To calculate the change in enthalpy ([tex]\(\Delta H\)[/tex]) for the reaction [tex]\(N_2 + 3 H_2 \rightarrow 2 NH_3\)[/tex], follow these steps:
1. Bond Energies:
- [tex]\(N \equiv N\)[/tex] bond energy: 942 kJ/mol
- [tex]\(H - H\)[/tex] bond energy: 432 kJ/mol
- [tex]\(N - H\)[/tex] bond energy: 386 kJ/mol
2. Calculation of Energy Required to Break Bonds (Reactants):
In the reactants, we have:
- 1 molecule of [tex]\(N_2\)[/tex], which requires breaking one [tex]\(N \equiv N\)[/tex] bond.
- 3 molecules of [tex]\(H_2\)[/tex], which require breaking three [tex]\(H - H\)[/tex] bonds.
Therefore, the total energy required to break the bonds in the reactants is:
[tex]\[
\text{Energy}_{\text{reactants}} = 1 \times 942 \, \text{kJ} + 3 \times 432 \, \text{kJ} = 2238 \, \text{kJ}
\][/tex]
3. Calculation of Energy Released in Forming Bonds (Products):
In the products, we have:
- 2 molecules of [tex]\(NH_3\)[/tex], which involve the formation of 6 [tex]\(N - H\)[/tex] bonds (since each [tex]\(NH_3\)[/tex] molecule has 3 [tex]\(N - H\)[/tex] bonds).
Therefore, the total energy released in forming the bonds in the products is:
[tex]\[
\text{Energy}_{\text{products}} = 6 \times 386 \, \text{kJ} = 2316 \, \text{kJ}
\][/tex]
4. Calculation of Change in Enthalpy ([tex]\(\Delta H\)[/tex]):
The change in enthalpy for the reaction is given by the difference between the energy released by forming bonds and the energy required to break bonds:
[tex]\[
\Delta H = \text{Energy}_{\text{products}} - \text{Energy}_{\text{reactants}}
\][/tex]
Substituting the values:
[tex]\[
\Delta H = 2316 \, \text{kJ} - 2238 \, \text{kJ} = 78 \, \text{kJ}
\][/tex]
Thus, the change in enthalpy for the reaction, expressed to two significant figures, is [tex]\( 78 \, \text{kJ} \)[/tex].
The enthalpy change for the reaction is [tex]\( \boxed{78} \)[/tex] kilojoules.
