4 Covalent Bonding And Molecular Shape 2009

COVALENT BONDING AND MOLECULAR SHAPE INTRODUCTION In this unit we will show a more detailed picture of how single, double and triple covalent bonds are formed. We will also show how Schrödinger’s model explains the geometry of molecules, that is, the orientation of the bonding electrons along specific directions suggested by experimental data. Before we study the covalent bond we should be able to answer the following question: how can we decide whether a chemical bond is a covalent bond? The simple criterion metal / non metal for ionic bonds and non metal / non metal for covalency, shows insufficient to explain the properties of substances such as aluminium trichloride. According to the usual criterion this is an ionic compound and consequently it should be a high melting point, water soluble and solvent insoluble solid. In addition, both molten aluminium trichloride and its aqueous solution should be very good conductors of electricity. But despite forming aqueous solutions with very good electric conductivity, aluminium trichloride dissolves in benzene and other organic solvents, sublimes, melts and is distilled at low temperatures (below 200ºC), and the molten salt is a poor conductor. These properties show that aluminium chloride cannot be classified as a typical covalent compound! Let us have a closer look to the ionic-covalent issue. ELECTRONEGATIVITY Electronegativity is a measure of the tendency of an atom to attract a bonding pair of electrons. The Pauling scale is the most commonly used. Fluorine (the most electronegative element) is assigned a value of 4.0, and values range down to caesium and francium which are the least electronegative at 0.7. Non polar bonds Consider a bond between two atoms, A and B. Each atom may be forming other bonds as well as the one shown - but these are irrelevant to the argument. If the atoms are equally electronegative, both have the same tendency to attract the bonding pair of electrons, and so it will be found on average half way between the two atoms. To get a bond like this, A and B would usually have to be the same atom (homopolar or homonuclear bonds). You will find this sort of bond in, for example, H2 or Cl2 molecules. These could be thought of as being a "pure" covalent bond - where the electrons are shared evenly between the two atoms. Polar bonds In case both atoms A and B are different the bond is called heteropolar or heteronuclear. Suppose B is slightly more electronegative than A. Then B will attract the electron pair rather more than A does.

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That means that the B end of the bond has more than its fair share of electron density and so becomes slightly negative. At the same time, the A end (rather short of electrons) becomes slightly positive. In the diagram, "δ" (read as "delta") means "slightly" - so δ+ means "slightly positive". This is described as a polar bond. A polar bond is a covalent bond in which there is a separation of charge between one end and the other - in other words in which one end is slightly positive and the other slightly negative. Examples include most covalent bonds. The hydrogen-chlorine bond in HCl or the hydrogenoxygen bonds in water are typical. What happens if B is a lot more electronegative than A? In this case, the electron pair is dragged right over to B's end of the bond. To all intents and purposes, A has lost control of its electron, and B has complete control over both electrons. Ions have been formed. The implication of all this is that there is no clear-cut division between covalent and ionic bonds. In a pure covalent bond, the electrons are held on average exactly half way between the atoms. In a polar bond, the electrons have been dragged slightly towards one end. How far does this dragging have to go before the bond counts as ionic? There is no real answer to that. You normally think of sodium chloride as being a typically ionic solid, but even here the sodium hasn't completely lost control of its electron. Because of the properties of sodium chloride, however, we tend to count it as if it were purely ionic. Lithium iodide, on the other hand, would be described as being "ionic with some covalent character". In this case, the pair of electrons hasn't moved entirely over to the iodine end of the bond. Lithium iodide, for example, dissolves in organic solvents like ethanol - not something which ionic substances normally do. Polar bonds and polar molecules In a simple molecule like HCl, if the bond is polar, so also is the whole molecule. What about more complicated molecules? In CCl4, each bond is polar. The molecule as a whole, however, isn't polar - in the sense that it doesn't have an end (or a side) which is slightly negative and one which is slightly positive. The whole of the outside of the molecule is somewhat negative, but there is no overall separation of charge from top to bottom or from left to right. By contrast, CHCl3 is polar. The hydrogen at the top of the molecule is less electronegative than carbon and so is slightly positive. This means that the molecule now has a slightly positive "top" and a slightly negative "bottom", and so is overall a polar molecule. Patterns of electronegativity in the Periodic Table The most electronegative element is fluorine and next comes oxygen. If you remember that fact, everything becomes easy, because electronegativity must always increase towards fluorine in the Periodic Table.

