to the magnitude of the charges on the ions and inversely proportional to the internuclear distance. The total energy of the system is a balance between the repulsive interactions between electrons on adjacent ions and the attractive interactions between ions with opposite charges.