7.5 Bond Strengths

Boy exerting effort and energy to break a stick.

Stable molecules owe their existence to covalent and polar covalent bonds that hold their atoms in place. The strength of these bonds are determined by the amount of energy required to . . . the energy needed to completely separate the bonded atoms.. Just as the breaking of a stick requires the input (addition) of energy, the breaking of a bond is also endothermic (+ΔH). The energy required to break a bond in a gaseous molecule is called the bond energy or the bond dissociation energy and typically reported in units of kJ/mol. Of course the opposite action (unbreaking a stick or making a bond) would be exothermic

Let's calculate the change in bond energy when Hydrogen reacts with Oxygen to form water. First, write the reactants and products showing all the bonding electrons as single, double or triple bonds:

       436                                    495                                                   463           463
2 H

---

H   +   O

---

---

---

O      2 H

---

O

---

H

Then, use this table to look up the bond dissociation energies (BDE) of bonds that are broken and made in the reaction. Notice that all the values in the table are positive - they represent the endothermic process of breaking a bond. However, the bonds on the product side of a reaction are being made, not broken . . . . this fact provides two approaches to calculating the enthalpy (ΔH) of a reaction.

1. Use a formula:
   ΔH =
   Σ
   BDE_{bonds broken} –
   Σ
   BDE_{bonds formed}
   ΔH =
   [
   (
   (2 mol H₂ ×  1 mol H-H 

   ---

    1 mol H₂  ×  436 kJ 

   ---

    1 mol H-H ) + (1 mol O₂ ×  1 mol O=O 

   ---

    1 mol O₂  ×  495 kJ 

   ---

    1 mol O=O )
   )
   –
   (
   2 mol H₂O ×  2 mol H-O 

   ---

    1 mol H₂O  ×  463 kJ 

   ---

    1 mol H-O 
   )
   ]
   
   ΔH = – 485 kJ/mol
   
   
2. Make the BDE of the bonds on the product side negative and add all the Energies.
   Bonds broken have a +ΔH . . . . bonds made have a –ΔH
   ΔH =
   (
   2 mol H₂ ×  1 mol H-H 

   ---

    1 mol H₂  ×  + 436 kJ 

   ---

    1 mol H-H 
   )
   +
   (
   1 mol O₂ ×  1 mol O=O 

   ---

    1 mol O₂  ×  + 495 kJ 

   ---

    1 mol O=O 
   )
   +
   (
   2 mol H₂O ×  2 mol H-O 

   ---

    1 mol H₂O  ×  – 463 kJ 

   ---

    1 mol H-O 
   )

Activity: use the Bond Dissociation Energy Table to calculate the approximate ΔH of the following reactions. After you have determined the answer, click  Show Answer  to check your work.

CH_{4 (g)} + H₂O_(g) → CO_(g) + 3 H_{2 (g)}

Write the Lewis Structure of the reactants and products.
Identify the bonds broken and formed.
Look up the BDE values.

ΔH = Σ[bonds broken] – Σ[bonds formed]

ΔH =

[

(

1 mol CH₄ ×  4 mol C–H 

---

 1 mol CH₄  ×  413 kJ 

---

 1 mol C–H 

)

               +     

(

1 mol H₂O ×  2 mol O–H 

---

 1 mol H₂O  ×  463 kJ 

---

 1 mol O–H 

)

]

      –

[

(

1 mol CO ×  1 mol C≡O 

---

 1 mol CO  ×  1072 kJ 

---

 1 mol C≡O 

)

               +     

(

3 mol H₂ ×  1 mol H–H 

---

 1 mol H₂  ×  436 kJ 

---

 1 mol H–H 

)

]

ΔH = [2578 kJ/mol] – [2380 kJ/mol]

ΔH = 198 kJ/mol

 Show Answer 

4 NH_{3 (g)} + 7 O_{2 (g)} → 4 NO_{2 (g)} + 6 H₂O_(g)

Write the Lewis Structure of the reactants and products.
Identify the bonds broken and formed.
Look up the BDE values.

ΔH = Σ[bonds broken] – Σ[bonds formed]

ΔH =

[

(

4 mol NH₃ ×  3 mol N–H 

---

 1 mol NH₃  ×  391 kJ 

---

 1 mol N–H 

)

               +     

(

7 mol O₂ ×  1 mol O=O 

---

 1 mol O₂  ×  495 kJ 

---

 1 mol O=O 

)

]

      –

[

(

4 mol NO₂ ×  1 mol O=N 

---

 1 mol NO₂  ×  607 kJ 

---

 1 mol O=N 

)

               +     

(

4 mol NO₂ ×  1 mol N–O 

---

 1 mol NO₂  ×  201 kJ 

---

 1 mol N–O 

)

               +     

(

6 mol H₂O ×  2 mol H–O 

---

 1 mol H₂O  ×  463 kJ 

---

 1 mol H–O 

)

]

ΔH = [8157 kJ/mol] – [8788 kJ/mol]

ΔH = -631 kJ/mol

 Show Answer