Chapter 8.6 - Three dimensional arrangement of atoms in Hydrocarbons

In the previous section, we saw the details and nomenclature of cyclic hydrocarbons. In this section we will learn about the position of various atoms in a hydrocarbon, in 3D space.

We have seen the arrangement of carbon and hydrogen atoms in various hydrocarbons. Consider methane. We have seen the structural formula here. So we know that there are 4 hydrogen atoms around a single carbon atom. 
Are the four hydrogen atoms placed in a circle around the carbon atom? 
Or are they placed in a square, with one atom at each corner of the square?
Or is it any other shape?

To find the answer, we must look into the 3D view of a methane molecule. 
1. In fig.8.17(a) below, a geometrical solid is shown. It is called a tetrahedron. 

Fig.8.17

Let us see the peculiarities of a tetrahedron in general:
• It is a triangular pyramid. That means, it is a pyramid, whose base is a triangle. The base triangle of our tetrahedron is named as ABC
• It has four faces. One base and three lateral faces.
• All the faces are triangles. 
    ♦ All those triangles are equilateral triangles. 
    ♦ All those equilateral triangles are identical
• It has four corners. In fig.a, they are named as A, B, C and D.
2. The four hydrogen atoms of methane are situated at the four corners of the tetrahedron as shown in fig.8.17(b). They are shown as four pink spheres.
3. The carbon atom is shown as a larger blue sphere. It is situated at the exact centroid of the tetrahedron.
4. The white cylinders indicate the bonds.
5. It is a ball and stick model
6. Upon seeing the arrangement in fig.b, our first impression would be this:
"There is no vertical symmetry"
We feel this because:
• The carbon atom is nearer to the base triangle. 
• The distance of the carbon atom from the top corner is greater than it's distance from the base triangle.
7. But the fact is that, the molecule as a whole is symmetrical in any direction. Even if we spin the molecule in any direction, it will be symmetrical. This is because, the distance of the carbon atom from any of the 4 hydrogen atoms is the same.

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Now we know the 3 dimensional arrangement of atoms in a molecule of methane. But it is difficult to draw 3D views every time. So we need a method to represent a 3 dimensional arrangement on paper.

1. Consider fig.8.18(a) below. It shows one molecule of methane. 

Fig.8.18

2. We want to represent it on paper. The 5 atoms are situated at different directions. There does not seem to be a way to bring them together.

3. But there is good news. On careful analysis, we find that three of them fall in one plane. This plane is shown in fig.8.18(b). The three atoms are:

• The hydrogen atom marked as C

• The hydrogen atom marked as D

• The carbon atom

4. This plane is our 'plane of paper'. The three atoms will fall on the paper. 

5. But two hydrogen atoms remain. 

• One of them marked as B, projects above the plane of paper, towards the viewer. 

• The other marked as A,  recedes below the paper, away from the viewer.

6. So we need special methods to represent them. This can be explained with the help of fig.8.19 below. 

Fig.8.19

The fig. is based on the following rules:

• All atoms at the ends of single lines fall on the plane of paper
• All atoms at the base of solid triangles are above the plane of paper
• All atoms at the base of dashed triangles are below the plane of paper
7. Let us see the example of Ethane. It is shown in fig.8.20(a) below

Fig.8.20

8. Fig.8.20(b) shows some more details. 
• All the atoms which fall in the thick red line, lies on the plane of paper. 
• The hydrogen atoms with in green circles lies above the plane of paper
• The hydrogen atoms with in yellow circles lies below the plane of paper

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So we have seen how the atoms are arranged in different molecules of hydrocarbons. In the next section, we will learn about Allotropes. 

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Chapter 8.1 - Properties and definition of Homologous Series

In the previous section, we saw the reasons for formation of very large number of carbon compounds. In this section we will see the arrangement of atoms in Carbon compounds. Based on that we will discuss about Homologous series.

Consider the molecule C₂H₆. It is a molecule of 'ethane'. We want to know how the atoms are arranged in the molecule. Let us find out:
Step 1: In C₂H₆, there are two carbon atoms. The first step is to connect those two, using a single bond. It is shown in fig.8.6(a) below:

Fig.8.6

Step 2: • Consider the carbon atom on the left. It is in single bond with the right side carbon atom. So it has acquired one electron through this single bond. Three more electrons are required. 
• So bond it to three hydrogen atoms. A bond between a carbon atom and a hydrogen atom is possible only through a single bond. This is because hydrogen has only one electron to share.
• Thus the left side carbon atom is bonded to three hydrogen atoms through single bonds. With this step, the left side carbon atom attains octet. The three hydrogen atoms also attain octet. This step is shown in fig.8.6(b)
Step 3: The same situation we saw in step 2, exists with the right side carbon atom. But we will write the steps again:
• Consider the carbon atom on the right. It is in single bond with the left side carbon atom. So it has acquired one electron through this single bond. Three more electrons are required. 
• So bond it to the remaining three hydrogen atoms. As mentioned above, a bond between a carbon atom and a hydrogen atom is possible only through a single bond. This is because hydrogen has only one electron to share.
• Thus the right side carbon atom is bonded to three hydrogen atoms through single bonds. With this step, the right side carbon atom attains octet. The three hydrogen atoms also attain octet. This step is shown in fig.c
■ With the above three steps, we get the final arrangement of atoms in a molecule of C₂H₆. The electron dot diagram is shown in the fig.8.7 below:

Fig.8.7

Note that the 'pair of electrons between the two carbon atoms' are both green in colour. This is different from all other pairs. The reader may write the reason for this 'difference in colour' in his/her own notebooks.

