Reading: Graphing Techniques Revised 3/6/12 GRAPHING TECHNIQUES


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1 GRAPHING TECHNIQUES Mathematical relationships between variables are determined by graphing experimental data. For example, the linear relationship between the concentration and the absorption of dilute colored solutions leads to Beer s Law (A=εCl). Once the mathematical relationship is known, experimental quantities can often be calculated from the slope or yintercept of a graph. For example, reaction enthalpy can be determined from the slope of a plot of ln k vs. inverse T. Furthermore, extrapolation of graphical data trends can be used to find information about conditions difficult to achieve in the laboratory, such as high or low temperatures and pressures. Plotting Variables A line graph consists of two axes at right angles. The horizontal xaxis, or abscissa, is typically chosen to represent the independent variable which is intentionally manipulated by the experimenter. The vertical yaxis, or ordinate, is chosen to represent the dependent variable which changes as the independent variable is manipulated. Example: A student wishes to measure the relationship between volume and temperature of a gas. If the student purposely increases the temperature and measures the resultant changes in gas volume, he should graph the values for T on the xaxis and the resulting values for V on the y axis. If the student reverses the experiment and purposely increases the volume of the gas and measures the resultant temperature, the variables are then reversed: V is plotted on the xaxis and T is plotted on the yaxis. Selecting a Title and Labeling the Axes The title must describe the type of reaction or system being investigated, chemicals used, and special conditions of the experiment. Examples: "Beer s Law Plot for Co(NO 3 ) 2 (aq) at 510 nm" or "Cooling Curve for Lauric Acid/Unknown Mixture". Do not state x vs. y in the title, that is easily determined by labeling the axes. Axes must be labeled with the name (or symbol) of the variable and include the units (if any). Examples: Temperature ( C) or V (ml). 1
2 Choosing an Appropriate Scale The scale of the graph should be chosen so the data completely fills the graph and is not restricted to one small region or corner. Examples are shown in Figure 1. Note that the scale does not have to begin with zero. 0.5 Absorbance vs. Wavelength for a Metal Complex Ion 0.4 Absorbance Wavelength (nm) Absorbance Absorbance vs. Wavelength for a Metal Complex Ion Wavelength (nm) Absorbance Absorbance vs. Wavelength for a Metal Complex Ion Wavelength (nm) Figure 1: The three plots are from the same data set, but use different scales for the dependent and independent variables. The top graph represents the data range most clearly. Note that each graph contains a title and the axes are labeled. Absorbance is unitless but the units for wavelength are given in nanometers. Drawing Data Points Data points can be represented either as a circle, dot, or bar. The size of the circle or bar is often used to represent the deviation or error in the data point. Recorded data should be included on the plot as a separate table. (Figure 2) 2
3 Data points from other experimenters should be represented with different symbols. Include a legend citing the source of the additional data points. Example: My data, Kim Nguyen's data, Sam Patel's data Use a solid line through the data points and a dashed line when extrapolating or extending beyond the collected data points. Drawing Lines or Curves Draw (have a computer program draw) a smooth curve or line when connecting data points. "Dottodot" connections should be avoided. If the data points do not exactly fit on the line, a bestfit line in which an equal number of data points lie an equal distance above and below the line should be drawn. The best fit line "smoothes" the data and helps eliminate random error. (Figure 2) Use a computer graphing program to generate the line and its equation. V (L) P (atm) 1/P (atm 1 ) Figure 2: Linear plot with a best fit line, including a data table. Computer Generated Plots All graphs must be computer generated. Caution: A computer plot must be scaled correctly, have labels, and all other expected information. Keep in mind the old addage: "garbage in, garbage out". Good data is necessary for good results. You must use the computer graphing program correctly and obtain a useful graph. Using Excel for Graphing The following are guidelines for acquiring a graph using Excel, including a bestfit line (called a trendline in the program). Be judicious about the data included. If a points lies far outside a 3
