Ionic Bonds - Maple Programming Help

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Ionic Bonds

Bond Types

There are several types of bonds to consider when analyzing the chemical composition of a compound. A bond may be defined as a force that holds groups of two or more atoms together, causing them to behave as a single unit. Bonds can be separated into two types: primary bonds and secondary bonds. Primary bonds are formed when the bonding process involves a transfer or sharing of electrons. Secondary bonds are formed from the subtle attraction forces between positive and negative charges. There is no transfer or sharing of electrons involved in a secondary bond.

 Primary Bonds Ionic Bond   The ionic bond is a result of an electron transfer from one atom to another. Consider the example of sodium (Na) bonding with chlorine (Cl) to produce sodium chloride (NaCl), also known as table salt. Na has one valence electron (an electron in the outermost orbital shell that can take part in bonding) while Cl has seven valence electrons. As a result, the transfer of one electron from Na to Cl is favored because both atoms will achieve a more stable electron configuration (full outer orbital shells of eight electrons). Due to the transfer of its electron, Na is considered a cation, with a net positive charge. Meanwhile, Cl now has a net negative charge and is considered an anion. The electrostatic or Coulombic attraction between oppositely charged ions is what is called the ionic bond. Ionic bonds form between atoms that vastly differ in their electronegativity values. A difference of 1.7 in electronegativity values generally suggests that if a bond forms, it will be ionic. Ionic bonds most frequently form between metals and non-metals.   Covalent Bond   The covalent bond is formed when adjacent atoms share valence electrons. Generally, sharing electrons in such a fashion allows each atom involved to achieve a more stable electron configuration. Consider two chlorine atoms each with 7 electrons in each respective outer shell. The atoms will share one of their outer electrons with the other, such that each individual atom effectively has a complete outer orbital. Covalent bonds form between atoms that have similar electronegativity values. This type of bond is common to organic compounds, where the atoms composing the compounds are non-metals.   Polar Covalent Bond   A polar covalent bond is bond that has a mix of ionic character and covalent character. It is important to understand that all ionic compounds (compounds formed by ionic bonds) have some measure of electron sharing (covalent bonding) even though an ionic bond is not considered to be a type of covalent bond. A large difference in the electronegativity of two atoms indicates a greater ionic character and is considered a purely ionic bond; whereas a very small, negligible difference is considered a purely covalent bond. A polar covalent bond exists when the electronegativity difference is somewhere in between, generally more towards the covalent side (small electronegativity difference). When a polar covalent bond is formed, the result is an unequal sharing of electrons between atoms. An example of a molecule with a polar covalent bond is hydrogen fluoride. In this molecule, hydrogen has a partial positive charge while fluorine has a partial negative charge.   Metallic Bond   Similar to the covalent bond, the metallic bond involves electron sharing. However, in a metallic bond, valence electrons are delocalized meaning that the electrons are mobile and can therefore be associated with any of the plentiful adjacent atoms. In this sense, the electrons form an electron cloud around the atoms, which is the basis for classic metallic properties such as: high electrical conductivity, ductility and luster.
 Secondary Bonds Secondary bonds, as opposed to primary bonds, are bonds with much smaller bonding energies that do not involve the transfer or sharing of electrons. These bonds are caused by permanent or temporary dipoles within the atom or molecule.   Van der Waals Bond   Van der Waals bonds are a result of an asymmetrical distribution of positive and negative charges inside each atom or molecule, which creates in a dipole. A temporary dipole is induced upon a normally symmetric atom/molecule due to external charges from another atom/molecule. The presence of these external charges causes a slight distortion of the symmetric charge, therefore creating areas that are more positive or more negative than others. Two such distorted atoms/molecules can feel a relatively small attraction to one another because of these induced dipoles. This results in a van der Waals bond. Conversely, a permanent dipole occurs when the shape of the molecule is already asymmetric causing permanent separation of charge. This results in a large dipole moment and greater attraction (although still relatively weak).

 Ionic Bonds An ionic bond is a nondirectional bond. In our NaCl example, this means that any negatively charged ion,, adjacent to one positive charged ion, ${\mathrm{Na}}^{+},$will feel the same amount of attraction as the other ${\mathrm{Cl}}^{-}$ions do. As a result, the structure of a material that is composed of ionic bonds is regular and repeating. See the following image for an illustration:   As previously mentioned, ionic bonds are formed due to the Coulombic attraction forces between oppositely charged atoms/molecules. For two oppositely charged ions, the Coulombic force of attraction is given by the expression: ${F}_{c}\phantom{\rule[-0.0ex]{1.0em}{0.0ex}}=\phantom{\rule[-0.0ex]{1.0em}{0.0ex}}\frac{-k\left({Z}_{1}q\right)\left({Z}_{2}q\right)}{{a}^{2}}$ where Z is the valence of the charged ion (+1 for ${\mathrm{Na}}^{+}$ and -1 for ${\mathrm{Cl}}^{-}$), q is the electron charge (0.16 * ${10}^{-18}$ C), $a$ is the distance between the centers of the ions, and k is the constant of proportionality (9 * ${10}^{9}$ $\frac{\mathrm{Vm}}{C}$).   The Coulombic force brings the ions closer together. However, this force is countered by an opposing, repulsive force. This repulsive force is generated because of overlapping electric fields (like charges repel) and also the repulsion force between positively charged nuclei of the ions. As a result, the equilibrium bond length for an ion pair occurs when two conditions are met: 1) the Coulombic force is equal to the repulsive force and 2) the Coulombic force is equal to the sum of two ionic radii.

Coordination Number

The coordination number (CN) refers to the number of adjacent atoms/ions surrounding a reference atom/ion. In the NaCl example, each ${\mathrm{Na}}^{+}$ion has a CN of six as there are six ${\mathrm{Cl}}^{-}$ions directly adjacent to it. For a visual representation, see the image below:

For an ionic compound, the CN is characterized by the ratio of the radii of the ions: (r/R), where r is the smaller ion and R is the larger ion. This shows that CN depends only on the relative sizes of the ions. For a certain range of radius ratios (r/R), a specific amount of the larger ions will be able to fit around the smaller one without overlapping.

Using the following activity, you can simulate determining the ranges of the radius ratio (r/R) for various CNs.

Note: the activity below is in 2D whereas actual atoms/ions are 3D objects. As a result, the minimum radius ratio for a given CN will be larger in this activity than the actual minimum radius ratio. This is because, while the atoms/ions appear to overlap in 2D, there is still ample space between 3D atoms.

 Radius Ratio:    Coordination Number:

The following table displays the actual range of the radius ratio (r/R) for different CNs.

 Coordination Number Radius Ratio (r/R) 2 0 < r/R < 0.155 3 0.155 < r/R < 0.225 4 0.225 < r/R < 0.414 6 0.414 < r/R < 0.732 8 0.732 < r/R < 1 12 1

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