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Now we will consider another example: C₃H₈. We will write the required steps as in the previous example.

Step 1: In C₃H₈, there are 3 carbon atoms. The first step is to connect the three using single bonds. It is shown in fig.8.8(a) below:

Fig.8.8

Step 2: • Consider the left most carbon atom. It is in single bond with the middle carbon atom. So it has acquired one electron through this single bond. Three more electrons are required.
• So bond it to three hydrogen atoms. A bond between a carbon atom and a hydrogen atom is possible only through a single bond. This is because hydrogen has only one electron to share.
• Thus the left most carbon atom is bonded to three hydrogen atoms through single bonds. With this step, the left most carbon atom attains octet. The three bonded hydrogen atoms also attain octet. This step is shown in fig.b
Step 3: Consider the middle carbon atom. It is already bonded to two carbon atoms. They are two single bonds. So it has already acquired two electrons (one from each bond). Two more electrons are required. 
• So this carbon atom is bonded to two hydrogen atoms. One at top and the other at bottom. With this step, the middle carbon atom attains octet. The two hydrogen atoms bonded to it also attains octet. This step is shown in fig.c.
Step 4: Now the only remaining carbon atom is the right most one. It is in the same situation as in the left most carbon atom. But we will write the steps again:
• Consider the right most carbon atom. It is in single bond with the middle carbon atom. So it has acquired one electron through this single bond. Three more electrons are required. 
• For that, bond it to the three remaining hydrogen atoms. With this step, the right most carbon atom attains octet. The three hydrogen atoms which remained also attain octet. This step is shown in fig.d
■ With the above four steps, we get the final arrangement of atoms in a molecule of C₃H₈. The electron dot diagram is shown in the fig.8.9 below:

Fig.8.9

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So we determined the arrangement of atoms in the following two molecules:

(i) Molecule with 2 carbon atoms and 6 hydrogen atoms
(ii) Molecule with 3 carbon atoms and 8 hydrogen atoms
• A pattern is beginning to emerge. The next two cases will be:
(iii) Molecule with 4 carbon atoms and 10 hydrogen atoms
(iv) Molecule with 5 carbon atoms and 12 hydrogen atoms
• Note that number of carbon atoms is increasing by 1. Also, number of hydrogen atoms is increasing by 2
• It is like a series. Let us tabulate the arrangement for the first six members of the series:

With the above table, the analysis about the series becomes easy. Let us learn the properties of the series:
Property 1:
• The 1^st member of the series has 1 carbon atom
And 4 hydrogen atoms
• The 2^nd member of the series has 2 carbon atoms
And 6 hydrogen atoms
• The 3^rd member of the series has 3 carbon atoms
And 8 hydrogen atoms
So on...
■ So there exists a definite relation between the two quantities below:
• No. of carbon atoms
• No. of hydrogen atoms
■ If the no. of carbon atoms is 'n', then the no. Of hydrogen atoms will be (2n+2)
So we can represent the members of the series by a general formula: C_nH_(2n+2)
Property 2:
• Consider the second row. Consider the item in the 'Condensed formula' column in this row. We have: CH₃ – CH₃
A Condensed formula is a system of writing molecules in the same line as other text. It shows all atoms, but omits the vertical bonds. It also omits most or all the horizontal single bonds. 
• Now consider the third row, same column. We have: CH₃ – CH₂ –  CH₃
The difference from the previous second row is a CH₂ group
• Now consider the fourth row, same column. We have:  CH₃ – CH₂ – CH₂ –  CH₃ 
Here also, the difference between the previous third row is a CH₂ group
• We will find the same difference through out the series. That is:
■ Successive members differ by a CH₂ group

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A series of compounds having the above two properties is called a homologous series. We can write the official definition:

■ A Homologous Series is a group of chemical compounds satisfying the following conditions:
• All members of the series can be represented by a general formula
• Successive members differ by a CH₂ group

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• Members of a homologous series show similarity in chemical properties

• There is a regular gradation in their physical properties. That is., as we move down the series, the melting point, boiling point etc., increases.

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So now we know what a 'homologous series' is. The series that we saw just above is given a special name: Alkanes. In the next section, we will see another homologous series. 

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