CHY116 Kinetics of Fading Indicators

Several factors influence the rates of chemical reactions: the identity and inherent chemical reactivity of the reactants; the concentrations of the reacting species which affects molecular collisions; and temperature which affects the energetics of the molecular collisions. By measuring the concentration of CV+ as it changes over time, the kinetics of this “fading” reaction can be followed. It is expected that as the reactant concentration P2- decreases, the rate of reaction will also decrease. Exactly how much the rate decreases depends on the rate law for the reaction. The rate expression for the reaction CV+ +  OH- --> CVOH has the general form  

          Rate = k[CV +]n[NaOH]m                                                                                  (Equation 2)

The exponents n and m are defined as the order of reaction for each reactant, and k is the rate constant for the reaction at a particular temperature. The unknowns k,n, and m, must be determined experimentally. By using a large excess of hydroxide ions, the reaction can be carried out under conditions where the concentration of OH- remains essentially constant. As a result, the rate law will reduce to a “pseudo-order” rate law

          Rate = k1[CV + ]n                                                                                              (Equation 3)

where k1 is the “pseudo” rate constant incorporating both the “true” rate constant k and the experimental constant [OH-]m term (k1 = k[OH-]m). In this pseudo-order approach, the concentrations of all reactants, other than the one being measured, are at least 104 times greater than the concentration of the measured reactant. Only the measured reactant concentration will change significantly during the course of the reaction. The other reactants have such large concentrations that they essentially do not change as the reaction proceeds, and their values can be combined with the rate constants to give the pseudo-order rate law. With a large excess of hydroxide ions, the “fading” reaction will behave as if it is n-order in reactant CV+; the dependence of rate on the hydroxide ion is now incorporated in the rate constant kl.

To determine the concentration of CV+, the absorbance of the violet color can be measured spectrophotometrically (UV-Vis spectroscopy).  According to Beer’s Law (Equation 4), absorbance (A) is directly proportional to the concentration of the absorbing species – a convenient way to measure changes in concentration is to monitor the absorbance.  

           A = EbC                                                                                                             (Equation 4)

where E is the molar absorptivity, b is the pathlength through the cell, and C is the concentration of the species of interest. For a given molecule at a specific wavelength, molar absorptivity is constant, and the pathlength is fixed by the cell or cuvette Consequently, absorbance A varies only with the concentration C of the absorbing species. In Reaction 1, the indicator is colored, while the hydroxy ions are colorless; the kinetics of the reaction can therefore be followed by monitoring the amount of light absorbed by the indicator over time. 

Graphing the results of absorbance vs. time can be done to determine the order of the reaction in CV+ and the pseudo-rate constant k1.  Mathematical treatment of the equations for the reaction rate and the rate law predicts the following outcomes:

•   If the “fading” reaction is first order in [CV+] (that is n = 1), a graph of the natural log (ln) of absorbance versus time will give a straight line. The slope of the line is equal to –k1.

• If the “fading” reaction is second order in [CV+] (that is n = 2), a graph of 1/absorbance versus time will give a straight line. The slope of the line is equal to k1.

Mathematically, m can be calculated from the pseudo-rate constant and the known concentrations of the NaOH solutions. Knowing the value of m, the order of the reaction in NaOH can be determined and the overall rate constant k can be calculated. Since k1 = k[OH-]m, k can be evaluated if the reaction rate is measured at several different concentrations of NaOH. If m = 0, then k will be equal to k1 for all concentrations of NaOH; if m = 1, then k equals k1 divided by [NaOH] and k1/[NaOH] will be constant for all concentrations of NaOH; if m = 2, then k equals k1 divided by [NaOH]2 and k1/[NaOH]2 will be constant for all concentrations of NaOH. 

Pre-lab Assignment (pdf version) 

Notebook Preparation

In your lab notebook, prepare the following information: 

•         The objectives of the lab. 