4 reasonable value, provide two plots for grading: one with the data point and one without. Also, you should perform a QTest and report the confidence level for rejecting the data point. (See Reading: Analysis of Errors.) Instructions for graphing with Excel: (1) Enter data points to be graphed in two adjacent columns. Data for the x axis should be in the left column and data for the y axis should be in the right column. (2) Highlight the two columns of data by holding down the left mouse button and dragging the mouse over the column heading letters. (3) Go to the Insert menu and select Chart. The Chart Wizard window should appear. (4) In the first window, Step 1 of 4, select XY Scatter for Chart Type and Scatter for Subchart Type (the choice without any lines connecting the data points). Click the Next button at the bottom of the Chart Wizard window. (5) In the second window, Step 2 of 4, make sure Series in Columns is chosen and then click the Next button. (6) In the third window, Step 3 of 4, there are five tabs: titles, axes, gridlines, legend, and data labels. In the Title tab enter the Chart Title and the Labels for the x and y axes (make sure that you include units). In the Gridlines tab check Major Gridlines for both x and y axes. And, in the Legend tab uncheck Show Legend. Click the Next button. (7) In the fourth window, Step 4 of 4, determine whether you want your graph on the same sheet with your data, or on a new sheet. Click the Finish button. The chart should appear. (8) Click on the data points so that only they are highlighted. Go to the Chart menu and choose Add Trendline. In the Add Trendline window, under the Type tab, choose the correct line type (which is usually linear for g chem. lab). Under the Options tab, check Display Equation on Chart and Display Rsquared Value on Chart. Click OK. Notes: 1) You may change locations, sizes, gridline units, fonts, et cetera of your chart by clicking to highlight the areas you wish to change. 2) Rsquared values indicate how well the trendline fits the data. If the slope is positive, the ideal fit is 1. If the slope is negative, the ideal fit is 1. 4
5 To extrapolate (extend) a data line: Click on the line so that it is highlighted. Go to the Chart menu and choose Add Trendline. Click on the Options tab. Under Forecast choose the number of periods necessary either forward or backward. Instructions for graphing with 2007 Excel: (1) Enter data points to be graphed in two adjacent columns. Data for the x axis should be in the left column and data for the y axis should be in the right column. (2) Highlight the two columns of data by holding down the left mouse button and dragging the mouse over the column heading letters. (3) Click on the Insert tab and select Scatter icon in the Charts section. Choose the Scatter with Only Markers chart type (the top left choice). The plot of data will appear. (4) Click on the plot that just appeared. Chart Tools should appear at the very top of the screen in the middle. Choose the Layout tab. a. In the Analysis section choose Trendline. Choose More Trendline Options at the bottom of the pull down window. Choose the Trend/Regression Type and click on the box next to Display Equation on chart. b. In the Label section choose Chart Title. Choose Above Chart and enter a title in the field that appears at the top of the plot. In the same section choose Axis Titles. Enter the titles. c. If the initial and final values of either axis needs to be changed, click on the Axis button in the Axis section and make the necessary changes. Gridlines can be altered by clicking on the Gridline button in the Axis section. To extrapolate (extend) a data line: Click on the line so that it is highlighted. The Chart Tools will show up on to the middle/right of the top tool bar. Choose the Layout menu/tab. Go to the Trendline and choose More Trendline Options. Under Forecast enter the number of periods necessary either forward or backward. 5
6 To change the x and y axes minimum and maximum values: Click on the plot so that "Chart Tools" is visible in top tool bar. Choose the Layout menu/tab. Click on "Axes" and choose "Primary Horizontal Axis", click on "More Primary Horizontal Axis Options". Set either or both the Minimum and Maximum to "Fixed" and then change the value in the field directly to the right. Repeat the process for the vertical axis (go to "Axes" and choose "Primary Vertical Axis", et cetera). Instructor Reviewed Information on the Web: Please report any links that are no longer active. Graphing with Excel, North Carolina State University: 6
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