## 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.

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`

Resources

- Web based calculation available at checalc.com
- Spreadsheet for Curve Fitting Data to Antoine equation