The following are images of how to use Excel to create the data tables and the graphs. I made up data so that it fits a first order rate law, r=k[A]. You may get different results. That is what you are supposed to be determining from your data. I also used "perfect" data. I have added the Beer's Law plot. I am assuming the Beer's Law graph (which you force through the origin) has a slope of 250 M-1. I generated the absorbance data for the boiled solutions so it would have this slope. I am assuming a starting concentration for Cr3+ of 3.00 x 10-3, 3.33 x 10-3, 3.67 x 10-3 and 4.00 x 10-3 for solutions 1, 2, 3 and 4, respecitively. The time is in minutes. The rate constant that I assumed is 0.010 min-1, as seen in graph 2.
This section shows Excel frames for Beer's Law (A = m * C), where A=absorbance, C=concentration, m=constant. I am assuming the Beer's Law graph (which you do just like the graphs below but you force through the origin) has a slope (m) of 250 M-1. Your line must go through the origin (0,0) for the Beer's Law plot and fit the other points as best it can while passing through the origin. Note that in the data table you include the point (0,0) as a data point so there are 5 data points (1 for the origin and 4 for the 4 boiled solutions). You can force a line through the origin in Excel for the linear regression. There is a checkbox in the "trendline" window under the options tab for setting the intercept and forcing the line through this intercept. By default it is set to pass through the origin (point (0,0)). You can see this in Frame 0k of the demo (frame 40 shows a line not forced through a particular intercept). You need the slope from this plot to calculate the [Cr(EDTA)-] from the absorbance for the 4 data tables. As I said above, I used "perfect" data so my line goes through all the points (R2=1). Your line will not be so "nice".
To graph 2 columns highlight the 2 columns. Since they are adjacent to each other you can click the left mouse button in the first cell and drag the pointer (mouse) while holding the button until you've highlighted the data you want to plot.
Frame 0a - Input Data
Frame 0b - Chose Scatter Plot (Click on Chart Icon in Menu Bar)
Frame 0c - Plot Highlighted Data
Frame 0d - Chart Options (Titles)
Frame 0e - Chart Options (Remove Grid Lines)
Frame 0f - Chart Options (Remove Legend - Not Needed Since Only One Data Set)
Frame 0g - Make Chart a New Sheet
Frame 0h - Go to New Chart
Frame 0i - Click on a Data Point and Go To Chart and Choose Trendline
Frame 0j - Choose Linear Regression
Frame 0k - Trendline Options (Check Options Shown at Bottom)
Frame 0l - Equation and R2 now Displayed on Chart
Frame 0m - Change Font for Equation Box
Frame 0n - Finished Graph
To enter an equation click on the cell (box) and then type the "equal" (=) key and then your equation.
The first set of "slides" is for the first data table for "solution 1". The columns in the spread sheet are (from left to right): time Abs [Cr(EDTA)-]t [Cr3+]t ln[Cr3+]t 1/[Cr3+]t
IMPORTANT: The nice thing about using Excel is what you can do once you have one data table done. After finishing table 1 for solution 1 you don't have to enter everything over again. What you do is highlight the whole table and then copy it. Then go to a new sheet (sheet 2) and paste it. It should look the same. Now here comes the neat part. All you have to do is change the first two columns, time and absorbance AND the initial concentration of [Cr3+] in the fourth column (column D). Edit Cell 1 in column D to change this concentration and then copy it to the other cells in column D. As you change the absorbance you will see ALL the other numbers in the other columns change automatically and you have the data table for solution 2 in the time it takes you to type in the absorbance values for solution 2 and change the initial concentration in column D. Then repeat for solutions 3 and 4 and you are done with the data for the other three solutions in about 10 minutes. How much simpler can it be? This will NOT give you new plots. Sorry, but you will have to do these over as you do for solution 1. Don't forget to format your data.
Frame 1 - Input Time Data
Frame 2 - Input Absorbance Data
Frame 3 - Input Eqn. to Calc. [Cr(EDTA)-]t from Abs. and Beer's Law Slope
Frame 4 - Result for Cell C1: [Cr(EDTA)-]t for Zero Abs.
Frame 5 - Copy Cell C1 (Copies the Eqn.)
Frame 6 - Highlight Remaining Cells in Column C
Frame 7 - Paste Cell C1 Contents (Eqn.) to Remaining Cells
Frame 8 - Results of Paste: [Cr(EDTA)-]t for each Abs. Automatically Calc.
Frame 9 - Input Eqn. to Calc. [Cr3+]t Using [Cr3+]0 (0.003 M) & [Cr(EDTA)-]t from Column C
Frame 10 - Copy Cell D1 (Copies the Eqn.)
Frame 11 - Paste Cell D1 Contents (Eqn.) to Remaining Cells of Column D
Frame 12 - Input Eqn. to Calc. ln[Cr3+]t for Time Zero Using [Cr3+]t from Cell D1
Frame 13 - Copy & Paste Cell E1 (Copies the Eqn.) to Remaining Cells of Column E
Frame 14 - Results of Paste: Calc. of ln[Cr3+]t for each Time Step
Frame 15 - Input Eqn. to Calc. 1/[Cr3+]t for Time Zero Using [Cr3+]t from Cell D1
Frame 16 - Copy & Paste Cell F1 (Copies the Eqn.) to Remaining Cells of Column F
Frame 17 - Results of Paste: Calc. of 1/[Cr3+]t for each Time Step
Frame 18 - Format Data to Show a Certain Number of Decimal Places (you decide how many)
Frame 19 - Format Data (cont.)
