Measuring Rates
You will turn in this assignment. It will count as a lab grade.
Experiment: 100 mL of 1 M HCl is added to about 60 g of CaCO3 (marble) chips.
CaCO3(s) + HCl(aq) = CO2(g) + CaCl2(aq) + H2O(l)
- Balance the equation
- Name two ways that one might measure the rate of this reaction.
- How does the rate of disappearance of HCl relate to the rate of formation of CO2?
- If the reaction is performed in an open container, why can we ignore the reverse reaction?
- What will happen to the rate as the reaction proceeds? Why?
- Although CaCO3 is consumed by the reaction, its consumption does not affect the rate of the reaction. Why?
- Reproduce and complete the following table in Excel. Rather than using your calculator, let Excel do the calculations for you. See me if you don’t know how to do this.
Time (s) / Mass (g) / Mass
loss (g) / Moles CO2
produced / Moles HCl
consumed / Moles HCl
remaining / [HCl] (M) / ln[HCl] / 1/[HCl]
(M-1) / Avg. Rate
(M-s-1)
(T = 30 s)
0.00 / ------
30.0
60.0
90.0
120.0
150.0
180.0
210.0
240.0
270.0
300.0
Note: For the last column, calculate the average rate of loss of HCl in each 30 second time interval. (Calculate the change in the concentration of HCl in each 30 second interval and divide by 30 s.
Make 3 graphs in excel:
a.[HCl] vs. time (Draw in a smooth curve by hand. Do NOT use excel to draw the curve.)
b.ln [HCl] vs. time
c.1/[HCl] vs. time
To determine whether this reaction is first or second order with respect to [HCl], add trend lines to graphs b and c and determine which graph gives a better straight line. Show the equation and the R2 value for each graph. The graph that gives an R2 value closest to one is the best line.
- The rate equation for this reaction is:
rate = k[HCl]x
Our job is to determine x and k
- Why is [CaCO3] not included in the equation?
- Based on your graphs, is the reaction first or second order with respect to [HCl]?
- What is value of the rate constant? (include the unit)
- What is the rate of the reaction if [HCl] = 2.00 M
- When the rate of CO2 production is 5.00 M-min-1, what is the concentration of HCl ? (Be careful with units and remember thatthe rate equation above gives the rate of consumption of HCl.)
- On your graph of [HCl] vs. time (graph a), indicate the first and second half-lives as you did in question 1 on page 6 of ws13.3. You may have to extrapolate to determine the second half-life.
- First half life (approximated from graph) = ______
Second half-life (approximated from graph) = ______
- Is the relationship between the first and second half-life consistent with the order of the reaction that you determined above? Explain.
- Calculate the first and second half-lives using the appropriate half life equation (see page 5 of ws13.3). If you use the second order half-life equation, [A]o is 1.00 M for the first half-life and 0.50 M for the second half-life. Compare your answers to those in part a.
First order half-life equation: Second order half-life equation:
(Note: You will use only one of these two equations depending on whether the reaction is 1st or 2nd order.)
- Use the appropriate integrated rate equation to calculate how long it would take for the concentration of HCl to drop from 1.0 M to 0.10 M.
First order integrated rate law: ln[A]t = -kt + ln[A]0
Second order integrated rate law:
(Note: You will use only one of these two equations depending on whether the reaction is 1st or 2nd order.)
Experiment 13H: The Reaction of Red Food Color with Bleach
Although we did not do Experiment 13H, you must understand the method used in the experiment. There is also an important new concept in the experiment that was not needed for the reaction of marble with hydrochloric acid:
How do you determine the rate equation for a reaction that has two aqueous reactants?
Read pages 1-3 of Expt. 13H and answer the following questions:
Preparation of Red Dye Solution by Serial Dilution
The concentration of the bleach (OCl−) added to each reaction was 0.821 M.
The red dye solution added to each reaction was prepared by diluting a 6.76 x 10-3 M stock solution as follows:
Dilution 1: Pipette 5.00 mL of 6.76 x 10-3 M Dye into a 100.0 mL volumetric flask and dilute to the mark with water. Mix by inversion.
Dilution 2: Pipette 5.00 mL of the solution made in dilution 1 into a 100.0 mL volumetric flaks and dilute to the mark. Mix by inversion.
Calculate the concentration of the red dye after dilution 2. (This is the solution added to each reaction.) Show your work below:
Starting the reactions
Three reactions were performed. The concentration of the red dye was the same in each reaction. The concentration of the bleach (OCl−) was different in each reaction. The table below shows how each reaction mixture was prepared. Calculate the initial concentrations of each reactant ([dye]o and [OCl−]o) and enter these values in the table. You do not have to show your work for these calculations.
Rxn # / Volume of dye added (mL) / Volume of OCl− added (mL) / Volume of water added (mL) / [dye]o (M) / [OCl−]o (M)1 / 2.00 / 1.00 / 3.00
2 / 2.00 / 2.00 / 2.00
3 / 2.00 / 3.00 / 1.00
Measuring reaction rates
The consumption of the red dye over time was monitored by measuring the absorbance every 30 seconds using light with a wavelength of 530 nm. The first reaction was monitored for 900 seconds. Reactions 2 and 3 were monitored for only 60 s. The data are shown below. Transfer the data to Excel. For all three reactions, use Beer’s law to calculate [red dye] at each time point. For reaction 1, calculate ln[red dye] and 1/[red dye] for each time point. Use formulas to do the calculations.
