Peter Keusch, University of Regensburg
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William W. Dorner The Alkaline Hydrolysis of Esters (Download) can be monitored by measuring the change in conductance of the reaction mixture with time. The following example shows the analysis of data, which were logged by a data acquisition system (e.g. Cassy or Chembox / Chemex). Excel File - Alkaline Hydrolysis of Ethyl Propionate (Download) Plot of conductivity k versus time t
To add new series in chart the Insert tab from the ribbon menu is selected. A click on Scatter allows to choose a sub type 'scatter with data points connected by smoothed lines without markers' (Table 1). 
Table 1: Highlighted data pairs, selection of the desired chart sub-type In order to move the chart embedded in the worksheet the Move Chart button is clicked. An entirely new worksheet is created by choosing the New Sheet option in the Move Chart window that appears. |
Editing the chart includes the following steps:
Deleting the legend
The legend is clicked and Delete is pressed.
Formatting the x-axis and y-axis
Right-click on the axis ® Format Axis
In the Format Axis dialog box, under Axis Options the scale of axes and the interval between the values can be specified. The options include those that fix the maximum and minimum amount for the first and last tick mark on the axis.
Axis Labeling
Right-click on the axis ® Font
A proper font size is selected.
Adding the Axis Titles
In the register Layout the Axis Titles button in the Labels group is clicked.
x-axis: Primary Horizontal Axis Title ® Title Below Axis is chosen.
y-axis: Primary Vertical Axis Title ® Horizontal Title is chosen.
The appropriate text is entered. If the text is long, Rotated Title is selected for labeling the y-axis.
Editing the curves
Right-click on the data series ® Format Data Series
The context menu allows to specify thickness and color of the line.
Labeling the Curves
The Text Box button from the Text group of the Insert ribbon is clicked.
The mouse cursor (it has changed to a different type of insertion pointer) is moved into the chart area. to create the text box on the chart. The object is moved in the desired location. Once the text is entered into the box, its edges are dragged to resize it. Anywhere outside of the test box is clicked to cancel editing mode.
Adding Gridlines
In the register Layout the Gridlines button in the Axes group is activated. For horizontal gridlines Primary Horizontal Gridlines is clicked. For vertical gridlines Primary Vertical Gridlines is chosen. In each case Major Gridlines is used to display gridlines only at major units.
Formatting Gridlines
Right-click on a gridline ® Format Gridlines
Under Line Style thickness and style (e.g. 'round dot') of the gridlines can be specified.
Figure 1: Line chart plot of conductivity versus time t
Hydrolysis of ethyl propionate at 48.3 °C (1) 52.1 °C (2) und 58.4 °C (3)
Application of the second order kinetics
Conversion of the measured data
The alkaline ester hydrolysis is a reaction second order.
The value for k¥ (e.g. 1,18) is found in the table. According to equation (15) Kinetic equations (Download), e.g. the following formula
is entered Into the first cell (e.g. F4), which is to obtain the value for y = ln (0,5 * (k 0 - k¥) / (k - k ¥) + 0,5) * 50
The formula is displayed in the formula bar when that cell is highlighted, and the result of the formula is displayed in the actual cell. The bottom-right corner of the active cell is dragged down to tabulate the rest of the values (Table 2).
A plot is created in which the measurement points are shown by markers (scatter plot).
Nonadjacent columns are highlighted using the following procedure: First the x-values (first column) are highlighted. Then, while holding down the control key (CTRL) on the keyboard, the block containing the y-values is selected. Under the menu point Insert Excel is instructed to generate a chart from the highlighted spreadsheet cells. A click on Scatter allows to choose a sub-type 'Scatter with only Markers' (Plot in Table 2).
Table 2: Conversion of the experimental data according to equation (15) Kinetic equations (Download)
and selection of the chart sub-type
Figure 2: Scatter plot according to equation (15) Kinetic equations (Download)
Determination of the rate constant k
As shown in the scattergram above the linear portion of the graph is apparent after an induction phase. The appropriate data are indicated in Table 3 (see Trend 1, 2 and 3).
