In the previous section 4.21, we completed the discussion on the VSEPR theory. In this section, we will see the Valence bond theory
■ So far, we have seen two methods for describing the structure of molecules: Lewis dot structures and VSEPR theory
• Lewis dot structures give us a basic idea about the bonds in a molecule. But:
♦ They do not tell us any thing about bond energies
♦ They do not tell us any thing about bond lengths
♦ They do not tell us any thing about the actual shapes of molecules
• The VSEPR theory gives us a basic idea about the actual shapes of the molecules. But:
♦ They do not tell us any thing about bond energies
♦ They do not tell us any thing about bond lengths
• In 1921 The valence bond (VB) theory and molecular orbital (MO) theory was put forward to overcome the above limitations
• First let us see how a bond between two hydrogen atoms is formed. It can be written in 14 steps:
1. Consider a hydrogen atom A
♦ Let it’s nucleus be NA
♦ Let it’s electron be eA
2. Consider another hydrogen atom B
♦ Let it’s nucleus be NB
♦ Let it’s electron be eB
3. Initially, the two hydrogen atoms are at a large distance apart
• So initially, there will be only two forces. We will call them as old forces. They are:
(i) The force between NA and eA (attraction)
(ii) The force between NB and eB (attraction)
4. Let the two atoms approach each other
• Now additional forces will begin to appear
• There will be 4 additional forces. We will call them as new forces. They are:
(i) The force between NA and eB (attraction)
(ii) The force between NB and eA (attraction)
(iii) The force between NA and NB (repulsion)
(iv) The force between eA and eB (repulsion)
5. All the forces can be shown using a color scheme:
• The attractive forces can be shown in green color
♦ Old attractive forces in dashed green
♦ New attractive forces in solid green
• The repulsive forces can be shown in yellow color
♦ Old repulsive forces in dashed yellow
♦ New repulsive forces in solid yellow
• But we do not have old repulsive forces. So there are only three types of arrows:
♦ Old attractive forces in dashed green
♦ New attractive forces in solid green
♦ New repulsive forces in solid yellow
6. Using this color scheme, the forces are shown in fig.4.126 below
• Note that, a total of six forces were mentioned in (3) and (4)
• There are indeed six lines in fig.4.126
7. Now we have an idea about the various forces
• We have to consider the following magnitudes:
(i) Magnitude of the net attractive force
(ii) Magnitude of the net repulsive force
■ Experiments show that (i) is greater than (ii)
■ That means, net attraction is greater than net repulsion
8. So the two atoms will move closer and closer to each other
• As they move closer, the energy of the system (the system consists of the two atoms) decreases
• This is graphically shown in the fig.4.127 below:
• Distance between the two nuclei is plotted along the x-axis
• Energy of the system is plotted along the y-axis
• Let us see the various features of the graph. The following steps from (9) to (14) will help us to clearly understand the features:
9. Usually, we read a graph from left to right. But in the present case, we have to read from right to left
(i) Put your finger tip on the extreme right end of the red curve
(ii) Move the finger tip slowly towards the left, through the curve
(iii) As the we proceed, the finger tip touches the various points on the curve
• Each of those points will have:
♦ a definite x coordinate
♦ a definite y coordinate
(iv) In the initial stage of the curve:
♦ The x coordinates decrease continuously
♦ But the y coordinates remain nearly the same
(v) This is so because, this stage of the curve is nearly horizontal
• This 'initial horizontal portion' is indicated in blue color (from A to B) in fig.4.128 below:
10. The reason for this horizontal nature of the curve can be explained in 3 steps:
(i) Initially, the two H atoms are at a large distance apart
♦ So there will be no interaction between them
(ii) Since there is no interaction, the energy of the system will be zero
♦ This 'zero energy condition' will continue up to the left end (point B) of the blue segment
♦ So the blue segment indicates that, actual interaction has not begun between the atoms
♦ The position 'I' shows a sample. At 'I', the atoms are far apart and hence there is no interaction
(iii) Note that, in addition to 'being nearly horizontal', the blue segment is very close to the x axis
♦ That means, all the points in the blue segment will have their y coordinates nearly zero
11. After the left end B of the blue segment, we see that, the curve dips
• This is indicated by the green segment BC
• We can write the details in 6 steps:
(i) As we move the finger tip through the green segment,
♦ The x coordinate decreases
♦ The y coordinate also decreases
(ii) The decrease in the x coordinate indicates that, the atoms are moving closer and closer to each other
♦ The position 'II' shows a sample. At 'II',. the atoms are closer to each other
♦ Hence there is some interaction
(iii) The decrease in y coordinate indicates that, the energy is decreasing
♦ This is the 'lowest energy' that the system can attain
(v) The ‘point of lowest energy’ is an important point
• We must note down the x coordinate at this point. It is equal to 74 pm
• So we can write:
