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EXPERIMENT 2
Reaction Order
Introduction
How a reaction progresses over time is an indication of its reaction order. In the rate laws, (Rate = k[A]m[B]n), found in the first experiment, you calculated the reaction order with respect to each of the reactants, (variables m and n), using the method of initial rates. This allowed you to predict how much the rate would increase when the initial concentrations of the reactants were changed. While these rate laws provided a means for predictably changing the rate of a reaction so that you could determine when a reaction would finish, no information could be gained about how the reaction was progressing. Questions such as “how much of my reactant is left after 5 minutes?” or “when will the reaction be finished?” could not be answered using the rate law alone. To find an answer to these questions, or any questions that relate time to the reactant concentration, a better understanding of the reaction orders is needed.
Reaction order In experiment 1, we determined that reaction order with respect to all reactants can be determined experimentally by the method of initial rates. In this experiment we will find the reaction order graphically by plotting the decrease in reactant concentration over time and use it to write a new rate law, called the integrated rate law that can be used to better define our reaction in terms of time. The 3 most commonly studied reaction orders are referred to as zero order reactions, first order reactions and second order reactions.
For simplification when graphing to find the order of a reactant, we look only at one reactant at a time. Unlike the rate equation, where we had A+ Bproducts, when finding the integrated rate law, the concentration of B is held constant so that you are only looking at a reaction that changes as a result of a single reactant, A. Therefore, the chemical equation effectively becomes A products. To find the integrated rate law with respect to B, you would need to perform a separate set of experiments where B products and A is held constant.
Zero order reactions Zero order reactions describe reactions where a reactant decreases at a steady rate regardless of the concentration. One example of a zero order reaction would be a reactant that breaks apart at a steady rate until there is no more reactant left at all in the reaction. It doesn’t break up any faster due to higher concentrations. Combustion reactions are zero order reactions. It doesn’t matter how much fuel you have, once you have reached a constant temperature, the fuel burns at a predictable rate. An increase in the amount of fuel initially will raise the intercept on the y-axis, but does not change the slope of the line which corresponds to the rate of the reaction. The rate of the burning would be constant regardless of how much fuel was present at any particular time. The first graph below is the result of the amount of fuel used versus time. The second graph demonstrates that when the initial amount of fuel is increased the rate of the reaction (slope) does not change. It is a constant that equals -0.02gallons/min for either graph.
y = -0.2x + 2 y = -0.2x + 4 R^2 = 1 R^2 = 1
The rate of the reaction is based on the linear equation y = mx + b which can be found by finding the slope of the line from the graph. “b” is the intercept on the y axis corresponding to your initial amount of reactant. The variables from the graphs are as follows:
y is the amount of your reactant at a particular time during the reaction x is a specific time during the reaction m is the slope of the line which is the rate of reaction (for combustion example = ∆fuel/∆ time) b is the y intercept that correlates to the initial amount of a reactant
The correlation coefficient (R^2 ) shown below each graph gives an indication of how closely the line fits the data. In general, a correlation coefficient of .99 or greater is necessary to be confident that the equation for the line is correct.
Gallons of Fuel vs. Time for a Zero Order Reaction
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1
2
(^0 2 4) Time (min) 6 8 10
G a llon s o f F u e l
G al l o ns of F ue l vs. T i me f o r a Ze r o O r de r Re ac t i o n
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3
4
0 2 4 6 8 10 T i me ( m i n )
First order reactions First order reactions are extremely common. These are reactions where the reaction rate is fast at the beginning of the reaction and slows down as the reaction progresses. Unlike a zero order reaction that gives you a straight line when plotting reactant concentration vs. time, you will get a curve for a first order reaction. The rate is continually decreasing over time, thus the mathematical equation for this curved line is more complicated than plotting the concentration/time data directly. However, if the natural log (ln) of the reactant concentration is plotted vs. time, you will now have a straight line which allows you to easily relate reaction time to reactant concentration. Radioactive decay is one example of a first order reaction.
y = 0.0004x^2 - 0.028x + 0.592 y = -0.0648x - 0. R 2 = 0.996 R 2 = 0.
