**Tutorial Created by:**

Eric Wiebe

Mathematics, Science, and Technology Education

NC State University

- Enter and format data in an Excel spreadsheet in a form appropriate for graphing
- Create a scatter plot from spreadsheet data
- Insert a linear regression line (trendline) into the scatter plot
- Use the slope/intercept formula for the regression line to calculate a x value for a known y value
- Explore curve fitting to scatterplot data
- Create a connected point (line) graph
- Place a reference line in a graph

- Entering and Formatting the Data in Excel
- Creating the Initial Scatter Plot
- Creating a Linear Regression Line
- Using the Regression Equation to Calculate Concentration
- Adjusting the Chart Display

- Creating a Scatter Plot of Titration Data
- Curve Fitting to Titration Data
- Changing the Scatter Plot to a Line Graph
- Adding a Reference Line
- Modifying the Chart Axis Scale

Beer's Law states that there is a linear relationship between concentration of a colored compound in solution and the light absorption of the solution. This fact can be used to calculate the concentration of unknown solutions, given their absorption readings. First, a series of solutions of known concentration are tested for their absorption level. Next, a scatter plot is made of this empirical data and a linear regression line is fitted to the data. This regression line can be expressed as a formula and used to calculate the concentration of unknown solutions.

Open Excel. On Unity/Eos computers, the program will be located on the Application Launcher. On other computers, it will probably be located under the Start Menu.

Your data will go in the first two columns in the spreadsheet (see Figure 1a).

**Title**the spreadsheet page in cell**A1****Label**Column A as the concentration of the known solutions in cell**A3**.**Label**Column Bas the absorption readings for each of the solutions in cell**B3**.

Begin by formatting the spreadsheet cells so the appropriate number of decimal places are displayed (see Figure 1a).

**Click and drag**over the range of cells that will hold the concentration data (A5 through A10 for the sample data)- Choose
**Format > Cells...**(this is shorthand for choosing Cells... from the Format menu at the top of the Excel window) - Click on the
**Number**tab - Under Category choose
**Number**and set Decimal places to**5** - Click
**OK** - Repeat for the absorbance data column (B5 through B10 for the sample data),
setting the decimal places to
**4**

**Figure 1a**

If you do not have your own data, you can copy the data seen in Figure 1b.

- Enter your data below the column titles
- You can also place the absorption readings for the unknown solutions below the other data.

**Figure 1b.**

The concentration data is probably better expressed in scientific notation.

- Highlight the concentration data and choose
**Format > Cells...**. - Choose the
**Scientific**Category and set the Decimal places to**2**.The last step before creating the graph is to choose the data you want to graph.

- Highlight the data in both the concentration and absorbance columns (but
not the unknown data)
This is shown in Figure 2.

**Figure 2.**

With the data you want graphed, start the chart wizard

- Choose the
**Chart Wizard**icon from the tool bar (Figure 3). If the Chart Wizard is not visible, you can also choose**Insert > Chart...**

**Figure 3.**

The first dialogue of the wizard comes up

- Choose
**XY (Scatter)**and the**unconnected points icon**for the Chart sub-type (Figure 4a)

**Figure 4a.**

- Click
**Next >**

The Data Range box should reflect the data you highlighted in the spreadsheet. The Series option should be set to Columns, which is how your data is organized (see Figure 4b).

**Figure 4b.**

- Click
**Next >**

The next dialogue in the wizard is where you label your chart (Figure 4c)

- Enter
**Beer's Law**for the Chart Title - Enter
**Concentration (M)**for the Value X Axis - Enter
**Absorbance**for the Value Y Axis

**Figure 4c**.

- Click on the
**Legend**tab - Click
**off**the**Show Legend**option (Figure 4d)

**Figure 4d**.

- Click
**Next >**

Keep the chart as an object in the current sheet (Figure 4e). **Note**:
Your current sheet is probably named with the default name of "Sheet 1".

**Figure 4e**.

- Click
**Finish**

The initial scatter plot is now finished and should appear on the same spreadsheet page as your original data. Your chart should look like Figure 5. A few items of note:

- Your data should look as though it falls along a linear path
- Horizontal reference lines were automatically placed in your chart, along with a gray background
- Your chart is highlighted with square 'handles' on the corners. When your
chart is highlighted, a special Chart floating palette should also appear,
as is seen in Figure 5.
**Note:**If the Chart floating palette does not appear, go to**Tools>Customize...**, click on the**Toolbars**tab, and then click on the**Chart**checkbox.If it still doesn't show up as a floating palette, it may be 'docked' on one of your tool bars at the top of the Excel window.With your graph highlighted, you can click and drag the chart to a wherever you would like it located on the spreadsheet page. Grabbing one of the four corner handles allows you to resize the graph.

**Note:**the graph will automatically adjust a number of chart properties as you resize the graph, including the font size of the text in the graph. You may need to go back and alter these properties. At the end of the first part of this tutorial, you will learn how to do this.