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As you go across a period the electronegativity increases. The chart shows electronegativities from sodium to chlorine - you have to ignore argon. It doesn't have any electronegativity, because it doesn't form bonds. As you go down a group, electronegativity decreases. The chart shows the patterns of electronegativity in Groups 1 and 7.

Explaining the patterns in electronegativity The factors affecting ionisation energies and electron affinities also govern the trends in electronegativity. The attraction that a bonding pair of electrons feels for a particular nucleus depends on: • • •

the number of protons in the nucleus; the distance from the nucleus the amount of screening by inner electrons.

ELECTRONEGATIVITY OF THE ELEMENTS H 2.1 Li Be 1.0 1.5

B C N O F 2.0 2.5 3.0 3.5 4.0

Na Mg 0.9 1.2

Al Si P S Cl 1.5 1.8 2.1 2.5 3.0

K Ca Sc 0.8 1.0 1.3

Ti V Cr Mn 1.5 1.6 1.6 1.5

Fe Co Ni Cu Zn Ga Ge As Se Br 1.8 1.9 1.9 1.9 1.6 1.6 1.8 2.0 2.4 2.8

Rb Sr Y 0.8 1.0 1.2

Zr Nb Mo Tc 1.4 1.6 1.8 1.9

Ru Rh Pd Ag Cd In Sn Sb Te I 2.2 2.2 2.2 1.9 1.7 1.7 1.8 1.9 2.1 2.5

Cs Ba La-Lu Hf Ta W Re 0.7 0.9 1.0-1.2 1.3 1.5 1.7 1.9

Os Ir Pt Au Hg Tl Pb Bi Po At 2.2 2.2 2.2 2.4 1.9 1.8 1.9 1.9 2.0 2.2

Fr Ra Ac 0.7 0.9 1.1

Th Pa U Np-No 1.3 1.4 1.4 1.4-1.3

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It is taken as “rule of thumb” that bonds between atoms that have electronegativity differences around 1.7 will show a 50 % of ionic character. If electronegativity differences are small then bonds will be either covalent (non-metals) or metallic (metals). We will consider a bond to be ionic if Δ electr. ≥ 2.0 (2/3 ionic). According to this aluminium chloride should be quite covalent although it is a metal / non-metal bond. In fact aluminium chloride can be easily distilled as any covalent substance and shows solubility in non aqueous solvents! The following chart and the graph show how ionic character relates to electronegativity difference.

Δelectroneg. 0.1 0.3 0.5 0.7 0.9 1.1 1.3 1.5 1.7 1.9 2.1 2.3 2.5 2.7 2.9 3.1 % ionic 0.5 2 6 12 19 26 34 43 51 59 67 74 79 84 88 91 character

SHAPES OF MOLECULES AND IONS The electron pair repulsion theory The shape of a molecule or ion is governed by the arrangement of the outer shell’s electron pairs around the central atom. All you need to do is to work out how many electron pairs there are at the bonding level, and then arrange them to produce the minimum amount of repulsion between them. You have to include both bonding pairs and lone pairs. How to work out the number of electron pairs You can do this by drawing dots-and-crosses pictures.  First you need to work out how many groups there are bonded around the central atom.

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





Now work out how many lone (non bonding) pairs of electrons there are. These pairs will count as a group. If there are multiple bonds, the second or third pairs of electrons forming the bond will not count Finally, work out the shape. Arrange the groups and lone electron pairs in space to minimise repulsions. How this is done will become clear in the examples which follow. Lone pairs being more “free to move” occupy more space and will push other groups backwards so that the angle between them and other groups is slightly wider.