Second order reactions Like first order reactions, second order reactions start out quickly and then slow down as the reaction progresses. The relationship between time and concentration for a second order reaction becomes linear when the reciprocal of the concentration (1/conc.) is plotted vs. time. Also note that the linear plot in second order reactions results in a line with a positive slope which will be reflected in the integrated rate laws described in the next section.
y = 0.0002x^2 - 0.0231x + 0.8229 y = 0.06x + 1. R^2 = 0.991 R^2 = 0.
Determining reaction order Once you have recorded experimental data for the decrease of a reactant over time, make the following 3 plots. First, plot concentration vs. time directly (zero order) then ln[A] vs. time (first order) and finally, 1/[A] vs time (second order). The graph with the line with the highest correlation coefficient, R^2 , is the one that best describes the reaction order with respect to the reactant that was plotted.
Integrated Rate Laws Once you have determined the order of your reaction, you can use the equation for that line to determine further information about your reaction. These equations are called integrated rate laws and are based on the chemical reaction: A Products. By convention, the following variables are substituted for the variables found in the equation of a line, y = mx +b when generating the integrated rate laws.
Old Variable Definition New Variable y concentration of reactant [A] or ln[A] or 1/[A] m slope =rate constant of reaction k x time t b y-intercept=initial amount of A [A 0 ] or ln[A 0 ] or 1/[A 0 ]
Conce ntration (M) vs. Time for a Firs t Order Reaction
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0 10 20 30 40 Time (min)
Concentration (M)
ln(concentration) vs. Time for a First Order Reaction
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0 10 20 30 Time (min)
ln(concentration)
Conce ntration (M) vs. Time for a Second Order Reaction
0.20.
0.40.
0.60.
0 20 40 60 T ime ( min)
Conce ntration (M) vs. Time for a Second Order Reaction
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0 20 40 60 T ime ( min)
A colorimeter assigns numerical values that correspond to the amount of light that is absorbed by a solution. These absorbance values can be correlated to the concentration of the solution. A colorless solution will allow light to go through uninhibited and therefore the value of the absorbance will be very small. As the concentration of a colored solution increases, it gets darker and absorbs more light. The absorbance values will increase at a linear rate as the concentration of the solution increases. In the crystal violet experiment, you will use the colorimeter to monitor the decrease in absorbance over time which correlates to the decrease in the concentration of the purple crystal violet in your solution as it is converted to colorless product.
Graphically determining the Order of a Reactant Once you have started your reaction, you will record the absorbance of the solution every minute. At the end of the experiment, your raw data will consist of a series of times and absorbance readings. After converting the absorbance to concentration, you will then determine the order of the reaction with respect to the crystal violet by making 3 plots. The first will be a graph of time versus concentration. The second is time versus the natural logarithm of the concentration and the third is a plot of time versus the inverse of the concentration (1/concentration). The plot that has the correlation coefficient (R^2 ) closest to 1 will be the one that tells you the reaction order with respect to crystal violet.
Determining the Rate Equation (Review Experiment 1) You will monitor the bleaching of the crystal violet with 2 different concentrations of sodium hydroxide. This will allow you to use the method of initial rates covered in experiment 1 to determine the order of reaction for the sodium hydroxide, calculate the rate constant of the overall reaction and finally write the rate equation associated with the reaction.
Determining the Integrated Rate Law for a Reaction One restriction to the integrated rate law for the crystal violet/sodium hydroxide reaction is that the integrated rate law written applies only when a designated concentration of sodium hydroxide is use. Thus, the new rate constant will incorporate the effect of a constant concentration of an additional reactant. This accounts for the difference in the values of the rate constants observed when plotting the graphs from the time/concentration studies for different concentrations of sodium hydroxide.