**Figure 5.**

When the chart window is highlighted, besides having the chart floating palette appear, a Chart menu also appears. From the Chart menu, you can add a regression line to the chart.

- Choose
**Chart > Add trendline...**A dialogue box appears (Figure 6a).

- Select the
**Linear**Trend/Regression type

**Figure 6a**.

- Choose the
**Options**tab and select**Display equation on chart**(Figure 6b)

**Figure 6b.**

- Click
**OK**to close the dialogue

The chart now displays the regression line (Figure 7)

**Figure 7**.

The linear equation shown on the chart represents the relationship between Concentration (x) and Absorbance (y) for the compound in solution. The regression line can be considered an acceptable estimation of the true relationship between concentration and absorbance. We have been given the absorbance readings for two solutions of unknown concentration.

Using the linear equation (labeled A in Figure 8), a spreadsheet cell can have an equation associated with it to do the calculation for us. We have a value for y (Absorbance) and need to solve for x (Concentration). Below are the algebraic equations working out this calculation:

y = 2071.9x + 0.111

y - 0.0111 = 2071.9x

(y - 0.0111) / 2071.9 = x

Now we have to convert this final equation into an equation in a spreadsheet cell. The equation associated with the spreadsheet cell will look like what is labeled C in Figure 8. 'B12' in the equation represents y (the absorbance of the unknown). The solution for x (Concentration) is then displayed in cell 'C12'.

**Highlight**a spreadsheet cell to hold 'x', the result of the final equation (cell C12, labeled B in Figure 8).**Click**in the**equation area**(labeled C, figure 8)**Type**an**equal sign**and then a**parentheses****Click**in the cell representing 'y' in your equation (cell B12 in Figure 8) to put this cell label in your equation- Finish typing your equation

Note: If your equation differs for the one in this example, use your equation

Duplicate your equation for the other unknown.

**Highlight**the original equation cell (C12 in Figure 8) and the cell below it (C13)- Choose
**Edit > Fill > Down**

Note that if you highlight your new equation in C13, the reference to cell B12 has also incremented to cell B13.

**Figure 8.**

The readability and display of the scatterplot can be further enhanced by modifying a number of the parameters and options for the chart. Many of these modifications can be accessed through the Chart menu, the Chart floating palette, and by double-clicking the element on the chart itself. Let's start by creating a better contrast between the data points and regression line and the background.

**Double-click**in the**gray**background area of the chart or by selecting**Chart Area**in the Chart floating palette and then clicking on the**Format**icon (Figure 9a).

**Figure 9a.**

In the Chart Area Format dialogue, set the border and background colors (see Figure 9b)

- Choose
**None**for a**Border** - Choose the
**white**square from the color palette for an**Area**color - Click
**OK**

**Figure 9b**.

Now, delete the horizontal grid lines

**Click**on the**horizontal grid lines**in the chart and press the**Delete**key

Now, adjust the color and line weight of the regression line and the color of the data points

**Double-click**on the**regression line**(or choose Series 1 Trendline 1 from the Chart floating palette and then click the Format icon)- Choose a
**thinner line**for the**Line Weight** - Click on the word
**Automatic**next to**Line Color**and the color palette appears. Choose**dark blue**from the color palette - Click
**OK** **Double-click**on one of the**data points**(or choose Series 1 and click the Format icon)- Choose
**dark red**from the color palette for the**Marker Foreground**and**Background** - Click
**OK**

Finally, you can move the regression equation to a more central location on the chart

**Click**and**drag**the regression equation

If necessary, resize the font size for text elements in the graph.

- Either
**double click**the text element or choose it from the floating palette - Click on the
**Fonts**tab - Choose a different
**font size**

The results can be seen in Figure 9c.

**Figure 9c.**

This is the end of the first half of the scatter plot tutorial.

In this next part of the tutorial, we will work with another set of data. In this case, it is of a strong acid-strong base titration (see Figure 10). With this titration, a strong base (NaOH) of known concentration is added to a strong acid (also of known concentration, in this case). As the strong base is added to solution, its OH- ions bind with the free H+ions of the acid. An equivalence point is reached when there are no free OH- nor H+ ions in the solution. This equivalence point can be found with a color indicator in the solution or through a pH titration curve. This part of the tutorial will show you how to do the latter.

Note that there should be two columns of data in your spreadsheet:

Column A: mL of 0.1 M NaOH added

Column B: pH of the 0.1 M HCl / 0.1M NaOH mixture

- Using a new page in the spreadsheet, enter your titration data. If you do not have your own data, use the data shown in Figure 10.
- Return to the beginning of the tutorial if you need hints on formatting the cells to the proper number of decimal places

**Figure 10**.

Now, create a scatter plot of titration data, just as you did with the Beer's Law plot.(Figure 11).

