how do i plot the gibbs isotherm equation in excel given concentration and surface tension? I'm looking for surface excess which is the slope on the graph, the equation is r=1/RT(dST/dln(c)), ST is the surface tension. Do I plot the ln of the concentration versus the surface tension?
To plot the Gibbs isotherm equation in Excel and determine the surface excess (slope), you can follow these steps:
1. Calculate the value of r, which is 1/RT(dST/dln(c)), where RT is the product of the universal gas constant (R) and temperature (T), dST is the change in surface tension, and dln(c) is the change in the natural logarithm of concentration (c). Make sure you have the appropriate values for R, T, dST, and dln(c) before proceeding.
2. Create a table in Excel with two columns. In the first column, list the values of ln(c) (natural logarithm of concentration), and in the second column, the corresponding values of surface tension (ST).
3. Insert the data points for ln(c) and ST into the Excel table. Make sure the values are accurate and appropriately formatted.
4. Select the data in your table, including both the ln(c) and ST columns.
5. Click on the "Insert" tab in the Excel ribbon, and then choose the desired chart type, such as scatter plot, depending on how you want to visualize the relationship between ln(c) and ST.
6. Once the chart is created, right-click on one of the data points and select "Add Trendline" from the context menu. Choose a linear trendline since you are interested in determining the slope.
7. In the "Format Trendline" pane that appears on the right side of the Excel window, check the "Display Equation on Chart" option.
8. The equation that is displayed on the chart represents the linear relationship between ln(c) and ST, which is the Gibbs isotherm equation. The coefficient associated with ln(c) in that equation represents the surface excess, which is the slope of the linear trendline.
By following these steps, you should be able to plot the Gibbs isotherm equation in Excel and determine the surface excess (slope) as you described.