Frame 20 - Format Data (cont.)
Frame 21 - Format Data (cont.)
Frame 21a - Highlight All of Table 1 in Sheet 1
Frame 21b - Copy Table 1
Frame 21c - Go to Sheet 2 & Highlight Cell A1 & Click on Paste
Frame 21d - Paste Contents of Table 1
Frame 21e - Clear Contents of Absorbance Column (Time Column Too if That is Diff. than Soln. 1)
Frame 21f - Result of Clear Contents (Note this Clears Column Containing [Cr(EDTA)-]t for Soln. 2)
Frame 21g - Highlight Cell D1 (Edit Eqn. to Calc. [Cr3+]t)
Frame 21h - Change [Cr3+]0 to Value for Soln. 2 (0.0033M)
Frame 21i - Copy Cell D1 (Copies Eqn. for [Cr3+]t for Soln. 2)
Frame 21j - Paste Eqn. from D1 to Remaining Cells of Column D
Frame 21k - Result of Paste
Frame 21l - Enter Absorbance Values for Soln. 2
Frame 21m - Result (Automatically Calc. the New Values for Soln 2; Repeat for Remaining Abs. Values)
You are NOT required to do a zero-order graph for the report. However, I suggest you at least do a rough graph in Excel so you can see what the graph looks like. It will help to see this graph and it can tell you if you have some bad data or have made a calculation error. You do not have to include it in the report. However, there is a question in the report dealing with a zero-order plot.
For the zero-order graph you plot [Cr3+]t vs. time for all 4 solutions on the same graph. You are supposed to draw best-fit curved lines. Do NOT draw jagged lines (i.e. the kind you see for the stock market where a straight line is drawn from one point to the next). In my example I knew ahead of time that my data was first order so I used an exponential fit. You could try that or some sort of polynomial fit (such as x2 or x3), although exponential generally works well. I only plotted solution 1. You need to plot the other 2 solutions in a similar manner. Since I had only one set of data plotted I removed the legend. Since you will have 3 different lines you will want to keep the legend (you can't tell the players apart without a scorecard). Change the legend for each data set to something meaningful (like "Soln 1", "Soln 2", etc.). Also, you will not want to make the equation and R2 as large as I did. You will need to do this for each line plotted and move them as close as possible to the proper line. You can even make the legend horizontal, move it into the graph area above the lines and put the equation for each line under the title for each line.
To graph 2 columns which are not adjacent to each other you need to click on the first column and then while holding the "control key" click and highlight the the second column.
Frame 22 - Highlight Data to Plot
Frame 23 - Click on Chart Icon in Menu Bar (Chose Scatter Plot)
Frame 24 - Plot Data
Frame 25 - Chart Options (Titles)
Frame 26 - Chart Options (Remove Grid Lines)
Frame 27 - Make Chart a New Sheet
Frame 28 - Go to New Chart (click on tab at bottom)
Frame 29 - Modify Chart Title (highlight 3+)
Frame 30 - Modify Chart Title (make 3+ a superscript)
Frame 31 - Modify Chart Title (select title to change attributes)
Frame 32 - Modify Chart Title (change font size and bold)
Frame 33 - Result of Chart Title Changes
Frame 34 - Modify Y-axis (select axis by clicking on it)
Frame 35 - Change Y-axis Scale (so plot takes up most of the plot area)
Frame 36 - Result of Y-axis Changes
Frame 37 - Click on Data Point (start of trendline procedure)
Frame 38 - Go To Chart and Choose Trendline
Frame 39 - Choose a Regression Type (I chose exponential)
Frame 40 - Trendline Options (check options shown at bottom)
Frame 41 - Equation and R2 now Displayed on Chart
Frame 42 - Select Equation and R2
Frame 43 - Change Font Size (something readable but not as large as mine)
Frame 44 - Change Plot Legend (I removed the legend since I have only one plot)
Frame 45 - "Almost" Finished Graph (Keep the legend since you will have 4 plots on same graph)
Frame 46 - Blow up of "Almost" Finished Graph
Look at the following link to get some overall pointers about what a good graph should look like. I've also included a finished graph using someone's data for graph 2 (zero-order plot). Use this as a guideline for what a good graph should look like for this report (and others).
Zero-order Graph - Examples of a good graph
You use graphs 2 & 3 to decide whether the reaction is 1st or 2nd order. Graph 2 is ln[Cr3+]t vs. time and Graph 3 is 1/[Cr3+]t vs. time. The way you use these graphs to decide the order of the reaction depends on whether doing the graphs by hand or using Excel (see below).
We no longer do "hand"-graphing and expect the graphs to be done using a graphing program such as Excel. The following has been left in to explain the pictures. Please follow the instructions given in the manual and for graphing using Excel below.
