Titik Gelembung, Titik Embun, dan Perhitungan Kilat

Untuk melakukan perhitungan bubble dan dew point, terlebih dahulu kita harus memahami teori Hukum Raoult untuk campuran ideal.

Hukum Raoult

Hukum Raoult menyatakan bahwa tekanan uap pelarut di atas larutan sama dengan tekanan uap pelarut murni pada suhu yang sama yang diukur dengan fraksi mol pelarut yang ada. Ada dua asumsi utama dalam hukum Raoult, yaitu:

• Fase uap adalah gas ideal, yang berarti hanya dapat digunakan dari tekanan rendah hingga sedang, dan
• Fase cair adalah larutan ideal, yang berarti hanya berlaku jika spesies kimia yang menyusunnya mirip secara kimiawi.

The mathematical equations which reflects the Raoult's law based on the two assumptions above is \[\ y_i\ .P=\ x_i\ .P_i^{sat} \quad \quad (i=1,2,...,N) \] where \(x_i\) is liquid-phase mole fraction of component \(i\), \(y_i\) is vapor-phase mole fraction of componen \(i\), \(P\) is the system pressure, and \(P_i^{sat}\) is the saturation pressure of component \(i\) which follows Antoine equation \[ln\,P_i^{sat}=A - {B\over T+ C}\] where \(A\),\(B\), and \(C\) are Antoine constants, and \(T\) is the system temperature. Please bear in mind that different Antoine constants from different references affects the unit of the \(P\) and the \(T\).

Bubble point, dew point, and flash calculations with Raoult's Law

There are five (5) classes to solve VLE problems

• BUBBLE P:  Calculate {\(y_i\)} and \(P\), given {\(x_i\)} and \(T\)
• DEW P:        Calculate {\(x_i\)} and \(P\), given {\(y_i\)} and \(T\)
• BUBBLE T:  Calculate {\(y_i\)} and \(T\), given {\(x_i\)} and \(P\)
• DEW T:        Calculate {\(x_i\)} and \(T\), given {\(y_i\)} and \(P\)
• P-T FLASH:  Calculate {\(x_i\)} and {\(y_i\)}, given \(P\) and \(T\)

For bubble point calculations which vapor-phase compositions are unknown, we can simplify the calculations by asumming \(\sum y_i=1\), so that the Raoult's law become \[P=\sum_i{x_i P_i^{sat}}\] While for dew point calculations, the unknown liquid-phase compositions can be simplified by asumming \(\sum x_i=1\), so that \[P= {1\over \sum_i{yi/P_i^{sat}}}\] For flash calculation, we calculate the composition based on material balance of the system, \[z_i=V.y_i+L.x_i\] where \(z_i\) is molar composition of the inlet feed, \(V\) is the vapor fractions, and \(L\) is the liquid fractions or \(L=1-V\). Bear in mind that flash calculation can't be calculated if feed exists as subcooled liquid or superheated vapor.

References

1. Smith, J. M., Van Ness, H. C., Abbott, M. M., & Swihart, M. T. (2018). Introduction to Chemical Engineering Thermodynamics (8th ed.). McGraw-Hill.

Bubble, Dew, and Flash Calculator

See how to use this calculator for step-by-step guide.

Example problem

Calculate the flash from a mixture of 15 mol water, 12 mol methanol, 22 mol ethanol, 36 mol propanol, and 15 mol acetone in a system of 1 bar and 50 degree Celsius!