FOUR ELECTRON PAIRS AROUND THE CENTRAL ATOM There are lots of examples of this. The simplest is methane, CH4. Carbon is in group 4, and so has 4 outer electrons. It is forming 4 bonds to hydrogens, adding another 4 electrons - 8 altogether, in 4 pairs. Because it is forming 4 bonds, these must all be bonding pairs. Four electron pairs arrange themselves in space in what is called a tetrahedral arrangement. A tetrahedron is a regular triangularly-based pyramid. The carbon atom would be at the centre and the hydrogen atoms at the four corners. All the bond angles are 109.5°. Other examples with four electron pairs around the central atom Ammonia, NH3 Nitrogen is in group 5 and so has 5 outer electrons. Each of the 3 hydrogens is adding another electron to the nitrogen's outer level, making a total of 8 electrons in 4 pairs. Because the nitrogen is only forming 3 bonds, one of the pairs must be a lone pair. The electron pairs arrange themselves in a tetrahedral fashion as in methane. In this case, an additional factor comes into play. Lone pairs are in orbitals that are shorter and rounder than the orbitals that the bonding pairs occupy. Because of this, there is more repulsion between a lone pair and a bonding pair than there is between two bonding pairs. Remember this: Greatest repulsion lone pair - lone pair lone pair - bond pair Least repulsion

bond pair - bond pair

Although the electron pair arrangement is tetrahedral, when you describe the shape, you only take notice of the atoms. Ammonia is pyramidal - like a pyramid with the three hydrogens at the base and the nitrogen at the top. Water, H2O Following the same logic as before, you will find that the oxygen has four pairs of electrons, two of which are lone pairs. These will again take up a tetrahedral arrangement. This time the bond angle closes slightly more to 104°, because of the repulsion of the two lone pairs. The shape isn't described as tetrahedral, because we only "see" the oxygen and the hydrogens - not the lone pairs. Water is described as bent or V-shaped. 5

The ammonium ion, NH4+ The nitrogen has 5 outer electrons, plus another 4 from the four hydrogens - making a total of 9. But take care! This is a positive ion. It has a 1+ charge because it has lost 1 electron. That leaves a total of 8 electrons in the outer level of the nitrogen. There are therefore 4 pairs, all of which are bonding because of the four hydrogens. The ammonium ion has exactly the same shape as methane, because it has exactly the same electronic arrangement. NH4+ is tetrahedral. Methane and the ammonium ion are said to be isoelectronic. Two species (atoms, molecules or ions) are isoelectronic if they have exactly the same number and arrangement of electrons (including the distinction between bonding pairs and lone pairs). ELECTRONS IN AN ATOM MUST GET TO THE PROPER ORIENTATION Some problems with the bonding in methane What is wrong with the dots-and-crosses picture of bonding in methane? We are starting with methane because it is the simplest case which illustrates the sort of processes involved. You will remember that the dotsand-crossed picture of methane looks like this: There is a serious mis-match between this structure, the actual shape of this and other molecules as we have previously described, and the accepted quantum chemistry’s electronic structure of carbon, 1s22s22px12py1. This shows that there are only 2 unpaired electrons for hydrogens to share with, instead of the 4 which the simple view requires. You can see this more readily using the electrons-in-boxes notation. Only the 2-level electrons are shown. The 1s2 electrons are too deep inside the atom to be involved in bonding. The only electrons directly available for sharing are the 2p electrons. Why then isn't methane CH2? Promotion of an electron When bonds are formed, energy is released and the system becomes more stable. If carbon forms 4 bonds rather than 2, twice as much energy is released and so the resulting molecule becomes even more stable. There is only a small energy gap between the 2s and 2p orbitals, and so it pays the carbon to provide a small amount of energy to promote an electron from the 2s to the empty 2p to give 4 unpaired electrons. The extra energy released when the bonds form more than compensates for the initial input.