•         A table of the chemicals that you will use in the experiment. The list of the chemicals and their Safety Data Sheets (SDS) can be found on the experiment’s page on the lab manual website. For each chemical, include the following: name, molecular formula, molar mass, any other useful properties (melting point, density, etc.), and hazardous effects from exposure. These can be found in Section 2 of the SDS under the subheading “Classification”.

•         A list of the equipment/glassware that you will need. Labeled diagrams are acceptable. 

•         An overview of the procedure. Use bullet points. 

•         Include the following preliminary calculations in your procedure overview.

Preliminary Calculations

Include these preliminary calculations in the procedure overview section of your notebook preparation. These represent the actual amounts that you will be using in the lab. 

Part 1 – Creation of Crystal Violet Calibration Curve

In this lab you will be preparing a series of solutions of crystal violet at different concentrations. Use the dilution equation (M1 * V1 = M2 * V2) to calculate the concentration of the crystal violet standard solutions after dilution (M­2). 

Crystal violet standards

Solution #1

Concentration of crystal violet stock solution (M): 0.0000300 M

Volume of crystal violet stock solution (mL): 0.00 mL

Volume of standard solution after dilution. (mL): n/a

Calculated concentration of standard solution (M­2): 0.00 M

Solution #2

Concentration of crystal violet stock solution (M): 0.0000300 M

Volume of crystal violet stock solution (mL): 1.00 mL

Volume of standard solution after dilution. (mL): 10.00 mL

Calculated concentration of standard solution (M­2): _______M

Solution #3

Concentration of crystal violet stock solution (M): 0.0000300 M

Volume of crystal violet stock solution (mL): 4.00 mL

Volume of standard solution after dilution. (mL): 10.00 mL

Calculated concentration of standard solution (M­2): _______M

Solution #4

Concentration of crystal violet stock solution (M): 0.0000300 M

Volume of crystal violet stock solution (mL): 8.00 mL

Volume of standard solution after dilution. (mL): 10.00 mL

Calculated concentration of standard solution (M­2):_______M

Solution #5

Concentration of crystal violet stock solution (M): 0.0000300 M

Volume of crystal violet stock solution (mL): n/a

Volume of standard solution after dilution. (mL): n/a

Calculated concentration of standard solution (M­2): _0.0000300_M

Part 2 – Measuring Absorbance as Crystal Violet Fades

In the lab you will be preparing four NaOH solutions varying in molarity between 0.10 M and 0.040 M. A stock solution of 0.10 M NaOH will be diluted to these concentrations and a volume of 25.00 mL. Use the dilution equation (M1V1 = M2V2) to calculate the volume of the 0.10 M NaOH stock solution that you will need to prepare the following mixtures: 

Mixture #2:   0.080 M NaOH

Mixture #3:   0.060 M NaOH

Mixture #4:   0.040 M NaOH

Procedure

Detailed procedures involving the use of Vernier LoggerPro equipment and software will be provided in the lab. 

Part 1 – Creation of Crystal Violet Calibration Curve

A calibration curve is a graph that establishes the mathematical relationship between the concentration of crystal violet and the absorbance. You will use this graph to derive an equation with which you can calculate the concentration of crystal violet from the measured absorbance. To make the calibration curve, you will prepare a series of solutions of crystal violet at different concentrations and then use the spectrophotometer to measure their absorbance. These solutions, whose concentration will be known, are known as standard solutions. 

o   Standard #1: fill a cuvette (rectangular plastic vial) about ¾ full of deionized water. This will be the blank solution. 

o   Standard #2: get a 10 mL graduated volumetric pipet. You will need to use this pipet to measure 1.00 mL of crystal violet stock solution. Notice how the pipet is labeled. Find the line that will allow you to measure and deliver 1.00 mL of solution. Use the pipet to accurately measure 1.00 mL of crystal violet stock solution into a 10 mL volumetric flask. Dilute to the 10.0 mL line with deionized water. Cap the flask and invert several times.

o   Standard #3: use a glass pipet to accurately measure 4.00 mL of crystal violet stock solution into a 10 mL volumetric flask. Dilute to the 10.0 mL line with deionized water. Cap the flask and invert several times.

o   Standard #4: a glass pipet to accurately measure 8.00 mL of crystal violet stock solution into a 10 mL volumetric flask. Dilute to the 10.0 mL line with deionized water. Cap the flask and invert several times.

o   Standard #5: fill a UV-Vis cuvette (rectangular plastic vial) about ¾ full of crystal violet stock solution. The concentration of the stock solution is 3.00 * 10-5 M (moles per liter). 