♦ When the two hydrogen atoms approach each other, the energy of the system continuously decreases
♦ The energy reaches the least possible value when the distance between the atoms become 74 pm
(vi) The ‘least possible energy’ is an ideal condition for the ‘formation of a bond’
■ So the bond length between the two H atoms in a H2 molecule will be 74 pm
12. Beyond the point C, we have the yellow segment CD. Here the situation changes dramatically. It can be written in 6 steps
(i) Beyond point C, the distance between the two H atoms is less than 74 pm
(ii) The atoms are so close to each other that,
♦ the two nuclei will begin to repel each other
♦ the two electrons will begin to repel each other
• So repulsive forces also come into play
(iii) Now the interactions are not so strong as in the green segment. This is because:
♦ The interaction is now the net of attraction and repulsion
♦ In the green segment, there was attraction only
(iv) Since the interactions are not so strong, the energy of the system begins to increase
• This is indicated by the yellow segment
• As we move the finger tip through the yellow segment,
♦ The x coordinate decreases
♦ The y coordinate increases
(v) The decrease in the x coordinate indicates that, the atoms are moving closer and closer to each other
(vi) The increase in y coordinate indicates that, the energy is increasing
13. Note that, up to the left end D of the yellow segment, the energy is negative
• This is because, though there is repulsion, the force of attraction still has an upper hand
• But beyond this point D, repulsion takes over
• The energy due to ‘repulsive interactions’ is positive
• So the magenta portion DE is above the x axis
• The energy due to attractive interaction is negative
• The energy due to repulsive interaction is positive
■ Why is there such a sign convention?
• We will see the answer in physics classes when we study the 'interactions between charged particles'
(i) When the two atoms are at a large distance apart, the energy of the system is zero
(ii) When the two atoms approach each other, the energy of the system decreases
♦ That means, the system gives off energy to the surroundings
■ When one mole of H atoms combine with another one mole of H atoms to form one mole of H2 molecules, we will get 435.8 kJ of energy
♦ The energy that we receive is -ve
■ Conversely, when we supply 435 kJ of energy to one mole of H2 molecules, we will get two mols of H atoms
♦ The energy that we supply is +ve
■ So far, we have seen two methods for describing the structure of molecules: Lewis dot structures and VSEPR theory
• Lewis dot structures give us a basic idea about the bonds in a molecule. But:
♦ They do not tell us any thing about bond energies
♦ They do not tell us any thing about bond lengths
♦ They do not tell us any thing about the actual shapes of molecules
• The VSEPR theory gives us a basic idea about the actual shapes of the molecules. But:
♦ They do not tell us any thing about bond energies
♦ They do not tell us any thing about bond lengths
• In 1921 The valence bond (VB) theory and molecular orbital (MO) theory was put forward to overcome the above limitations
• First let us see how a bond between two hydrogen atoms is formed. It can be written in 14 steps:
1. Consider a hydrogen atom A
♦ Let it’s nucleus be NA
♦ Let it’s electron be eA
2. Consider another hydrogen atom B
♦ Let it’s nucleus be NB
♦ Let it’s electron be eB
3. Initially, the two hydrogen atoms are at a large distance apart
• So initially, there will be only two forces. We will call them as old forces. They are:
(i) The force between NA and eA (attraction)
(ii) The force between NB and eB (attraction)
4. Let the two atoms approach each other
• Now additional forces will begin to appear
• There will be 4 additional forces. We will call them as new forces. They are:
(i) The force between NA and eB (attraction)
(ii) The force between NB and eA (attraction)
(iii) The force between NA and NB (repulsion)
(iv) The force between eA and eB (repulsion)
5. All the forces can be shown using a color scheme:
• The attractive forces can be shown in green color
♦ Old attractive forces in dashed green
♦ New attractive forces in solid green
• The repulsive forces can be shown in yellow color
♦ Old repulsive forces in dashed yellow
♦ New repulsive forces in solid yellow
• But we do not have old repulsive forces. So there are only three types of arrows:
♦ Old attractive forces in dashed green
♦ New attractive forces in solid green
♦ New repulsive forces in solid yellow
6. Using this color scheme, the forces are shown in fig.4.126 below
• Note that, a total of six forces were mentioned in (3) and (4)
• There are indeed six lines in fig.4.126
 |
| Fig.4.126 |
• We have to consider the following magnitudes:
(i) Magnitude of the net attractive force
(ii) Magnitude of the net repulsive force
■ Experiments show that (i) is greater than (ii)
■ That means, net attraction is greater than net repulsion
8. So the two atoms will move closer and closer to each other
• As they move closer, the energy of the system (the system consists of the two atoms) decreases
• This is graphically shown in the fig.4.127 below:
 |
| Fig.4.127 |
• Energy of the system is plotted along the y-axis
• Let us see the various features of the graph. The following steps from (9) to (14) will help us to clearly understand the features:
