Estimate the boiling point of carbon tetrachloride given the following thermodynamic parameters.
CCl4(l) CCl4(g)
Change fH (kj/mol-rxn) -128.4 -96.0
S (J.K. mol-rxn) 214.4 309.7
Change fG (kj/mol-rxn) -57.6 -53.6
The Correct Answer and Explanation is :
To estimate the boiling point (( T_b )) of carbon tetrachloride (( CCl_4 )), we use the thermodynamic criterion for phase equilibrium:
[
\Delta G = \Delta H – T \Delta S = 0
]
At the boiling point, the liquid and gas phases are in equilibrium, meaning the Gibbs free energy change (( \Delta G )) for the phase transition is zero.
Step 1: Calculate the Enthalpy Change (( \Delta H_{vap} ))
The enthalpy change of vaporization (( \Delta H_{vap} )) is given by:
[
\Delta H_{vap} = H_g – H_l
]
[
\Delta H_{vap} = (-96.0) – (-128.4) = 32.4 \text{ kJ/mol}
]
Step 2: Calculate the Entropy Change (( \Delta S_{vap} ))
The entropy change for the phase transition is:
[
\Delta S_{vap} = S_g – S_l
]
[
\Delta S_{vap} = (309.7) – (214.4) = 95.3 \text{ J/(mol·K)}
]
Step 3: Solve for ( T_b )
At equilibrium:
[
T_b = \frac{\Delta H_{vap}}{\Delta S_{vap}}
]
Converting ( \Delta H_{vap} ) to J/mol:
[
32.4 \times 10^3 \text{ J/mol}
]
[
T_b = \frac{32.4 \times 10^3}{95.3} = 340.1 \text{ K}
]
Final Answer
The estimated boiling point of carbon tetrachloride is 340 K (67°C).
Explanation (300 Words)
The boiling point of a liquid is the temperature at which its vapor pressure equals atmospheric pressure. At this point, the Gibbs free energy change (( \Delta G )) for the phase transition is zero, leading to the fundamental relation:
[
\Delta G = \Delta H – T \Delta S = 0
]
where ( \Delta H ) is the enthalpy change (heat required to convert liquid to gas), and ( \Delta S ) is the entropy change (degree of molecular disorder increase).
For carbon tetrachloride, we obtained:
- ( \Delta H_{vap} = 32.4 ) kJ/mol
- ( \Delta S_{vap} = 95.3 ) J/(mol·K)
By dividing ( \Delta H_{vap} ) by ( \Delta S_{vap} ), we determine the boiling temperature as 340 K. This calculation aligns well with experimental values (~349 K or 76°C), suggesting minor deviations due to ideal assumptions.
The boiling point reflects intermolecular forces: stronger forces lead to higher boiling points. ( CCl_4 ) exhibits only van der Waals interactions (no hydrogen bonding), explaining its relatively low boiling point compared to polar compounds.
This thermodynamic approach provides an accurate estimate and highlights the fundamental role of entropy and enthalpy in phase transitions.