Bent out of Shape

7409 /www/nrich/html/content/id/7409/ 1 2011-02-01T00:00:01 <mdoxml version="1.0"> <ul id="stemLinks"> <li><a href="http://nrich.maths.org/7306">Warm-up</a></li> <li><a href="http://nrich.maths.org/2690">Try this next</a></li> <li><a href="http://nrich.maths.org/6451">Think higher</a></li> <li><a href="http://plus.maths.org/content/os/latestnews/may-aug10/ice/index">Read: mathematics</a></li> <li><a href="http://www.chem.ufl.edu/~myers/chm2045/shapes.htm">Read: science</a></li> <li><a href="http://motivate.maths.org/conferences/conference.php?conf_id=106">Explore further</a></li> </ul> <div> </div> When a molecule consists of one central atom with several others covalently bonded to it the electrons in these bonds repel each other. The result of this is that the bonded atoms will be oriented as far away from each other as possible, eg. <mdo:image alt="" height="31" src="co2.png" width="150"></mdo:image> The angle formed between the two oxygen atoms (the "bond angle") is $180^\circ$ - given that the length of the bonds are fixed the oxygen atoms could not be further apart. <mdo:image alt="" height="91" src="bf3.PNG" width="120"></mdo:image> Here, the central boron has three fluorine atoms bonded to it. The angle between any two fluorines is the same and it is $120^\circ$ . Again, the three F atoms could not have arranged themselves to be further apart. This occurs because the bonds are formed of pairs of electrons, which carry a negative charge. If two bodies (in this case bonds) are negatively charged they will repel each other. Draw diagrams to represent the structures of the following molecules. Can you work out what the bond angles are? (You don't need to know anything about the molecules!) NH$_{4}^{+}$ CH$_{4}$ BeH$_{2}$ AlCl$_{3}$ PCl$_{5}$ SF$_{6}$ Water (H$_{2}$O) has a bond angle of $104.5^\circ$. What would you have expected the bond angle to be? Why do you think it might be different? <mdo:image alt="" height="62" src="water2.png" width="120"></mdo:image> Similarly, NH$_{3}$ has a bond angle of $107.5^\circ$. As is the case for water, this is because the nitrogen atom has an unbonded pair of electrons in its outer shell - a lone pair. This acts much like a bond, repelling the electrons in the covalent bonds. Why do you think the bond angle is not the same as for NH$_{4}$? Draw the two molecules side by side. How does the orientation of the hydrogen atoms differ? How many covalent bonds is the lone pair here equivalent to in terms of repulsive effect? Is this the same as for the lone pairs in water? Does this surprise you?</mdoxml> <mdoxml version="1.0"> If you are having trouble picturing how these molecule might look, try using blu tack and string to make models of the atoms and their bonds. If you're still stuck, scroll down on this page to see diagrams of the molecules. For the question about water, it will help you to think about the electrons in oxygen. How many valence electrons does oxygen have? What happens to the valence electrons that don't get used in bonding? Structures of molecules given: You will notice that in some of these diagrams some bonds are shown as normal lines, some as thick lines and some as dashed lines. This says nothing about the chemical nature of the bonds but describes their orientation in three dimensions. A normal line indicates a bond in the plane of the page (or screen); a thick line indicates a bond coming out of the page and a dashed line indicates a bond going into the page. If this is confusing, don't worry! Try using these diagrams to help you make a model of the molecules or ask your teacher to explain further. <mdo:image alt="" height="120" src="nh4.png" width="109"></mdo:image>NH$_{4}^{+}$ CH$_{4}$ has the same structure as NH$_{4}^{+}$ <mdo:image alt="" height="37" src="beh2.png" width="120"></mdo:image>BeH$_{2}$ AlCl$_{3}$ has the same structure as BF$_{3}$ <mdo:image alt="" height="136" src="pcl5.png" width="150"></mdo:image> PCl$_{5}$ </mdoxml> <mdoxml version="1.0"> Assuming the central atom has no lone pairs of electrons in its outer shell, here are the bond angles: <table border="1"> <tbody> <tr> <td style="text-align: center; vertical-align: middle;"> Number of ligands bound to central atom </td> <td style="text-align: center;">Bond angle(s)</td> <td style="text-align: center;">Molecules with these angles</td> </tr> <tr> <td>2</td> <td>$180^{o}$</td> <td>BeH$_{2}$</td> </tr> <tr> <td>3</td> <td>$120^{o}$</td> <td>AlCl$_{3}$</td> </tr> <tr> <td>4</td> <td>$109.5^{o}$</td> <td>NH$_{4}^{+}$, CH$_{4}$</td> </tr> <tr> <td>5</td> <td>$90^{o}$, $120^{o}$</td> <td>PCl$_{5}$</td> </tr> <tr> <td>6</td> <td>$90^{o}$, $180^{o}$</td> <td>SF$_{6}$</td> </tr> </tbody> </table> The angle of $109.5^{o}$ is quite tricky to derive, it's known as the 'tetrahedral angle'. There's a cunning derivation on the Ask NRICH forum <a href="https://nrich.maths.org/discus/messages/117730/143782.html?1207921624">here</a>. If we didn't know anything about the water molecule, we'd expect it to be like BeH$_{2}$. However, oxygen has six electrons in its outer shell. Two of these form covalent bonds with hydrogen atoms, leaving two "lone pairs". These repel against each other and also against the electrons in the covalent bonds, and force the bonds to be closer than we might initially guess. It seems the lone pairs repel other electrons more strongly than electrons in covalent bonds. This could then explain the different shapes of NH$_{4}^{+}$ and NH$_{3}$ as the lone pair forces the covalent bonds in NH$_{3}$ to be closer together than in NH$_{4}^{+}$ (which is symmetric). In water, the two lone pairs force the O - H bonds even closer together than the N - H bonds in NH$_{3}.$ </mdoxml> 5 4 0 0 0 1 1 Bent out of Shape An introduction to bond angle geometry. Using, Applying and Reasoning about Mathematics Real world Using, Applying and Reasoning about Mathematics Visualising Applications chemistry Coordinates and Coordinate Geometry Polar coordinates Using, Applying and Reasoning about Mathematics Working systematically 3D Geometry, Shape and Space 2D representations of 3D shapes 3D Geometry, Shape and Space Angles between lines & planes Applications STEM - General Applications chemistry Using, Applying and Reasoning about Mathematics Investigations