In the complete oombustion of butanol `C_4H_9OH (I)", if "triangleH` is enthalpy of combustion and AE is the heat of combustion at constant volume, then

Options

A. `triangleH lt triangleE`
B. `triangleH=triangleE`
C. `triangleH gt triangleE`
D. `triangleH, triangle` relation cannot be predicted

Answer

To solve the problem regarding the complete combustion of butanol (C₄H₉OH) and the relationship between the enthalpy of combustion (ΔH) and the heat of combustion at constant volume (ΔE), we can follow these steps:

### Step 1: Write the balanced equation for the combustion of butanol.
The complete combustion of butanol can be represented by the following balanced chemical equation:

\[ C_4H_9OH (l) + O_2 (g) \rightarrow CO_2 (g) + H_2O (g) \]

### Step 2: Identify the number of gaseous products and reactants.
From the balanced equation, we need to determine the number of moles of gaseous products and reactants.

- **Gaseous Products**:
- For every mole of butanol, we produce carbon dioxide (CO₂) and water (H₂O).
- If we assume complete combustion, we will produce 4 moles of CO₂ and 5 moles of H₂O, totaling 9 moles of gaseous products.

- **Gaseous Reactants**:
- The only gaseous reactant is O₂.

### Step 3: Calculate Δn (change in the number of moles of gas).
Δn is calculated as:

\[ Δn = \text{(moles of gaseous products)} - \text{(moles of gaseous reactants)} \]

Assuming we have 6 moles of O₂ as a reactant:

\[ Δn = 9 - 6 = 3 \]

### Step 4: Relate ΔH and ΔE.
The relationship between the enthalpy change (ΔH) and the internal energy change (ΔE) at constant volume is given by the equation:

\[ ΔH = ΔE + ΔnRT \]

Where:
- R is the universal gas constant (8.314 J/mol·K)
- T is the temperature in Kelvin

### Step 5: Analyze the signs of ΔH and ΔE.
Since both ΔH and ΔE are negative for exothermic reactions (like combustion), we can express this as:

- ΔH is negative (exothermic)
- ΔE is also negative (exothermic)

### Step 6: Compare the magnitudes of ΔH and ΔE.
From the equation \( ΔH = ΔE + ΔnRT \), we can see that since Δn is positive (3 in this case), the term \( ΔnRT \) is also positive. Therefore:

\[ ΔH = ΔE + \text{(positive term)} \]

This implies that the magnitude of ΔH is less than the magnitude of ΔE:

\[ |ΔH| < |ΔE| \]

### Conclusion:
Thus, the correct relationship is:

\[ ΔH < ΔE \]

### Final Answer:
The correct option is A: \( ΔH < ΔE \).

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