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ChemWiki: The Dynamic Chemistry E-textbook > Theoretical Chemistry > Chemical Bonding > General Principles > Bond Order and Lengths

Bond Order and Lengths

Bond order and bond length indicate the type and strength of covalent bonds between atoms. Bond order and length are inversely proportional to each other. When bond order is increased, bond length is decreased.

Bond Order

Bond order is the number of bonding pairs of electrons between two atoms. In a covalent bond between two atoms, a single bond has a bond order of one, a double bond has a bond order of two, a triple bond has a bond order of three, and so on. Table I below summarizes these relationships:

Table 1 - Bond Orders and their Symbols

Bond Order Chart.JPG

To determine the bond order between two covalently bonded atoms, follow these steps:

  1. Draw the Lewis Structure.
  2. Figure out the type of bond between the two atoms.

 

Example 1: \(CN^-\)

Determine the bond order for cyanide: \(CN^-\).

SOLUTION

1) Draw the Lewis Structure.

cyanide.JPG

2) Figure out the type of bond between the two atoms.

Since there are 3 dashes, that means that it is a triple bond. A triple bond means that there is a bond order of 3.

 

Example 2: \(H_2\)

Determine the bond order for hydrogen gas: H2.

SOLUTION

1) Draw the Lewis Structure.

hydrogen gas.JPG

2) Figure out the type of bond between the two atoms.

Since there is only 1 dash, that means that it is a single bond. A single bond means that there is a bond order of 1.

When there are more than two atoms in the molecule, follow these steps to determine the bond order:

  1. Draw the Lewis Structure.
  2. Count the total number of bonds.
  3. Count the number of bonds between individual atoms.
  4. Divide the number of bonds between atoms by the total number of bond groups in the molecule. 

 

Example 3: \(NO_3\)

Determine the bond order for nitrate: NO3.

SOLUTION

1) Draw the Lewis Structure.

1 nitrate.JPG

 2) Count the total number of bonds.

2 nitrate.JPG

The total number of bonds is 4.

3) Count the number of bonds between individual atoms.

3 nitrate.JPG

The number of bonds between individual atoms is 3.

4) Divide the number of bonds between individual atoms by the total number of bonds.

4/3= 1.33 The bond order is 1.33

 

Example 4: \(NO^+_2\)

Determine the bond order for nitronium ion: NO2+.

SOLUTION

1) Draw the Lewis Structure.

1 nitronium.JPG

2) Count the total number of bonds.

 2 nitronium.JPG

The total number of bonds is 4.

3) Count the number of bonds between individual atoms.

3 nitronium.JPG

The number of bonds between atoms is 2.

4) Divide the bonds between individual atoms by the total number of bonds.

4/2 = 2. The bond order is 2.

A high bond order causes more attraction between electrons. A higher bond order also means that the atoms are held together tighter. This correlation is the same for a low bond order. With a lower bond order, there is less attraction between electrons and this causes the atoms to be held together looser. Bond order also indicates the stability of the bond. The higher the bond order, the more electrons holding the atoms together, and therefore the greater the stability.

In the molecular orbital theory, the following formula is used to find the bond order of a molecule:

\[ \dfrac{ \text{(bonding electrons) - (anti-bonding electrons)} }{2}\]

For example, when we fill out the molecular orbital energy diagram for B2, we get a diagram that looks like this:

 Bond Order B2.png

From this diagram, we can see that B2 has four bonding electrons and two anti-bonding electrons. When we plug these numbers into the formula, we get the equation:

\[ \dfrac{4-2}{2}\]

By using this formula, we have found that the bond order for B2 is 2.

Trends in the Periodic Table

Bond order increases across a period and decreases down a group. 

 ChemWiki Periodic Table 2.png

Bond Length

Bond length is the distance between the centers of two covalently bonded atoms. The bond length varies for each type of bond and a comparison of bond lengths is shown below in Table 2.

Table 2 - Bond Length Notation 

  Comparison between bond lengths.JPG

Therefore, the bond length of a triple bond < double bond < single bond.

The length of the bond is determined by the number of bonded electrons (the bond order). The higher the bond order, the stronger the pull between the two atoms and the shorter the bond length. Generally, the length of the bond between two atoms is approximately the sum of the covalent radii of the two atoms, X + Y. Bond length is given in picometers.

