There is no ring strain in cyclohexane, but cyclobutane has an angle strain of `9^(@)` 44'. If `Delta H_(c)^(@)` of cyclohexane per `(CH_(2))` group is 660 kJ `mol^(-1)` and `Delta H_(c)^(@)` of cyclobutane is 2744 kJ `mol^(-1)`, what is the ring strain in kJ `mol^(-1)` of cyclobutane ?

Options

A. -104
B. 104
C. -2084
D. 2084

Explanation

To find the ring strain in cyclobutane, we can follow these steps:

### Step 1: Understand the given data
- The heat of combustion (ΔHc) of cyclohexane per (CH2) group is given as 660 kJ/mol.
- The total heat of combustion (ΔHc) of cyclobutane is given as 2744 kJ/mol.
- Cyclobutane has 4 (CH2) groups.

### Step 2: Calculate the total ΔHc for the (CH2) groups in cyclobutane
Since cyclobutane has 4 (CH2) groups, we can calculate the total ΔHc for these groups as follows:

\[ \text{Total } \Delta H_c \text{ for (CH2) groups} = 4 \times 660 \text{ kJ/mol} \]

Calculating this gives:

\[ 4 \times 660 = 2640 \text{ kJ/mol} \]

### Step 3: Calculate the ring strain in cyclobutane
The ring strain can be calculated by subtracting the total ΔHc for the (CH2) groups from the total ΔHc of cyclobutane:

\[ \text{Ring Strain} = \Delta H_c \text{ of cyclobutane} - \text{Total } \Delta H_c \text{ for (CH2) groups} \]

Substituting the values:

\[ \text{Ring Strain} = 2744 \text{ kJ/mol} - 2640 \text{ kJ/mol} \]

Calculating this gives:

\[ \text{Ring Strain} = 104 \text{ kJ/mol} \]

### Final Answer
The ring strain in cyclobutane is **104 kJ/mol**.

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