Interpretation:
Estimate V, HR, GR and SR for a binary vapor mixture of acetone and 1,3 butadiene.
Concept introduction:
Volume can be calculated with the help of compressibility factor (Z) which is defined as the ratio of real gas volume to ideal gas volume as described in equation 3.36 in book:
Residual properties in
Equation 6.54, 6.55, 6.56 and 10.62 mentioned in question are:
Where,
T = temperature
Where,
Similarly,
Answer to Problem 10.34P
The volume of vapor mixture of acetone and 1,3 butadiene is 15694 cm3/mol.
Reduced enthalpy, Gibbs free energy and entropy of acetone and 1,3 butadiene mixture is -344. J/mol, -101.7 J/mol and -0.0727 J/mol.K respectively.
Explanation of Solution
Composition for binary mixture of gases (Given):
Y1 = 0.28 and Y2 = 0.72
Temperature (given) = 600C or 333.15K (60+273.15)
Pressure (given) = 170 kpa
Refer APPENDIX-B and Table-B.1 to determine critical properties and acentric factor of acetone(1)/1,3 butadiene (2) as:
Component | Tc (K) | Vc (cm3/mol) |
|
Zc |
Acetone (1) | 508.2 | 209 | 0.307 | 0.233 |
1,3 Butadiene (2) | 425.2 | 220.4 | 0.190 | 0.267 |
Where,
Pc = critical pressure
Tc = critical temperature
Vc = critical volume
Zc = critical compressibility factor
Reduced temperature for both gases can be calculated as:
Similar to the above calculated matrix we will calculate the reduced temperature as follows:
Critical volume of both the gases in the mixture can be calculated as given below:
With the help of critical volume and critical temperature, critical pressure of gases in the mixture can be calculated as follows:
The reduced compressibility factor can be calculated as:
After putting all values in the critical pressure formula, we will get:
At this calculated value of reduced temperature, we can calculate correlation constant as:
Overall correlation constant value in gas mixture can be calculated by equation:
Using above calculated value compressibility factor and molar volume of gas can be calculated as given below:
Reduced property can be calculated by finding the value of dB/dT and putting in equations given in book as follows:
The volume of vapor mixture of acetone and 1,3 butadiene is 15694 cm3/mol.
Reduced enthalpy, Gibbs free energy and entropy of acetone and 1,3 butadiene mixture is -344. J/mol, -101.7 J/mol and -0.0727 J/mol.K respectively.
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