## Curve fitting data to an Antoine Equation

Sun, 09 Aug 2015

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.

Example

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

Pressure (mm Hg) Temperature (°C)
16.5 1
42.3 5
55.7 10
69.8 20
85.5 40
95.5 60
108.6 100
128.4 200
150.6 400
174.1 760

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

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.

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

A = 17.375
B = 4438.364
C = 238.953

Solving Cubic Equation of State