The molar heat of fusion of benzene is 9930 J/mol and ∆s= 35.7 j/mol-deg. Calculate the melting point.
dG = dH - TdS
At the melting point, the process is in equilibrium; therefore, dG is 0
Set dG to zero, you know dH and dS, solve for T.
To calculate the melting point of a substance using its molar heat of fusion and entropy change (∆s), you can use the following equation:
∆G = ∆H - T∆S
Where:
∆G is the change in Gibbs free energy
∆H is the molar heat of fusion
T is the temperature (in Kelvin)
∆S is the entropy change
At the melting point, the Gibbs free energy change (∆G) is equal to zero. Therefore, we can set ∆G to zero and solve for the temperature (T).
0 = ∆H - T∆S
Rearranging the equation, we have:
T = ∆H / ∆S
Now, plug in the given values:
T = 9930 J/mol / 35.7 J/mol-deg
To calculate the melting point, we need to convert J/mol-deg to J/K by dividing ∆S by the molar quantity (1 mol):
T = 9930 J/mol / (35.7 J/K-mol)
Now, divide the Joules to find the temperature:
T ≈ 277.79 K
The melting point of benzene can be estimated to be around 277.79 Kelvin (K).