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Hybridisation Now that we've got 4 unpaired electrons ready for bonding, another problem arises. In methane all the carbon-hydrogen bonds are identical, but our electrons are in two different kinds of orbitals. You aren't going to get four identical bonds unless you start from four identical orbitals. The electrons rearrange themselves again in a process called hybridisation. This reorganises the electrons into four identical hybrid (mixed) orbitals called sp3 hybrids (because they are made from one s orbital and three p orbitals). You should read "sp 3" as "s p three" - not as "s p cubed". The sp3 hybrid orbitals look a bit like half a p orbital, and they arrange themselves in space so that they are as far apart as possible. You can picture the nucleus as being at the centre of a tetrahedron (a triangularly based pyramid) with the orbitals pointing to the corners. For clarity, the nucleus is drawn far larger than it really is. What happens when the bonds are formed? Remember that hydrogen's electron is in a 1s orbital - a spherically symmetric region of space surrounding the nucleus where there is some fixed chance (say 95%) of finding the electron. When a covalent bond is formed, the atomic orbitals (the orbitals in the individual atoms) merge to produce a new molecular orbital which contains the electron pair which creates the bond.

Four molecular orbitals are formed, looking rather like the original sp3 hybrids, but with a hydrogen nucleus embedded in each lobe. Each orbital holds the 2 electrons that we've previously drawn as a dot and a cross. The principles involved (promotion of electrons if necessary and hybridisation, followed by the formation of molecular orbitals) can be applied to any covalently-bound molecule. What has been said about methane can be applied to water, ammonia and any other molecules with four electron pairs in the valence shell of atoms. A very closely related case that allows for further generalisation is the bonding in ethane. Ethane C2H6 The formation of molecular orbitals in ethane Ethane is a simple example of how a carboncarbon single bond is formed.

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Each carbon atom in the ethane promotes an electron and then forms sp3 hybrids exactly as we've described in methane. So just before bonding, the atoms look like this: The hydrogen atoms bond with the two carbons to produce molecular orbitals just as they did with methane. The two carbon atoms bond by merging their remaining sp3 hybrid orbitals endto-end to make a new molecular orbital. The bond formed by this end-to-end overlap is called a sigma (σ) bond. In methane we find s-sp3 σ bonds; in ethane we find sp3-sp3 σ bonds. The bonds between the carbons and hydrogen atoms are also s-sp3 σ bonds. In any sigma bond, the most likely place to find the pair of electrons is on a line between the two nuclei. Free rotation about the carbon-carbon single bond The two ends of this molecule can spin quite freely about the sigma bond so that there are, in a sense, an infinite number of possibilities for the shape of an ethane molecule. Some possible shapes are:

In each case, the left hand CH3 group has been kept in a constant position so that you can see the effect of spinning the right hand one. THE SHAPE OF MOLECULES WITH THREE GROUPS AROUND THE CENTRAL ATOM The simple cases of this would be BF3 or BCl3. Boron is in group 3, so starts off with 3 electrons. It is forming 3 bonds, adding another 3 electrons. There is no charge, so the total is 6 electrons - in 3 pairs. Because it is forming 3 bonds there can be no lone pairs. The 3 pairs arrange themselves as far apart as possible. They all lie in one plane at 120° to each other. The arrangement is called trigonal planar. In the diagram, the other electrons on the fluorine atoms have been left out because they are irrelevant. Methanal (CH2O), ethene (ethylene C2H4) and the nitrate anion (NO3-) belong to this group. Next section explains how carbon copes with the spatial orientation of bonds in ethene. DOUBLE BONDS: A DIFFERENT WAY TO HYBRIDISE The simple view of the bonding in ethene