Beer’s law is: A = cl where A is the measured absorbance, is the molar absorptivity of the red dye
(M-1-cm-1), c is the concentration of the red dye (M), and l is the path length (cm). For this experiment, M-1-cm-1 and l = 1.00 cm.
Reaction 1:
Time (s) / Absorbance / [red dye] (M) / ln[red dye] / 1/[red dye] (M-1)0 / 0.349
30 / 0.334
60 / 0.318
90 / 0.304
120 / 0.289
150 / 0.281
180 / 0.266
210 / 0.255
240 / 0.242
270 / 0.232
300 / 0.220
330 / 0.210
360 / 0.200
390 / 0.190
420 / 0.182
450 / 0.173
480 / 0.164
510 / 0.157
540 / 0.148
570 / 0.140
600 / 0.134
630 / 0.126
660 / 0.118
690 / 0.113
720 / 0.106
750 / 0.101
780 / 0.095
810 / 0.090
840 / 0.086
870 / 0.081
900 / 0.077
Reaction 2:
Time (s) / Absorbance / [red dye] (M)0 / 0.324
30 / 0.302
60 / 0.263
Reaction 3:
Time (s) / Absorbance / [red dye] (M)0 / 0.333
30 / 0.286
60 / 0.240
You will use the graphical method to determine the order with respect to the dye (a). You will use the initial rate method to determine the order with respect to OCl¯ (b) and the rate constant (k).
Graphical method (finding a)
In order to use the graphical method, the concentration of only one reactant can change during the reaction. Look at the initial concentrations of the reactants calculated on page 5 and explain why the concentration of the bleach does not change significantly during the reactions.
The rate equation for this reaction is:
Rate = k[red dye]a[OCl¯]b
Since [OCl¯] does not change during this reaction, [OCl¯]b is a constant and can be combined with k to give what is called a “pseudo rate constant” whose symbol is k’.
k’ = k[OCl¯]b
Use the data from reaction 1 and the graphical method to determine the order of the reaction with respect to the red dye. Record the order below:
a =
How would you change the experiment if you wanted to use the graphical method to calculate the order with respect to OCl¯?
Unlike the reaction between calcium carbonate and HCl which had only one aqueous reactant, the magnitude of the slope of your straight line is NOT the rate constant. Instead, it is the pseudo rate constant. What is the value of k’ (include the unit)?
K’ =
Initial Rate Method (finding b and k)
Use the first 60 seconds of each of the three reactions to calculate the initial rate (rateo) of each reaction. Recall that the initial rate is the instantaneous rate at time zero. Although it is impossible to measure this rate, it can be approximated as the average rate after a very short period of time. Calculate the average rate of each reaction for the first 60 seconds and complete the table below. (Copy the initial concentrations from the table above.) Show your work for reaction 1 below the table.
Rxn # / [dye]o (M) / [OCl−]o (M) / rateo (M-s-1)(in first 60 s)
1
2
3
Use the initial rate data above to determine the order of the reaction with respect to OCl−. Show your work or explain your logic. Enter the value of b below.
b =
Use the rate equation and the initial rate data to calculate the value of the rate constant (include the unit). Remember that the rate equation is: rate = k[red dye]a[OCl¯]b and you now know the values of a and b. You have 3 different values for [OCl−] so calculate 3 values for k and determine the average. Show your work for one of the calculations and complete the table below.
Rxn # / k(include the correct unit)
1
2
3
Avg.
Another way to calculate the value of the rate constant is to use the pseudo rate constant determined above:
k’ = k[OCl¯]b
You determined k’ for reaction 1 and you determined b from the initial rate data. Use the concentration of OCl¯ in reaction 1 and the equation for k’ to calculate the value of k (include the unit). This should give you the same value for k as you calculated above. Show your work below.
k =
Write the rate equation for this reaction by inserting your experimental values for a, b, and k:
rate =
Directions for report:
- Answer all of the questions on the worksheet in the spaces provided. Clearly show all of your work for calculations (unless told that no work is required). Since you will use Excel to complete the calculations for the spreadsheet, you don’t have to show your work for those calculations.
- Print your excel spreadsheets and graphs and attach them to the worksheet. Send me your Excel file as an e-mail attachment. I will check them to make sure that you used Excel to do the calculations in the spreadsheet.
Guidelines for tables made in excel (see me if you need help with any of the following):
- The column headings should be centered over the data in each column.
- Column heading should include units when appropriate.
- Use the correct number of significant figures.
Guidelines for graphs made in excel
- Graph should have a descriptive title.
- Label axes with a descriptive title. Give units in parentheses.
- Make graph big enough to see easily.
- Delete the legend unless there is more than one curve shown on the graph (this will make your graph larger).
- Number the scale on each axis but avoid crowding of the numbers and use a minimal number of digits.
- Adjust the scale on each axis so the curve fills as much of the graph as possible (don’t waste space). You do not necessarily have to start a scale at zero!
Make sure that the spreadsheet is formatted so each table and graph fit on a single page when they are printed. (Students’ printouts often have ½ of a table or graph on one page and the other half on another page!)
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