In your lab, you will be doing the experiment using 2 different concentrations of sodium hydroxide to determine how the change in concentration affects the rate constant of the crystal violet/sodium hydroxide reaction. After determining the order of reaction for the crystal violet from one of the graphs, you will use the equation for a line defined by your data to find the intercept and the slope in the equation for your integrated rate law. You will find the integrated rate laws for both concentrations of sodium hydroxide and observe how the rate constant varies as a result of the change in hydroxide concentration. Your discussion questions will require you to use the rate laws you calculated to predict the results of hypothetical experiments.
Laboratory Equipment Procedures
Chemical Hazards
Crystal Violet Solution
NFPA RATING: HEALTH: 2 FLAMMABILITY: 0 REACTIVITY: 0
DERMAL EXPOSURE: Wash off with soap and plenty of water. Stains clothing and skin. EYE EXPOSURE: Flush with copious amounts of water for at least 15 minutes. Assure adequate flushing by separating the eyelids with fingers. Contact your TA immediately.
Sodium Hydroxide Solutions
NFPA RATING: HEALTH: 0 FLAMMABILITY: 0 REACTIVITY: 1
ORAL EXPOSURE Caustic. If swallowed, wash out mouth with water provided person is conscious. Do not induce vomiting. Contact your TA immediately. DERMAL EXPOSURE Caustic. In case of extensive skin contact, flush with copious amounts of water for at least 15 minutes. Remove contaminated clothing and shoes. Contact your TA immediately. EYE EXPOSURE Caustic. In case of contact with eyes, flush with copious amounts of water for at least 15 minutes. Assure adequate flushing by separating the eyelids with fingers. Contact your TA immediately.
Laboratory Procedures
Part 1: Absorbance of Initial Solution
- Calibrate the colorimeter according to the Equipment Procedure.
- Record the concentration of the crystal violet in your laboratory notebook.
- Dispense 2 mL of distilled water into a 10 mL graduated cylinder.
- Pour the water into the sample cuvette.
- Dispense 2 mL of 1 x 10-5M of crystal violet into a second 10 mL graduated cylinder.
- Carefully pour the crystal violet solution into the same sample cuvette
- Cap the cuvette, invert to mix the contents and wipe the sides with a kimwipe.
- Place the cuvette in the sample holder (S) and close the cover on the colorimeter.
- Record the absorbance in your laboratory notebook.
- Remove the sample cuvette and dump the contents into a 100 mL waste beaker.
- Rinse the cuvette with distilled water and dry the inside of the cuvette with a kimwipe before proceeding.
- Dispose of solution in a 50 mL waste beaker.
Part 2: Monitoring the Reaction of Crystal Violet and Sodium Hydroxide
- Record the concentration of the 2 NaOH solutions in your laboratory notebook.
- Dispense 2.00 mL of 1.0 x 10-5M of crystal violet to a 10 mL graduated cylinder.
- Transfer the solution to your sample cuvette.
- Dispense 2.00 mL of 0.010M NaOH into a second graduated cylinder.
- Pour the sodium hydroxide into the sample cuvette.
- Immediately press START/STOP on the MeasureNet station.
- Cap the cuvette, mix quickly by inverting the cuvette and wipe the sides with a kimwipe.
- Place the cuvette in the sample holder (S) and close the cover on the colorimeter.
- Press START/STOP to start the data acquisition.
- Record the absorbance after 30 seconds and at 60 seconds in your laboratory notebook.
- Note: If you miss the 30 second mark, immediately record the time and absorbance as soon as possible.
- Continue recording the absorbance at one minute intervals until you reach 1800 seconds.
- Remove the sample cuvette and dump the contents into the waste beaker.
- Dry the inside of the cuvette with a kimwipe before proceeding.
- Repeat previous steps of Part 2 using the 0.020M NaOH.
- Be careful to fully rinse out both cuvettes with water before returning them to your drawer.