**Highlight**the titration data and the Column headers- Click on the
**Chart wizard**icon - Choose
**XY (Scatter)**and the**scatter**Chart sub-type

**Figure 11**.

Continue through steps 2 through 4 of the Chart wizard:

- The defaults for
**step 2**should be fine if you properly highlighted the data - In
**step 3**enter the chart**title**and x and y axis**labels**and**off**the**legend** - In
**step 4**, leave as an object in the current page

The resulting plot should look like Figure 12:

**Figure 12**.

The next logical question that you might ask is whether a linear regression line or a curved regression line might help us interpret the titration data. You may remember that our goal with this plot is to calculate the equivalence point, that is, what amount of NaOH is needed to change the pH of the mixture to 7 (neutral)?

Create a linear regression line:

- Choose
**Chart > Add Trendline...** - Pick
**Linear**sub-type

Looking at the data (Figure 13a), it is clear that the first 45 ml of NaOH do little to alter the pH of the mixture. Then between 45 ml and 55 ml, there is a sharp rise in pH before leveling off again. The data trend does not seem linear at all and, in fact, a linear regression line does not fit the data well at all.

**Figure 13a.**

The next approach might be to choose a different type of trendline (Figure 13b):

**Click**on the**linear regression line**in the plot and press the**delete**key to delete the line- Choose
**Chart > Add Trendline...** - Pick
**Polynomial**subtype - Set the
**Order**of the curve to**2**

**Figure 13b**.

You can see that a second order polynomial curve does not capture the steep rise of the data well. A higher order curve might be tried (Figure 13c):

**Double-click**on the**curved regression line**- Set the
**Order**of the curve to**3**

**Figure 13c**.

Still, the third order polynomial does not capture the steep part of the curve where it passes through a pH of 7. Even higher order curves could be created to see if they fit the data better. Instead, a different approach will be taken for this data. Go ahead and delete the regression curve:

**Click**on the**curved regression line**in the plot and press the**delete**key

Instead of adding a curved regression line, all of the points of the titration
data are connected with a smooth curve. With this approach, the curve is guaranteed
to go through all of the data points. This is both good and bad. This option
can be used if you have **only one** **pH reading per amount of NaOH added**.
If you have multiple pH readings for each amount added on the scatter plot,
you will not end up with a smooth curve. To change the scatter plot is a (smoothed)
line graph (Figure 14a):

- Choose
**Chart > Chart Type...** - Select the
**Scatter connected by smooth lines**Chart subtype

**Figure 14a**.

The result should look like Figure 14b:

**Figure 14b**.

This smooth, connected curve helps locate where the steep part of the curve passes through pH 7.

The chart can be enhanced by adding a reference line at pH 7. This clearly marks the point where the curve passes through this pH.

- A set of drawing tools should be visible at the bottom of the window. If
not, click on the
**Draw**icon two to the right of the Chart wizard icon. - Make sure your
**chart**is**highlighted** - Choose the
**line**tool at the bottom of the window **Draw**a horizontal line at pH 7 across the width of the chart by clicking and dragging a line across the chart area.- With the horizontal line still highlighted, choose a
**3/4 pt line thickness**and a**dashed line type**at the bottom of the window

Further refinements in the chart can be made by (as you did with the Beer's law chart):

**removing**the other**horizontal grid lines**- turning
**off**the**border** **changing chart colors****Thickening**the**curve**and**shrinking**the**data points**emphasizes the fitted curve over the individual data points

The result should look like Figure 15.

**Figure 15**.

The above chart gives a good overview of the entire titration. If you would like to focus exclusively on the steep part of the curve between 45 and 55 ml of added NaOH, a new chart can be created which limits the X Axis range. Start by making a copy of the current chart:

**Select**the**current chart**by clicking near its border- Choose
**Edit > Copy** **Click**a**spreadsheet cell**about 10 rows below the current chart- Choose
**Edit > Paste**

With the new chart highlighted (Figure 16):

- Choose
**Value (X) Axis**from the Chart floating palette - Click on the
**Format**icon - Set the
**Minimum**to**45**,**Maximum**to**55** - Set the
**Major unit**to**1**and**Minor unit**to**0.25** - Click
**OK**

**Figure 16**.

Next, both vertical and horizontal gridlines can be added to more accurately locate the equivalency point (Figure 17):

- Choose
**Chart > Chart Options...** - Click on the
**Gridlines**tab - Select
**X****axis****Major gridlines**and**Y****axis****Major gridlines** - Click
**OK**

**Figure 17**.

With enhancements similar to what you did to the other chart, the result will look like Figure 18.

**Figure 18**.

Even with this smooth curve passing through all of the data points, it is still an estimation of what intermediate mL added/pH data points would be. A clear inaccuracy is where the curve moves in a negative X direction between the 50 and 51 mL data points. More data points collected between 49 and 51 mL would both better smooth the curve and give a more accurate estimation of the equivalency point.

This is the end of the second half of the tutorial.

*Rev 2/00 EW*