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At a simple level, ethene is drawn showing two bonds between the carbon atoms. Each line in this diagram represents one pair of shared electrons. Ethene is actually much more interesting than this. An orbital view of the bonding in ethene Ethene is built from hydrogen atoms (1s1) and carbon atoms (1s22s22px12py1). The carbon atom doesn't have enough unpaired electrons to form the required number of bonds, so it needs to promote one of the 2s2 pair into the empty 2pz orbital. This is exactly the same as happens whenever carbon forms bonds - whatever else it ends up joined to. Now there's a difference, because each carbon is only joining to three other atoms rather than four - as in methane or ethane. When the carbon atoms hybridise their outer orbitals before forming bonds, this time they only hybridise three of the orbitals rather than all four. They use the 2s electron and two of the 2p electrons, but leave the other 2p electron unchanged. The new orbitals formed are called sp2 hybrids, because they are made by an s orbital and two p orbitals reorganising themselves. The sp2 orbitals look rather like sp3 orbitals that you have already come across in the bonding in methane, except that they are shorter and fatter. The three sp2 hybrid orbitals arrange themselves as far apart as possible which is at 120° to each other in a plane. The remaining p orbital is at right angles to them. The two carbon atoms and four hydrogen atoms would look like this before they joined together:

The various atomic orbitals which are pointing towards each other now merge to give molecular orbitals, each containing a bonding pair of electrons. These are sigma bonds just like those formed by end-to-end overlap of atomic orbitals in, say, ethane. The p orbitals on each carbon aren't pointing towards each other, and so we'll leave those for a moment. In the diagram, the black dots represent the nuclei of the atoms. Notice that the p orbitals are so close that they are overlapping sideways. This sideways overlap also creates a molecular orbital, but of a different kind. In this one the electrons aren't held on the line between the two nuclei, but above and below the plane of the molecule. A bond formed in this way is called a pi bond. For clarity, the sigma bonds are shown using lines - each line representing one pair of shared electrons. The various sorts of line show the directions the bonds point in. An ordinary line represents a bond in the plane of the screen (or the paper if you've printed it); a broken line is a bond going back away from you, and a wedge shows a bond coming out towards you. Be clear about what a pi bond is. It is a region of space in which you can find the two electrons which make up the bond. Those

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two electrons can live anywhere within that space. It would be quite misleading to think of one living in the top and the other in the bottom. The pi bond dominates the chemistry of ethene. It is very vulnerable to attack - a very negative region of space above and below the plane of the molecule. It is somewhat distant from the control of the nuclei and so is a weaker bond than the sigma bond joining the two carbons. All double bonds (whatever atoms they might be joining) will consist of a sigma bond and a pi bond. THE SHAPE OF MOLECULES WITH TWO GROUPS AROUND THE CENTRAL ATOM Two groups around the central atom The simplest case is beryllium chloride, BeCl2. The electronegativity difference between beryllium and chlorine isn't enough to allow the formation of ions. Beryllium has 2 outer electrons because it is in group 2. It forms bonds to two chlorines, each of which adds another electron to the outer level of the beryllium. There is no ionic charge to worry about, so there are 4 electrons altogether - 2 pairs. It is forming 2 bonds so there are no lone pairs. The two bonding pairs arrange themselves at 180° to each other, because that's as far apart as they can get. The molecule is described as being linear.

HCN (hydrogen cyanide) and ethyne (acetylene, C2H2) belong to this group TRIPLE BONDS: A FURTHER CASE OF HYBRIDISATION A share of three pairs of electrons will form a triple bond. A triple bond appears in the nitrogen molecule, the hydrogen cyanide molecule and acetylene among other simple molecules. There are no new issues in triple bond formation: a 2s electron is promoted to a 2p sublevel and hybridization mixes in this case just one p orbital and the s orbital forming a so called sp hybrid. The sp hybrid orbitals are in turn fatter and shorter than sp2 hybrids (they show more “s character” so they look more “rounded”). The remaining two 2p orbitals lie along the y and z axes. In the nitrogen molecule both atoms approach and their sp orbitals overlap (frontally) forming an sp-sp σ bond. The other two sp orbitals are occupied by unshared electron pairs. The p orbitals overlap laterally to form two mutually perpendicular π bonds. The resulting set is a compact molecule

The two N atoms

The N2 molecule

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Both C atoms in ethyne or acetylene (C2H2) are bonded the same way. The sp orbitals occupied by the electron pairs in the case of nitrogen, are now sp-s σ orbitals bonding both C atoms to the H atoms on the molecule.

