ChemSOF

Tips & Tricks for Chemical Engineers

Curve fitting data to an Antoine Equation

Antoine equation describes relation of vapor pressure and temperature for pure components. Equation is represented as :

 log(P) = A - B / ( T + C )

where, P is vapor pressure, T is temperature and A, B, C are Antoine constants.

Linearization

Antoine equation is converted into a linearized equation.

 log(P) = A - B / ( T + C )
T.log(P) + C.log(P) = A.T + A.C - B
log(P) = A + (A.C-B)/T - C.log(P)/T
y = a0 + a1.x1 + a2.x2

where, a0, a1 and a2 are constants; y(= log(P)), x1(= 1/T) and x2(= log(P)/T ) are variables.

Multiple Linear Regression

LINEST function in Excel is used to perform multiple linear regression analysis to get constants a0,a1 and a2.

Experimental vapor pressure data for n-Decane is to be fitted to Antoine equation.

Pressure (mm Hg) Temperature (°C)
16.51
42.35
55.710
69.820
85.540
95.560
108.6100
128.4200
150.6400
174.1760

Values for y, x1 and x2 are calculated for each data point.

Vapor Pressure Data n-Decane

LINEST function formula is copied in an empty cell e.g I8.

 =LINEST(D10:D19,E10:F19,TRUE,TRUE)

After copying the formula, select the range I8:K10 starting with formula cell. Press F2, and then press CTRL+SHIFT+ENTER. Resulting array I8, J8 & K8 provides value for a2,a1 & a0.

LINEST Function example

Constants a0, a1 & a2 are solved to get values for Antoine constants as following.

 A = 17.375
B = 4438.364
C = 238.953

Plot of experimental versus fitted equation.

Antoine equation curve

Download excel spreadsheet for curve fitting data to Antoine equation.

Web based calculation at CheCalc.com

Old Programs

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