- Dispose of waste solution in waste container in the hood when finished.
Laboratory Data
Create tables for the following data in your lab notebook before coming to class. Record the data shown in your laboratory notebook during the lab in pen. Include the signed white copy of this table when you turn in your lab report. Include the correct number of significant figures for each measurement.
Concentration of stock solution of crystal violet _________M
Concentration of stock solution of sodium hydroxide _________M
Abs of diluted crystal violet (abs of time 0) _________
You will need separate tables that each go up to 1800sec for each NaOH solution.
0.010M NaOH 0.020M NaOH Time Absorbance Time Absorbance ______sec ______ ______sec ______
Laboratory Results
Graphs Include a table of these results for each time/abs pair in your lab report for each experiment. The tables must be typed but can be taken directly from the Excel spreadsheet.
Time(s) Time (min) absorbance concentration ln concentration 1/concentration
Include the 6 graphs created from these data. There should be 3 graphs from each concentration of NaOH used.
Calculated Results Remember to show one example of each calculation either handwritten or typed on a separate sheet. Data determined from Excel, such as the correlation coefficient or the slope, is considered part of the graph and does not need to be hand calculated.
Include a typed copy of this table with your lab report. 0.010M NaOH 0.020M NaOH
Plot that gives the best straight line __________ ___________ Order of reaction with respect to crystal violet: __________ ___________
Diluted concentration of sodium hydroxide __________M ___________M Diluted concentration of crystal violet __________M ___________M
Absorbance per molar concentration __________abs/M
Rate of disappearance of crystal violet: __________ ___________ Order of reaction with respect to sodium hydroxide: __________ ___________
Average rate constant, k: ___________ Overall rate law equation: ______________________
Equation for each line: ___________________ __________________ Integrated rate law equations: ___________________ __________________
You have now generated a table that starts out similar to the one below. Your table should have at least 1800 seconds as the last time value. If in the future you want to use other formulas, look for the Σ sign on the toolbar at the top of the page. Click on the down arrow to bring up commonly used functions. Click on the one you want to use. If the function you need is not listed, click on the “More Functions” tab at the bottom of the box to bring up a list of additional functions.
Graphing Data in Excel
- Highlight the data for your first graph by clicking on cell C1 and dragging across to cell D1 and down to the end of your data table. When you release the cursor, your data should show up with a darker background.
- Click on the chart wizard icon shown below. This will bring up a box with instructions to generate different types of graphs. Alternatively, you can click on Insert at the top of the toolbar to bring up a pull-down menu containing a “chart” option. Click on chart to bring up the same box shown below.
- Click on XY (Scatter) to generate a plot using the data in column C as your x-axis and the data in column D as your y-axis. Click Next>
- Select subtype “Scatter”. This only shows the data points, not a line. Click Next>.
- Your data range will show up in the next box, Click Next> again.
- The next data box allows you to enter titles for the graph and x and y axes. Enter appropriate titles and click Next>.
- Click Next> to move the next box.
- Click Finish to accept your graph. Concentration (M) vs Time
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0 5 10 15 20 25 30 35 Time (min)
Concentration (M)
Note: To make additional graphs with data that is not in adjacent columns, click on cell C1 and select the time data as done before. Now, instead of dragging to the next column, hold down the Ctrl key and then click on cell E1 and drag down to select the logarithmic data. You should then have 2 columns highlighted. This is the data that will be plotted. The first column will be your time data that will be plotted on the x-axis and the second column selected is the y-axis data. Follow the instructions above to generate the graph associated with a first order reaction. Repeat these instructions for the final graph which will be 1/A vs. time.
Data Analysis in Excel To determine the linearity of a graph, you need to find the correlation coefficient, R^2 , and the equation for the line. Use the following instructions to add a trendline and these statistics to your graph.
- Click on a data point , right click to open up a selection box and select “Add Trendline”.