Table 3: Editing the data series
After a right click on a data series in the chart (Fig. 2 Select Data option from the Data group is chosen. A Select Data Source window will open.
A click on the Add button opens a Edit Series dialog box. A name for the new data series is typed in the Series name field. The two other fields allow to specify the data range. Next is clicked the Collapse Dialog button at the right end of the Series X-values box. This will temporally shrink the dialog window. The mouse can be used to highlight the x-values in the worksheet that will be plotted along the horizontal axis. When the cells are selected, their reference appears in the X-values box. When finished the Restore Dialog button is clicked which will return the dialog window to maximum size. Now is clicked the Collapse Dialog button at the right end of the Series Y-values box and the above procedure is repeated for the y-values which will be plotted on the vertical axis. OK is clicked to return to the Select Data Source dialog box. After clicking the OK button in this box the newly added data series will displayed on the chart in a different color with different markings as data points (Fig. 3).
Figure 3: Highlighting of the measurement points in the linear range
To get to the linear regression menu a right click on any one of the added data points is performed. Once the data points of the linear portion appear highlighted, Add Trendline on the main menu is chosen. The Format Trendline dialog box opens. Under Trendline Options, the option Linear is selected. The Forecast option in the menu is used to extend the best-fit line beyond the first and last points of the graph. Some units are added to either the forward or backward boxes. Next Display Equation on chart is selected. An equation in the form y = mx + b is displayed on the chart. m is the slope and b is the y-intercept. The slope of the line corresponds to the rate constant k.
The dialog box Format Trendline where style and color of the line can be changed also allows the user to specify type, color and size of the markers.
Figure 4: Linear regression addition of a trendline straight line equation
The Bromination of reactive Aromatics (Download) is followed by measuring the change in absorbance with time.
Excel File - Bromination of Acetanilide (Download)
Suppose the reaction obeys a pseudo first order rate law. On that condition the pseudo first order rate constant can be evaluated from a plot of absorbance versus time. According to equation (7) Kinetic equations (Download) Excel is used to fit a exponential curve to highlighted data points (Fig. 7). In the Add Trendline dialog box, under Trend/Regression Type, Exponential is chosen. Next Display Equation on chart is selected. The exponential trendline fits data to the expression y = A e - kx where k' is the pseudo order rate constant (Fig. 7).
Figure 5: Bromination of acetanilide at different reaction temperatures
1: 12.6 °C 2: 17.5 °C 3: 23.5 °C
Plot of absorbance vs time Evaluation of rate constant k'
Messung |
(According to the reaction conditions: k = k' / 0.1875)
Excel File - Determination of the Activation Parameters: Activation Energy, Frequency Factor, Activation Enthalpy, Gibbs Energy, Activation Entropy
Bromination of Acetanilide
If the reaction temperatures and the corresponding rate constants (Tab. 5) are entered into the table of Excel file Activation parameter (Download), then all activation parameters (Tab. 5) will be calculated and the ARRHENIUS and the EYRING plot will be generated (Fig. 6).
Tab. 5: Calculation of the activation parameters
Fig. 6: ARRHENIUS (1) and EYRING plot (2)
Determination of the Michaelis Constant Km and the Maximal Velocity Vmax
According to equation (11) Kinetic equations (Download PDF file) 1 / v is plotted versus 1 / cS (Fig. 7). If the velocity constants k and the appropriate substrate concentrations cS are entered into the table of the Excel file Lineweaver-Burk (Download) (Tab. 6), the values for the Michaelis constant Km and the maximal reaction veloctiy vmax will be calculated.
Tab. 6: Excel file Determination of Km and vmax
Fig. 7: Lineweaver-Burk plot T = 50 °C (1) T = 40 °C (2)
