Calculate heat of formation of isoprene using bond energy data.
`5C(s) + 4H_(2)(g) rarr H_(2)C = underset(CH_3)(|)(C ) - HC =CH_(2)`
Given `C - H = 98.8 kcal`
`H - H = 104 kcal`
C – C= 83 kcal
C = C = 147 kcal and `C(s) rarr C(g) = 171 kcal`

Options

A. `-21 kcal`
B. `21 kcal`
C. `40 kcal`
D. `50 kcal`

Answer

To calculate the heat of formation of isoprene using bond energy data, we will follow these steps:

### Step 1: Write the balanced chemical equation
The reaction for the formation of isoprene (H₂C=CH(CH₃)-C=CH₂) from its elements is given as:
\[ 5C(s) + 4H_2(g) \rightarrow H_2C=CH(CH_3)-C=CH_2 \]

### Step 2: Identify the bonds in the reactants
In the reactants, we have:
- 5 Carbon atoms (C)
- 4 Hydrogen molecules (H₂)

The bonds present in the reactants are:
- 5 C-C bonds (since we are considering elemental carbon in solid form, we will convert it to gaseous form)
- 4 H-H bonds

### Step 3: Calculate the bond energies of the reactants
Using the given bond energy data:
- The bond energy for C(s) to C(g) is 171 kcal (for each C atom).
- The bond energy for H-H is 104 kcal (for each H₂ molecule).

Calculating the total bond energy for the reactants:
- For 5 C atoms:
\[ 5 \times 171 \text{ kcal} = 855 \text{ kcal} \]
- For 4 H₂ molecules:
\[ 4 \times 104 \text{ kcal} = 416 \text{ kcal} \]

Total bond energy of reactants:
\[ 855 \text{ kcal} + 416 \text{ kcal} = 1271 \text{ kcal} \]

### Step 4: Identify the bonds in the products (isoprene)
The structure of isoprene contains:
- 2 C=C double bonds
- 1 C-C single bond
- 6 C-H bonds (since isoprene has 5 carbon atoms and each carbon in the methyl group is bonded to 3 hydrogen atoms)

### Step 5: Calculate the bond energies of the products
Using the given bond energy data:
- The bond energy for C=C is 147 kcal (for each double bond).
- The bond energy for C-C is 83 kcal (for each single bond).
- The bond energy for C-H is 98.8 kcal (for each bond).

Calculating the total bond energy for the products:
- For 2 C=C bonds:
\[ 2 \times 147 \text{ kcal} = 294 \text{ kcal} \]
- For 1 C-C bond:
\[ 1 \times 83 \text{ kcal} = 83 \text{ kcal} \]
- For 6 C-H bonds:
\[ 6 \times 98.8 \text{ kcal} = 592.8 \text{ kcal} \]

Total bond energy of products:
\[ 294 \text{ kcal} + 83 \text{ kcal} + 592.8 \text{ kcal} = 969.8 \text{ kcal} \]

### Step 6: Calculate the heat of formation
The heat of formation (ΔH_f) can be calculated using the formula:
\[ \Delta H_f = \text{Bond energy of reactants} - \text{Bond energy of products} \]

Substituting the values:
\[ \Delta H_f = 1271 \text{ kcal} - 969.8 \text{ kcal} = 301.2 \text{ kcal} \]

### Step 7: Final Answer
The heat of formation of isoprene is approximately:
\[ \Delta H_f \approx 301.2 \text{ kcal} \]