Just a word complicated cases

about some

There are cases in which five or six covalent bonds are formed around an atom. This is the case of PCl5: there are 10 electrons around the P atom so it shows a case where the rule of eight doesn’t hold! This will not be the case for the molecules we will find in this course but it shows what happens when d orbitals play a role in bonding. In this case promotion of an s electron to a d level occurs.

COVALENT MACROSTRUCTURES Sometimes atoms bond covalently but not to form relatively small particles (the molecules) but into a repetitive pattern that extends for millions or maybe billions of atoms forming gigantic covalent structures many times called macromolecules (though the word molecule meaning a “small particle” has lost its original meaning!). we will call them covalent macrostructures to avoid any confusion. Diamond graphite and quartz belong to this group of substances. The structure of diamond Carbon has an electronic arrangement of 2,4. In diamond, each carbon shares electrons with four other carbon atoms - forming four single bonds. In the diagram some carbon atoms only seem to be forming two bonds (or even one bond), but that's not really the case. We are only showing a small bit of the whole structure. This is a giant covalent structure - it continues on and on in three dimensions. It is not a molecule, because the number of atoms joined up in a real diamond is completely variable depending on the size of the crystal. The structure of graphite Graphite has a layer structure which is quite difficult to draw convincingly in three dimensions. The diagram below shows the arrangement of the atoms in each layer, and the way the layers are spaced.

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Notice that you can't really draw the side view of the layers to the same scale as the atoms in the layer without one or other part of the diagram being either very spread out or very squashed. In that case, it is important to give some idea of the distances involved. The distance between the layers is about 2.5 times the distance between the atoms within each layer. The layers, of course, extend over huge numbers of atoms - not just the few shown above. Bonding in graphite Each carbon atom uses three of its electrons to form simple bonds to its three close neighbours. That leaves a fourth electron in the bonding level. These "spare" electrons in each carbon atom become delocalised over the whole of the sheet of atoms in one layer. They are no longer associated directly with any particular atom or pair of atoms, but are free to wander throughout the whole sheet. The important thing is that the delocalised electrons are free to move anywhere within the sheet - each electron is no longer fixed to a particular carbon atom. There is, however, no direct contact between the delocalised electrons in one sheet and those in the neighbouring sheets. The atoms within a sheet are held together by strong covalent bonds - stronger, in fact, than in diamond because of the additional bonding caused by the delocalised electrons. So what holds the sheets together? In graphite you have the ultimate example of van der Waals dispersion forces (to be explained later). As the delocalised electrons move around in the sheet, very large temporary dipoles can be set up, which will induce opposite dipoles in the sheets above and below - and so on throughout the whole graphite crystal. The structure of silicon dioxide, SiO2 (quartz) Crystalline silicon has the same structure as diamond. To turn it into silicon dioxide, all you need to do is to modify the silicon structure by including some oxygen atoms as shown in the figure Notice that each silicon atom is bridged to its neighbours by an oxygen atom. Don't forget that this is just a tiny part of a giant structure extending on all 3 dimensions PROBLEMS 1- According to the VEPRET theory predict the geometry of the following molecules or ions and compare them: H2O NH3 BF3 SO4- SO2 SO3 SO3- NO32- Explain the different shapes for ammonia and boron trifluoride. 3- State the hybridisation of C atoms in the following molecules:

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CO2

C2H2

C2H4

C2H6

HCN

H2CO

4- Tell how many σ (sigma) and how many π (pi) bonds are there formed in each of the molecules of problem Nr 3. 5- Suggest the hybridisation of Carbon in diamond and in graphite. Explain your suggestion. 6- What could be the hybridisation of Silicon and of Oxygen in quartz? Explain.

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