A laboratory reports the following vapor-pressure data for a particular organic chemical:

Question

What will be an ideal response?

Answer 1

This can be done using many different software packages. The Microsoft Excel spreadsheet shown below illustrates one way of doing such nonlinear regression:



Error Sum



The first and third columns have the data given in the problem statement. The second column has the temperature in K, and the 4th column has the natural logarithm of the vapor pressure data. The fifth column has the result of



With parameters A, B, and C as shown at the top of the spreadsheet. The sixth column has the square of the difference between the actual and model values of The cell labeled “Error Sum” has

the sum of those differences. The Solver function in MS Excel was used to minimize that cell (the sum of the squares of the differences between the data and fit values) by simultaneously varying the values of A, B, and C.

The 6th column has the vapor pressure predicted by the fit, and the 7th column has the relative error in the vapor pressure at each point, which is (fit value – actual value)/actual value. The two plots show the data and fit in two formats, in each case with the data as discrete points and the fit as a smooth curve. The one on the left is what is actually used in the fitting. That is, the sum of the squares of the distances between the points and the curve was minimized to obtain the parameters. The one on the right shows the data and fit in the original format in which the data was given.

The boiling point is the temperature at which If one already has the spreadsheet shown above, then the simplest way to determine this is to vary one of the temperatures until the fitted pressure is equal to 101.325 kPa. This gives a value of 56.3 °C.