9. Usually, we read a graph from left to right. But in the present case, we have to read from right to left
(i) Put your finger tip on the extreme right end of the red curve
(ii) Move the finger tip slowly towards the left, through the curve
(iii) As the we proceed, the finger tip touches the various points on the curve
• Each of those points will have:
♦ a definite x coordinate
♦ a definite y coordinate
(iv) In the initial stage of the curve:
♦ The x coordinates decrease continuously
♦ But the y coordinates remain nearly the same
(v) This is so because, this stage of the curve is nearly horizontal
• This 'initial horizontal portion' is indicated in blue color (from A to B) in fig.4.128 below:
 |
| Fig.4.128 |
(i) Initially, the two H atoms are at a large distance apart
♦ So there will be no interaction between them
(ii) Since there is no interaction, the energy of the system will be zero
♦ This 'zero energy condition' will continue up to the left end (point B) of the blue segment
♦ So the blue segment indicates that, actual interaction has not begun between the atoms
♦ The position 'I' shows a sample. At 'I', the atoms are far apart and hence there is no interaction
(iii) Note that, in addition to 'being nearly horizontal', the blue segment is very close to the x axis
♦ That means, all the points in the blue segment will have their y coordinates nearly zero
11. After the left end B of the blue segment, we see that, the curve dips
• This is indicated by the green segment BC
• We can write the details in 6 steps:
(i) As we move the finger tip through the green segment,
♦ The x coordinate decreases
♦ The y coordinate also decreases
(ii) The decrease in the x coordinate indicates that, the atoms are moving closer and closer to each other
♦ The position 'II' shows a sample. At 'II',. the atoms are closer to each other
♦ Hence there is some interaction
(iii) The decrease in y coordinate indicates that, the energy is decreasing
When the distance decreases, the energy of the system also decreases. This is similar to an 'earth-stone' system that we see in the physics classes. When the stone is very high up, the potential energy of the earth-stone system is high. When the stone is at a lower height, the potential energy of the earth-stone system is low. We will see a more detailed explanation when we learn about 'interactions between charged particles' in physics classes
(iv) At the bottom end of the green segment, the energy value is -435.8 kJ/mol
(v) The ‘point of lowest energy’ is an important point
• We must note down the x coordinate at this point. It is equal to 74 pm
• So we can write:
♦ When the two hydrogen atoms approach each other, the energy of the system continuously decreases
♦ The energy reaches the least possible value when the distance between the atoms become 74 pm
(vi) The ‘least possible energy’ is an ideal condition for the ‘formation of a bond’
■ So the bond length between the two H atoms in a H2 molecule will be 74 pm
12. Beyond the point C, we have the yellow segment CD. Here the situation changes dramatically. It can be written in 6 steps
(i) Beyond point C, the distance between the two H atoms is less than 74 pm
(ii) The atoms are so close to each other that,
♦ the two nuclei will begin to repel each other
♦ the two electrons will begin to repel each other
• So repulsive forces also come into play
(iii) Now the interactions are not so strong as in the green segment. This is because:
♦ The interaction is now the net of attraction and repulsion
♦ In the green segment, there was attraction only
(iv) Since the interactions are not so strong, the energy of the system begins to increase
• This is indicated by the yellow segment
• As we move the finger tip through the yellow segment,
♦ The x coordinate decreases
♦ The y coordinate increases
(v) The decrease in the x coordinate indicates that, the atoms are moving closer and closer to each other
(vi) The increase in y coordinate indicates that, the energy is increasing
13. Note that, up to the left end D of the yellow segment, the energy is negative
• This is because, though there is repulsion, the force of attraction still has an upper hand
• But beyond this point D, repulsion takes over
• The energy due to ‘repulsive interactions’ is positive
• So the magenta portion DE is above the x axis
■ We see a sign convention:
• The energy due to repulsive interaction is positive
■ Why is there such a sign convention?
• We will see the answer in physics classes when we study the 'interactions between charged particles'
14. Let us note an important inference from the above graph. It can be written in steps:
(ii) When the two atoms approach each other, the energy of the system decreases
♦ That means, the system gives off energy to the surroundings
■ When one mole of H atoms combine with another one mole of H atoms to form one mole of H2 molecules, we will get 435.8 kJ of energy
♦ The energy that we receive is -ve
■ Conversely, when we supply 435 kJ of energy to one mole of H2 molecules, we will get two mols of H atoms
♦ The energy that we supply is +ve
We have seen the formation of a bond between two H atoms. Based on this, we will see valence bond theory in the next section
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