The following thermodynamic data was obtained for an unknown compound. Delta Hvap = 31.3 kj/mol and Delta S Vap= 79.7 kj/mol .Calculate the normal boiling point of this compound in Celcius..
Thank you!
dG = dHvap - TdSvap
dG at boiling point = 0; therefore,
dHvap = TdSvap
You know dHvap and dSvap, solve for T. Check to make sure you typed the problem correctly. Check that dSvap is really in kJ/mol (or is it J/mol instead).
T will be in kelvin, convert to C.
To find the normal boiling point of the compound, we need to use the Clausius-Clapeyron equation, which relates the vapor pressure of a substance to its enthalpy of vaporization and entropy of vaporization.
The Clausius-Clapeyron equation is given by:
ln(P2/P1) = (-ΔHvap/R) * (1/T2 - 1/T1)
Where:
P1 and P2 are the initial and final vapor pressures of the substance
ΔHvap is the enthalpy of vaporization of the substance (31.3 kJ/mol)
R is the ideal gas constant (8.314 J/(mol·K))
T1 and T2 are the initial and final temperatures in Kelvin
Since we are looking for the boiling point in Celsius, we need to convert it to Kelvin by using the formula T(K) = T(°C) + 273.15.
At the normal boiling point, P2 is at atmospheric pressure (1 atm). To find T2, we can rearrange the Clausius-Clapeyron equation to solve for T2:
T2 = (1 / (ln(P2/P1) * (-ΔHvap/R) + (1/T1))
Substituting the given values:
ΔHvap = 31.3 kJ/mol
R = 8.314 J/(mol·K)
P1 = vapor pressure at the boiling point (1 atm)
T1 = boiling point in Kelvin
Let's calculate the normal boiling point:
Step 1: Convert the given ΔHvap from kJ/mol to J/mol:
ΔHvap = 31.3 kJ/mol * 1000 J/1 kJ = 31,300 J/mol
Step 2: Convert the boiling point to Kelvin:
T1(K) = boiling point(°C) + 273.15
Step 3: Substitute the values into the equation and solve for T2:
T2 = (1 / (ln(1/P1) * (-ΔHvap/R)) + (1/T1)
For P1, we assume that the vapor pressure at normal boiling point is 1 atm.
Step 4: Convert the final temperature from Kelvin to Celsius:
T(°C) = T(K) - 273.15
By following these steps, you should be able to calculate the normal boiling point of the compound in Celsius.