Let's analyze the given reaction step by step:
### Given Reaction
[tex]\[ 2 H_2 + O_2 \rightarrow 2 H_2O \][/tex]
### Bond Energies from the Table
- [tex]\( H - H \)[/tex]: 436 kJ/mol
- [tex]\( O - H \)[/tex]: 464 kJ/mol
- [tex]\( O = O \)[/tex]: 497 kJ/mol
### a) Which bonds are broken?
In the reaction, the bonds that need to be broken are:
- The bonds in two [tex]\( H_2 \)[/tex] molecules.
- The bonds in one [tex]\( O_2 \)[/tex] molecule.
### b) What is the total bond energy of the bonds that are broken?
To find the total bond energy of the bonds broken:
- Each [tex]\( H_2 \)[/tex] molecule has one [tex]\( H-H \)[/tex] bond.
- Energy for one [tex]\( H-H \)[/tex] bond: 436 kJ/mol
- For 2 [tex]\( H_2 \)[/tex] molecules: [tex]\( 2 \times 436 \)[/tex] kJ/mol = 872 kJ/mol
- [tex]\( O_2 \)[/tex] molecule has one [tex]\( O=O \)[/tex] bond.
- Energy for one [tex]\( O=O \)[/tex] bond: 497 kJ/mol
Total bond energy for bonds broken:
[tex]\[ 872 + 497 = 1369 \text{ kJ/mol} \][/tex]
### c) Which bonds are formed?
In the reaction, the bonds that are formed are the [tex]\( O-H \)[/tex] bonds in the water molecules:
- Each [tex]\( H_2O \)[/tex] molecule has two [tex]\( O-H \)[/tex] bonds.
- Since 2 [tex]\( H_2O \)[/tex] molecules are formed, there will be [tex]\( 2 \times 2 = 4 \)[/tex] [tex]\( O-H \)[/tex] bonds formed.
### d) Calculate the total energy given out when the bonds are formed?
To find the total bond energy of the bonds formed:
- Each [tex]\( O-H \)[/tex] bond has energy: 464 kJ/mol
- For 4 [tex]\( O-H \)[/tex] bonds: [tex]\( 4 \times 464 \)[/tex] kJ/mol = 1856 kJ/mol
### e) Calculate [tex]\(\Delta H\)[/tex] for the reaction and state whether it is endothermic or exothermic.
The enthalpy change [tex]\(\Delta H\)[/tex] for the reaction is calculated as:
[tex]\[ \Delta H = \text{Total bond energy of bonds broken} - \text{Total bond energy of bonds formed} \][/tex]
Given:
- Total bond energy of bonds broken: 1369 kJ/mol
- Total bond energy of bonds formed: 1856 kJ/mol
Thus:
[tex]\[ \Delta H = 1369 - 1856 = -487 \text{ kJ/mol} \][/tex]
Since [tex]\(\Delta H\)[/tex] is negative, the reaction releases energy, making it exothermic.
### Conclusion
- Total bond energy of bonds broken: 1369 kJ/mol
- Total bond energy of bonds formed: 1856 kJ/mol
- [tex]\(\Delta H\)[/tex] for the reaction: -487 kJ/mol
Therefore, the reaction is exothermic.
