At `27^(@) C`, the combustion of ethane takes place according to the reaction `C_(2) H_(6)(g) + 7/2O_(2)(g) rightarrow 2CO_(3)(g) + 3H_(2)O(l)`
`Delta E - Delta H ` for this reaction at `27^(@)C` will be

Options

A. `+1347.1 J`
B. `-1247.1 J`
C. `6235.5 J`
D. `+6235.5 J`

Answer

To solve the problem of finding \( \Delta E - \Delta H \) for the combustion of ethane at \( 27^\circ C \), we can follow these steps:

### Step 1: Write the Reaction
The combustion of ethane is given by the reaction:
\[ C_2H_6(g) + \frac{7}{2}O_2(g) \rightarrow 2CO_2(g) + 3H_2O(l) \]

### Step 2: Identify the Change in Moles of Gas (\( \Delta n_g \))
To find \( \Delta n_g \), we need to calculate the difference in the number of moles of gaseous products and reactants.

- **Products:**
- \( 2CO_2(g) \): 2 moles of gas
- \( 3H_2O(l) \): 0 moles of gas (since water is in liquid form)

Total moles of gas in products = \( 2 \)

- **Reactants:**
- \( C_2H_6(g) \): 1 mole of gas
- \( \frac{7}{2}O_2(g) \): 3.5 moles of gas

Total moles of gas in reactants = \( 1 + 3.5 = 4.5 \)

Now, we calculate \( \Delta n_g \):
\[ \Delta n_g = \text{Moles of products} - \text{Moles of reactants} = 2 - 4.5 = -2.5 \]

### Step 3: Use the Relationship Between \( \Delta E \) and \( \Delta H \)
The relationship between \( \Delta E \) and \( \Delta H \) is given by:
\[ \Delta H = \Delta E + \Delta n_g RT \]

Rearranging this gives:
\[ \Delta E - \Delta H = -\Delta n_g RT \]

### Step 4: Substitute Values into the Equation
We need to substitute the values into the equation. We know:
- \( \Delta n_g = -2.5 \)
- \( R = 8.31 \, \text{J/(mol K)} \)
- Temperature \( T = 27^\circ C = 300 \, \text{K} \)

Now substituting these values:
\[ \Delta E - \Delta H = -(-2.5) \times 8.31 \times 300 \]

### Step 5: Calculate the Result
Calculating the right-hand side:
\[ \Delta E - \Delta H = 2.5 \times 8.31 \times 300 \]
\[ = 2.5 \times 2493 = 6232.5 \, \text{J} \]

### Conclusion
Thus, the value of \( \Delta E - \Delta H \) for the combustion of ethane at \( 27^\circ C \) is approximately:
\[ \Delta E - \Delta H \approx 6232.5 \, \text{J} \]