Find bond enthalpy of C=O (in kJ/mol) using following information :
`DeltaH_("atomisation")[C(s)]=700` kJ/mol
`DeltaH_(f)[CO_(2)(g)]=-400` kJ/mol
`BE_(o=o=500` kJ/mol
Resonance energy of `CO_(2)=-150` kJ/mol

Answer

To find the bond enthalpy of the C=O bond using the provided information, we can follow these steps:

### Step 1: Write the formation reaction of CO2
The formation of carbon dioxide (CO2) from its elements can be represented as:
\[ \text{C(s)} + \text{O}_2(g) \rightarrow \text{CO}_2(g) \]

### Step 2: Use the given enthalpy of formation
The enthalpy of formation (\(\Delta H_f\)) of CO2 is given as:
\[ \Delta H_f[\text{CO}_2(g)] = -400 \, \text{kJ/mol} \]

### Step 3: Write the expression for the reaction enthalpy
The reaction enthalpy (\(\Delta H_r\)) can be expressed as:
\[ \Delta H_r = \text{Bond enthalpies of reactants} - \text{Bond enthalpies of products} \]

### Step 4: Identify the bond enthalpies of reactants
For the reactants:
- The bond enthalpy of solid carbon (C(s)) is given as the atomization energy:
\[ \Delta H_{\text{atomization}}[C(s)] = 700 \, \text{kJ/mol} \]
- The bond enthalpy of O2 (as a double bond) is given as:
\[ BE_{O=O} = 500 \, \text{kJ/mol} \]

Thus, the total bond enthalpy of reactants is:
\[ \text{Bond enthalpy of reactants} = 700 + 500 = 1200 \, \text{kJ/mol} \]

### Step 5: Identify the bond enthalpies of products
For the products:
- CO2 has two C=O bonds, so we denote the bond enthalpy of C=O as \( x \). Therefore, the bond enthalpy for two C=O bonds is \( 2x \).
- The resonance energy of CO2 is given as:
\[ \text{Resonance energy} = -150 \, \text{kJ/mol} \]

Thus, the total bond enthalpy of products is:
\[ \text{Bond enthalpy of products} = 2x + (-150) = 2x - 150 \]

### Step 6: Set up the equation using the reaction enthalpy
Now we can set up the equation using the reaction enthalpy:
\[ -400 = 1200 - (2x - 150) \]

### Step 7: Solve for \( x \)
Rearranging the equation gives:
\[ -400 = 1200 - 2x + 150 \]
\[ -400 = 1350 - 2x \]
\[ 2x = 1350 + 400 \]
\[ 2x = 1750 \]
\[ x = \frac{1750}{2} = 875 \, \text{kJ/mol} \]

### Step 8: Conclusion
The bond enthalpy of C=O is:
\[ \text{Bond enthalpy of C=O} = 875 \, \text{kJ/mol} \]