Answer:
ΔH° reaction= 27.4 kJ/mol
ΔS° reaction= 106.8 J/mol.K
Boiling point= -30.64 °C
Pv = 0.079 torr
Explanation:
To solve this problem, we have to analyze the process that we are going to study:
Carbon disulfide is changing from liquid state to gas state.
As you must know, the gas state is more entropic than the liquid state, so we going to expect an increase in S, and also involves a change in heat, an increase in H.
a. Calculate ΔH° and ΔS°
Remember that the ° means “standard conditions”, you can find this values for de CS2 in a table, for each one of these state:
CS2 (l) :
ΔH° = 87,9 kJ/mol
ΔS° = 131,0 J/mol.K
CS2 (g) :
ΔH° = 115,3 kJ/mol
ΔS° = 237,8 J/mol.K
Note that the ΔH° of the product (CS2 (g)) is bigger than reactant CS2 (l).
With this data, you can calculate the ΔH° for the reactions using the following equation:
ΔH° reaction= ΔH° products - ΔH° reactants
So:
ΔH° reaction= 115,3 kJ/mol-87,9 kJ/mol = 27.4 kJ/mol
And as is obtained a ΔH° reaction > 0 , iit means positive, it is an endothermic process, so, these reactions require to apply external energy or heat to be doing.
Now we going to calculate ΔS°reaction
ΔS° reaction= ΔS° products - ΔS° reactants
Where
ΔS° products = 237,8 J/mol.K
ΔS° reactants = 131,0 J/mol.K
Replacing on the equation:
ΔS° reaction= 237,8 J/mol.K - 131,0 J/mol.K
ΔS° reaction= 106.8 J/mol.K
b. Estimate the boiling point of carbon disulfide, in °C, from this data.
To make this estimation, we have to assume constant pressure:
To calculate this boiling temperature, we have to use the following equation who relates entropy with enthalpy and free Gibbs energy:
ΔG° = ΔH° – T ΔS°
The values of ΔG° can be found in the same table of H° and ΔS°:
CS2 (l) :
ΔG° = 63,6KJ/mol
CS2 (g) :
ΔG° =65,1KJ/mol
With this we can calculate ΔG°:
ΔG°= ΔG° products - ΔG° reactants
ΔG°= 65,1kJ/mol -63,6 kJ/mol = 1.5 kJ/mol
And we this value we replace in the equation as follow:
ΔG° = ΔH° – T ΔS°
1.5 kJ/mol = 27.4 kJ/mol – T ×106.8 J/mol.K
And from this equation, obtain T:
-106.8 J/mol.K × T = 1.5 kJ/mol – 27.4 kJ/mol
-106.8 J/mol.K × T = -25.9 kJ/mol
