Calculate the standard internal energy of formation of liquid methyl acetate `(CH_(3)COOCH_(3))` from its standard enthalpy of foramtion, which is `-44.291 kJ "mole"^(-1)` at `25^(@)C`

Options

A. `-433`
B. `+433`
C. `-452.82`
D. `452.82`

Explanation

To calculate the standard internal energy of formation of liquid methyl acetate (CH₃COOCH₃) from its standard enthalpy of formation, we can use the relation between enthalpy (ΔH) and internal energy (ΔU). The equation we will use is:

\[ \Delta H = \Delta U + \Delta N_g RT \]

Where:
- ΔH = standard enthalpy of formation
- ΔU = standard internal energy of formation
- ΔN_g = change in the number of moles of gas
- R = universal gas constant (8.314 × 10⁻³ kJ/mol·K)
- T = temperature in Kelvin

### Step-by-Step Solution:

1. **Identify the given values:**
- Standard enthalpy of formation (ΔH) = -442.91 kJ/mol
- Temperature (T) = 25°C = 298 K (since 25 + 273 = 298)
- Universal gas constant (R) = 8.314 × 10⁻³ kJ/mol·K

2. **Write the balanced reaction for the formation of methyl acetate:**
\[ 3 \text{C} (s) + 3 \text{H}_2 (g) + \frac{1}{2} \text{O}_2 (g) \rightarrow \text{CH}_3\text{COOCH}_3 (l) \]

3. **Calculate ΔN_g:**
- Moles of gaseous products = 0 (since methyl acetate is a liquid)
- Moles of gaseous reactants = 3 (from H₂) + 0.5 (from O₂) = 3.5
- Therefore, ΔN_g = 0 - 3.5 = -3.5

4. **Substitute the values into the equation:**
\[ \Delta U = \Delta H - \Delta N_g RT \]
\[ \Delta U = -442.91 \, \text{kJ/mol} - (-3.5) \times (8.314 \times 10^{-3} \, \text{kJ/mol·K}) \times (298 \, \text{K}) \]

5. **Calculate the second term:**
- Calculate \(-3.5 \times 8.314 \times 10^{-3} \times 298\):
\[ = -3.5 \times 8.314 \times 10^{-3} \times 298 \approx -8.224 \, \text{kJ/mol} \]

6. **Final calculation of ΔU:**
\[ \Delta U = -442.91 \, \text{kJ/mol} + 8.224 \, \text{kJ/mol} \approx -434.686 \, \text{kJ/mol} \]

7. **Round to appropriate significant figures:**
\[ \Delta U \approx -433 \, \text{kJ/mol} \]

### Final Answer:
The standard internal energy of formation of liquid methyl acetate is approximately \(-433 \, \text{kJ/mol}\).