Covalent radius.JPG

To find the bond length, follow these steps:

  1. Draw the Lewis structure.
  2. Look up the chart below for the radii for the corresponding bond.
  3. Find the sum of the two radii.

 

Example: CCl4

Determine the carbon-to-chlorine bond length in CCl4.

 carbon chlorine.JPG

In table 3 below, we see that a C single bond has a length of 75 picometers and that a Cl single bond has a length of 99 picometers. When we add them together, the bond length of a C-Cl bond is approximately 174 picometers.

 

Determine the carbon-to-oxygen bond length in CO2.

 carbon dioxide.JPG

In table 3 below, we see that a C double bond has a length of 67 picometers and that an O double bond has a length of 57 picometers. When we add them together, the bond length of a C=O bond is approximately 124 picometers.

Trends in the Periodic Table

Since the bond length is proportional to the atomic radii, the bond length trends in the periodic table follow the same trends of atomic radius. Bond length decreases across a period and increases down a group (identical to atomic radius).

ChemWiki Periodic Table.png

Problems

  1. What is the bond order of O2?
  2. What is the bond order of NO3-?
  3. What is the carbon-to-nitrogen bond length in HCN?
  4. Is the carbon-to-oxygen bond length greater in CO2 or CO?
  5. What is the nitrogen-to-fluoride bond length in NF3?

Solutions

1. To solve this problem we must first write the Lewis structure for O2.

Oxygen.png

We can see from the structure that there is a double bond between the two oxygen atoms. A double bond tells us that the bond order of the molecule is 2.

2. To solve this problem we must first write the Lewis structure for NO3-.

 

Nitrate.png

To find the bond order of this molecule, we must take the average of the bond orders. N=O has a bond order of two, and both N-O bonds have a bond order of one. When we add these together and divide by the number of bonds (3), we find that the bond order of nitrate is 1.33.

3. To find the carbon-to-nitrogen bond length in HCN, we must first draw the Lewis structure of HCN.

 HCN.png

We can see from the structure that the bond between carbon and nitrogen is a triple bond. When we refer to the table above, we find that a triple bond between carbon and nitrogen has a bond length of approximately 60 + 54 =114 pm.

4. After drawing the Lewis structures for CO2 and CO, we find that there is a double bond between the carbon and oxygen in CO2 and a triple bond between the carbon and oxygen in CO.

CO2 and CO.png

We can see from the structure that the bond between carbon and nitrogen in CO is a double bond.We can also see from the structure that the bond between carbon and nitrogen in CO2 is a triple bond. When we refer to the table above, we find that double bond between carbon and oxygen has a bond length of approximately 67 + 57 = 124 pm and a triple bond between carbon and nitrogen has a bond length of approximately 60 + 53 =113 pm. Therefore, the bond length is greater in CO2.

To use another method, know that the more electron bonds between the atoms the tighter the electrons are pulling the atoms together. Therefore, the bond length is greater in CO2.

5. To find the nitrogen-to-fluorine bond length in NF3 we must first draw the Lewis structure for this molecule.

NF3.png

We can see from the structure that the bond between fluorine and nitrogen is a single bond. When we refer to the table above, we find that a single bond between fluorine and nitrogen has a bond length of approximately 64 + 71 =135 pm.

References

  1. Campbell, Neil A., Brad Williamson, and Robin J. Heyden. Biology: Exploring Life. Boston, Massachusetts: Pearson Prentice Hall, 2006.
  2. Petrucci, Ralph H., Harwood, William S., Herring, F. G., and Madura Jeffrey D. General Chemistry: Principles & Modern Applications. 9th Ed. New Jersey: Pearson Education, Inc., 2007. Print.
  3. Cordero, Beatriz, Verónica Gómez, Ana E. Platero-Prats, Marc Revés, Jorge Echeverría, Eduard Cremades, Flavia Barragán and Santiago Alvarez. Dalton's Transactions." Covalent radii revisited 2008: 
  4. Pekka Pyykkö and Michiko Atsumi, Chem. Eur. J. Molecular Double-Bond Covalent Radii for Elements Li–E112 2009

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19:05, 21 Jan 2014

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