The enthalpy of reaction, `2HC = CH + 5O_(2) rightarrow 4CO_(2) + 2H_(2)O`
If the bond energies of `C-H, C=C, O=O, C=O and O-H` bonds are p,q,r,s,t repectively

Options

A. `[8s + 4t] - [4p + 2q + 5r]`
B. `[4p + 2q + 5r] - [8s + 4t]`
C. `[4p + 2q + 5r + 8s + 4t]`
D. `[2p + q + 5r] - [8s + 4t]`

Answer

To calculate the enthalpy of the reaction given by:

\[ 2HC \equiv CH + 5O_2 \rightarrow 4CO_2 + 2H_2O \]

we will follow these steps:

### Step 1: Identify the bonds in the reactants
In the reactants, we have:
- 2 molecules of \( HC \equiv CH \)
- 5 molecules of \( O_2 \)

For \( 2HC \equiv CH \):
- Each \( HC \equiv CH \) has:
- 2 C-H bonds (bond energy = \( 2P \))
- 1 C=C bond (bond energy = \( Q \))

Thus, for 2 molecules:
- Total C-H bonds = \( 2 \times 2P = 4P \)
- Total C=C bonds = \( 2 \times Q = 2Q \)

For \( 5O_2 \):
- Each \( O_2 \) has 1 O=O bond (bond energy = \( R \))
- Thus, for 5 molecules:
- Total O=O bonds = \( 5R \)

### Step 2: Calculate the total bond energy of the reactants
The total bond energy of the reactants can be calculated as:
\[ \text{Bond energy of reactants} = 4P + 2Q + 5R \]

### Step 3: Identify the bonds in the products
In the products, we have:
- 4 molecules of \( CO_2 \)
- 2 molecules of \( H_2O \)

For \( 4CO_2 \):
- Each \( CO_2 \) has:
- 2 C=O bonds (bond energy = \( S \))

Thus, for 4 molecules:
- Total C=O bonds = \( 4 \times 2S = 8S \)

For \( 2H_2O \):
- Each \( H_2O \) has:
- 2 O-H bonds (bond energy = \( T \))

Thus, for 2 molecules:
- Total O-H bonds = \( 2 \times 2T = 4T \)

### Step 4: Calculate the total bond energy of the products
The total bond energy of the products can be calculated as:
\[ \text{Bond energy of products} = 8S + 4T \]

### Step 5: Calculate the enthalpy of the reaction
The enthalpy of the reaction (\( \Delta H \)) can be calculated using the formula:
\[ \Delta H = \text{Bond energy of products} - \text{Bond energy of reactants} \]
Substituting the values we calculated:
\[ \Delta H = (8S + 4T) - (4P + 2Q + 5R) \]

### Final Expression
Thus, the final expression for the enthalpy of the reaction is:
\[ \Delta H = 8S + 4T - 4P - 2Q - 5R \]

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