CCl3F boils at 23.8 degrees Celcius, and its molar heat of vaporization is 24.8 kJ/mol. Calculate the molar entropy of vaporization of CCl3F (l)
delta Hvap = Tvap x delta Svap.
Solve for delta Svap
To calculate the molar entropy of vaporization (ΔSvap) of CCl3F (l), we can use the Clausius-Clapeyron equation:
ln(P2/P1) = (ΔHvap/R) * (1/T1 - 1/T2)
where P1 and T1 are the initial pressure and temperature (in this case, 1 atm and 273.15 K) and P2 and T2 are the final pressure and temperature (in this case, 1 atm and 23.8°C or 23.8 + 273.15 = 297.95 K).
Now, rearranging the equation, we can solve for ΔHvap:
ΔHvap = R * (ln(P2/P1)) / (1/T1 - 1/T2)
R is the ideal gas constant, which is equal to 8.314 J/(mol·K).
Substituting the given values:
ΔHvap = (8.314 J/(mol·K)) * (ln(1/1)) / (1/273.15 - 1/297.95)
ΔHvap = 8.314 J/mol·K * ln(1) / (0.003660 K^-1)
Simplifying:
ΔHvap = 8.314 J/mol·K * 0 / (0.003660 K^-1)
Since ln(1) is equal to 0, the numerator becomes 0.
Therefore, the molar heat of vaporization (ΔHvap) of CCl3F is 0 J/mol·K.
Now, to obtain the molar entropy of vaporization (ΔSvap), we can use the equation:
ΔSvap = ΔHvap / T2
Substituting the values:
ΔSvap = 0 J/mol·K / 297.95 K
Simplifying:
ΔSvap = 0 J/mol·K
Therefore, the molar entropy of vaporization of CCl3F (l) is 0 J/mol·K.
To calculate the molar entropy of vaporization, we need to use the equation:
ΔSvap = ΔHvap / T
where:
ΔSvap = molar entropy of vaporization
ΔHvap = molar heat of vaporization
T = boiling point temperature in Kelvin
First, we need to convert the boiling point temperature from Celsius to Kelvin:
T = 23.8°C + 273.15 = 296.95 K (rounded to two decimal places)
Now we can substitute the values into the equation:
ΔSvap = 24.8 kJ/mol / 296.95 K
Note that the units for temperature need to be consistent for the equation, so we use Kelvin.
To calculate the molar entropy of vaporization, divide the molar heat of vaporization by the boiling point temperature in Kelvin:
ΔSvap = 0.0834 kJ/(mol·K) (rounded to four decimal places)
So, the molar entropy of vaporization of CCl3F is approximately 0.0834 kJ/(mol·K).