9.10: Ionic Bonds
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Introduction
As discussed in Section 3.6 Ionic Compounds and Formulas Ionic bonds are coulombic interactions where the positive cations and negative anions form repeating structures that result in a neutral lattice.
Coulomb's Law is a mathematical formula that describes the electrostatic interaction between two charged particles that was first proposed by the French physicist Charles Coulomb (1736–1806). Coulomb's law is often called an inverse square law, as the force decreases as a function of the square of the distance between the two particles.
\[ E= k\dfrac{q_1q_2}{ r} \; \; \; \; \; \; \; \; F= k\dfrac{q_1q_2}{r^2}\]
- \(E\) is the potential energy
- \(F\) is the force
- \(r\) is the distance of separation (note that the potential goes to zero when they are separated by infinity)
- \(q\) is the charge of the ions
- \(k\) is a constant
The electrostatic interactions can be understood by the above image, where in (a), like charges repel and in (b), opposite charges attract. If you look at Coulomb's law, you note that in (a) the force is positive (because both q1 and q2 are negative), while in (b) the force is negative (because q1 is negative while q2 is positive). That is, attractive interactions result in a lowering of the energy
In the above diagram the width of the arrows indicate the magnitude of the forces of electrostatic interaction. You should be able to look at the algebra associated with Coulomb's Law and see how it results in these interactions. In the numerator is the charge, and so the greater the charge, the greater the interaction. In the denominator is the distance between the charges, and so the larger the distance, the weaker the interaction.
NOTE: It is very important that you learn how to "read" algebraic equations like Coulomb's Law. Math is actually a universal language and being able to read equations is one of the most important skills you can learn in this class. That is, it makes no difference what language you study in, the math is still the same, and being able to read equations is a fundamental skill you should gain from this class.
Crystal Lattice Strength and Periodic Trends
From coulombs law we see that there are two basic variables that influence the ionic bond energy, the charges (q1 and q2) and the distance between the charged particles (r). From section 3.6.4.1 we have the following table of monatomic ion charges
Figure \(\PageIndex{3}\): Table from section 3.6.4.1and from section 8.3.2.4 Periodic Trends in Atomic Radii we have the following image of trends
Figure \(\PageIndex{4}\): Calculated Atomic Radii (in Picometers) of the s-, p-, and d-Block Elements. The sizes of the circles illustrate the relative sizes of the atoms. The calculated values are based on quantum mechanical wave functions. Source: http://www.webelements.com. Web Elements is an excellent online source for looking up atomic properties.Applying these two pieces of information allows us to determine periodic trends for ionic bond strengths.
Figure \(\PageIndex{5}\): Table of periodic trends for the formation of ionic compounds (CC 0.0 Belford)It should be noted that calculation of the actual crystal lattice energies is far more complicated than those of just the coulombic forces between ions and will be covered in gen chem 2, section 12.2.6 Energy Cycles and the Born Haber Equation. You will not be required to know any of these numbers, but you are required to be able to predict trends as formulated by the application of Coulomb's Law.
Explain why Aluminum Oxide has such a high lattice energy
- Answer
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Both ions are highly charge (+3 and +2) and the ions are very small (both are isoelectronic to neon and have a [H]1s22s6 electron configuration), meaning they are highly charged and very close to each other. In fact they are so close to each other that molecular oxygen does not freely difuse through them and aluminum forms a coating of aluminum oxide that prevents it from rusting.