I've used Excel to do the "hand"-graphing. The lab manual stated to use the data for solution 3 and draw a smooth best-fit curve for each graph and decide which looks more like a straight line. This can sometimes be a little hard to tell. If you look at the graph from the side edge of the paper you can sometimes see the curvature of a line a little better. Decide which plot gives a straighter line. An alternative is to fit each plot to a straight line and see which graph better fits the points. You will see one of the graphs has a straight line with the points close to the line. The other graph has points that aren't as close a fit to a straight line (probably looks like a parabola compared to the line straight line drawn). You can leave them both as straight lines or redraw the one that isn't a good linear fit as a curved fit (as I did in my example). The plot that gives the better straight line tells you the order of the reaction. If graph 2 (1st order plot) gives the better fit to a straight line then the reaction is 1st order. If graph 3 (2nd order plot) gives the better fit to a straight line then the reaction is 2nd order. Note in my example, Graph 2 (1st Order Plot) gives a perfect fit to a straight line (R2=1) while Graph 3 (2nd Order Plot) is not fit as well as a straight line (R2=0.99). This makes sense since I chose my data to correspond to a 1st order reaction in Cr3+. I then redrew Graph 3 to make the fit a nonlinear curve. I chose a polynomial fit which gave an R2=1 (meaning the data fit a polynomial curve better than a linear curve). The slope of Graph 2 (1st Order Plot) is -0.01 min-1. This slope corresponds to -k (ln[Cr3+]t = -k*t + ln[Cr3+]0). Therefore, my value for the rate constant, k, is 0.01 min-1. The intercept corresponds to the natural log of the initial concentration of Cr3+ (intercept = ln[Cr3+]0). Once you do this and decide the order of the reacton go on to graph 4 and graph all three solutions on the same graph according to the order you decided (either 1st or 2nd order) above.
Frame 47 - Start 1st Order Plot: ln[Cr3+]t vs. Time
Frame 48 - Choose Scatter Plot
Frame 49 - Plot after Formatting Titles and Removing Legend
Frame 50 - Highlight Y-Axis for Formatting (Moving X-axis)
Frame 51 - Format Y-Axis (Moving X-axis)
Frame 52 - Format Y-Axis (change Value Where X-axis crosses Y-Axis)
Frame 53 - X-axis Markings Moved from Top to Bottom of Graph
Frame 54 - Draw the Trendline - Choose Linear Regression
Frame 55 - Finished Graph with Line, Eqn and R2 (Perfect Fit - R2=1)
Frame 56 - 2nd Order Plot: 1/[Cr3+]t vs. Time with Data Points
Frame 57 - Draw the Trendline - Choose Linear Regression
Frame 58 - Finished Graph with Line, Eqn and R2 (Poorer Fit - R2=0.99)
Frame 59 - Redraw 2nd Order Plot as a Curved Trendline (Chose Polynomial)
Frame 60 - Finished 2nd Order Plot as a Polynomial (Better Fit - R2=1)
For graph 4 you decide whether the reaction is 1st or 2nd order and then graph all 3 soltuions on the same graph whether it is a 1st or 2nd order graph. You decide this based on whether graph 2 (1st order plot) or graph 3 (2nd order plot) gives a better linear fit (straight-line fit). In my example I chose 1st order since graph 2 above gave a better linear fit than graph 3. Therefore, my Graph 4 would be ln[Cr3+]t vs. time for all 3 solutions. On this graph you want to have a legend which shows the different symbols used to plot the data points for each solution and the best fit lines corresponding to these data points.
You use graphs 2 & 3 to decide whether the reaction is 1st or 2nd order.
Graph 2 is ln[Cr3+]t vs. time and Graph 3 is 1/[Cr3+]t vs. time.
Do ALL 3 solns on the 1st and 2nd order plots (graphs 2 and 3).
Use LINEAR trendlines for both graphs and just leave them as linear
fits. Include the equation for the line and the correlaton coefficent
(R2. You should NOT use the correlaton coefficent (R2)
values to decide which set of data fit a linear trend line better (what
is the correct order). The R2 values will be very close for
both graphs. Instead look to see which graph, first or second order,
gives 3 more nearly parallel lines. Remember, the slope is related
to the rate constant. That means if you have perfect data you should
have 3 parallel lines on the graph which is the correct order.
The other graph will have lines that start converging at one end and
diverging at the other (aren't as nearly parallel).
This is also in the lab manual.
The slope of a line corresponds to the rate constant.
For a first-order reaction the slope equals '-k' (ln[Cr3+]t = -k*t + ln[Cr3+]0).
For 1st-order the intercept corresponds to the natural log of the initial
concentration of Cr3+ (intercept = ln[Cr3+]0).
For a second-order reaction the slope equals 'k' (1/[Cr3+]t = k*t + 1/[Cr3+]0).
For 2nd-order the intercept corresponds to the the reciprocal of the initial
concentration (intercept = 1/[Cr3+]0)
Graphs 2 & 3 - Exs of what Graphs 2 & 3 might look like