- A selection of options for adding trendlines will arise. Make sure the box labeled “linear” is selected and then click on the Options tab.
- Select “Display Options” on Chart
- Click on box in front of “Display R^2 Value on Chart and “Display Equation on Chart” to put arrows in the selection boxes.
- Click OK.
- Your graph will now have these statistics on the graph.
Formatting Graphs in Excel You will need to format your graph to make it easier to read. Use the following instructions to change the graph as needed.
Text boxes All 3 titles and the legend box act as text boxes and can also be directly edited as a text box. The box within the graph containing the statistics also can be manipulated as a text box. Right clicking on “clear” will remove the box.
Axes You can format the axes by clicking on the axis and right clicking to bring up the format axis box. There are several tabs that allow you to change the scale on the axis and edit the font, alignment and several other attributes associated with the axes.
Other graph features The legend box to the right of the graph, the gridlines and the plot area can all be edited by clicking on them and then right clicking to bring up a text box with different options. Clicking Clear will remove the legend box, gridlines and the color of the plot area.
Size and shape of graph Clicking in an open area of the graph treats the graph as an object and allows you to stretch it or shrink it horizontally or vertically to achieve the look you desire.
Importing graph into other programs Click on the graph so that small black boxes show up on the outer borders of the graph. Right click to bring up a dropdown menu of options. Click “copy” to copy the graph and then “paste” into other document. If you prefer to print each graph separately, when the black boxes are showing on the graph, it is all set to print out as a full-size page.
Concentration (M) vs Time
y = -2E-07x + 6E- R^2 = 0.
-0.
0
0 5 10 15 20 25 30 35 Time (min)
Concentration (M)
Determining the integrated rate Laws for experiments 1 and 2 Use the table below to find the integrated rate law that corresponds to the order of reaction with respect to the crystal violet.
Order of reaction Rate equation Integrated rate law Zero order: Rate = k [CV] = -kt + [CV 0 ] First order: Rate = k[CV] ln[CV] = -kt + ln[CV 0 ] Rearrange: ln([CV]/[CV 0 ]) = -kt Second order: Rate = k[CV] 2 1/[A] = kt + 1/[A 0 ]
Record the equations for a line from each of the graphs that you used to determine the order of reaction with respect to crystal violet.
Writing the integrated rate laws for experiments 1 and 2 Use the table below to make the correct substitutions to convert the equation for a line that you used to find the order of reaction for crystal violet into the integrated rate law for each experiment. Note that the two integrated rate laws be different because the rate of disappearance of crystal violet varies due to the concentration of the sodium hydroxide.
Old Variable Definition New Variable y concentration of reactant (M) [CV] or ln[CV] or 1/[CV] m slope =rate constant of reaction k (not same k as found in initial rates) x time in minutes t b y-intercept=initial amount of CV (M) [CV 0 ] or ln[CV 0 ] or 1/[CV 0 ]
Discussion Questions
You must use your data to answer these questions. If the answer you give does not reflect YOUR data and results, you will receive no credit for the question.
Write the rate law equation that you developed for the crystal violet/sodium hydroxide reaction. Based on this experimentally determined rate law equation, calculate the reaction rate if you doubled the initial concentration of crystal violet. Show all work. (This problem may be hand written)
Give two specific sources of error in your experiment. Explain the impact of these errors on generating the order of the reaction with respect to the crystal violet. Explain how they could be minimized in the future. (If you use the phrase “human error” in your experiment, you lose all credit!)
Write the two integrated rate law equations for your two experiments. Explain why there are differences between these two equations. What restrictions were required for you to generate the integrated rate law equations?
Calculate the concentration of crystal violet in the solution after 5.0 minutes using your integrated rate law equation when the concentration of sodium hydroxide is 0.01M and again at 0.02M. Show all work. (This problem may be handwritten)
Give 1 example each explaining how knowing the rate law equation and the integrated rate law can help you to modify a reaction.
