The difference between `DeltaH and DeltaU (DeltaH - DeltaU)`, when the combustion of one mole of heptane (l ) is carried out at a temperature T, is equal to: `–xRT`. The value of x is_____.

Options

A. `-4 RT`
B. `4 RT`
C. `-3 RT`
D. `3 RT`

Explanation

To solve the problem, we need to find the value of \( x \) in the equation \( \Delta H - \Delta U = -xRT \) for the combustion of one mole of heptane.

### Step-by-Step Solution:

1. **Understand the Definitions**:
- \( \Delta H \) is the change in enthalpy (heat content) at constant pressure.
- \( \Delta U \) is the change in internal energy at constant volume.

2. **Use the Relationship Between \( \Delta H \) and \( \Delta U \)**:
- The relationship is given by the formula:
\[ \Delta H = \Delta U + \Delta N_g RT \]
- Here, \( \Delta N_g \) is the change in the number of moles of gas during the reaction, \( R \) is the universal gas constant, and \( T \) is the temperature in Kelvin.

3. **Write the Combustion Reaction for Heptane**:
- The combustion of heptane (\( C_7H_{16} \)) can be represented as:
\[ C_7H_{16} + 11 O_2 \rightarrow 7 CO_2 + 8 H_2O \]
- In this reaction, 1 mole of heptane reacts with 11 moles of oxygen to produce 7 moles of carbon dioxide and 8 moles of water.

4. **Calculate \( \Delta N_g \)**:
- Count the number of moles of gaseous reactants and products:
- Reactants: \( 11 \) moles of \( O_2 \) (since \( C_7H_{16} \) is a liquid and does not contribute to \( \Delta N_g \)).
- Products: \( 7 \) moles of \( CO_2 \) (water is in liquid form and does not contribute).
- Therefore:
\[ \Delta N_g = \text{moles of gaseous products} - \text{moles of gaseous reactants} = 7 - 11 = -4 \]

5. **Substitute \( \Delta N_g \) into the Relationship**:
- Now, substitute \( \Delta N_g \) into the equation:
\[ \Delta H - \Delta U = \Delta N_g RT = -4RT \]

6. **Identify the Value of \( x \)**:
- From the equation \( \Delta H - \Delta U = -xRT \), we can see that:
\[ -xRT = -4RT \]
- Thus, we find that:
\[ x = 4 \]

### Final Answer:
The value of \( x \) is **4**.