Now you will measure the absorbance of the standard solutions. In the pre-lab assignment, you calculated the concentration of crystal violet in the standard solutions. Generate a table in your lab notebook with the first column labeled "crystal violet standard #,' the second column labeled "calculated concentration of standard solution (M),' and the third column labeled "measured absorbance of standard at ___nm (λmax)." Fill in the calculated concentrations from the pre-lab assignment.

o   After you have made the standard solutions, you will measure their absorbance in the spectrophotometer. There will be instructions in the lab to guide you through this process. 

o   Record the calculated concentrations, the corresponding absorbance values, and the analytical wavelength (λmax) in your lab notebook.

Part 2 – Measuring Absorbance as Crystal Violet Fades

This part of the lab involves running the fading reaction four times. In each run, the concentration of sodium hydroxide will be changed. As a result, each mixture will contain a different number of ions. To keep the ionic strength constant, you will combine each sodium hydroxide solution with a complementary volume of sodium chloride solution (NaCl). 

o   Get a 25 mL volumetric flask. Accurately measure 25.00 mL of the 0.10 M NaOH stock solution into the volumetric flask. Pour the mixture into a 125 mL (or similar size) Erlenmeyer flask. 

o   Measure 15.0 mL of crystal violet stock solution into a 25 mL graduated cylinder. Don’t add it to the flask yet. 

o   Prepare the spectrophotometer to read absorbance over time. There will be instructions in the lab to guide you through this process.

o   Pour the crystal violet into the NaOH solution. Swirl to mix and then quickly fill a cuvette ¾ full of the mixture. Put the cuvette into the spectrophotometer and let the experiment run for the prescribed time. Copy the time and absorbance data into your lab notebook.

o   Run the procedure with the NaOH solution at 0.080 M. Use the volumes of NaOH that you calculated from the pre-lab. Use the NaCl solution to bring the total volume of the NaOH/NaCl mixture to 25.00 mL. Use 15.0 mL of crystal violet solution for each run. 

o   Repeat the procedure with NaOH at 0.060 M and then at 0.040 M. 

References

Lois Nicholson, Kinetics of the Fading of Phenolphthalein in Alkaline Solution J. Chem. Ed. 1989, 66(9), 725-726.

www.unomaha.edu/tiskochem/APchem/AP_labs/kinetics_Fading_of_Indicators.pdf

http://faculty.ccri.edu/aahughes/GenChemII/Lab%20Experiments/Phenolphthalein_NaOH_Kinetics.pdf

CHY116 Grading Rubric (pdf)

Post Experimental Analysis complete the following REPORT FORM.

Report Form   (pdf version)                                                                         

CHY 116: Kinetics of Fading Indicators                                                    Name                                                        

1.) Enter the time (t) and absorbance (A) data for each solution into an Excel spreadsheet. Then use Excel to calculate ln(A) and 1/A for each solution. Your spreadsheet may be set up similar to the following:

When calculating ln(A) in Excel, type =ln(cell number) in an empty cell next to the corresponding absorbance and time value. The equal sign tells Excel that you are doing a calculation and the cell number is ColumnRow (ex: B3). To calculate 1/A, type =(1/cell number). For example =(1/B3).

2.) Use Excel to plot the data as ln(A) (vertical axis) vs. time (horizontal axis) and 1/(A) (vertical axis) vs. time (horizontal axis) for each concentration of NaOH. Put all six curves for ln(A) vs. time on the same graph; likewise, plot all six curves for 1/(A) vs. time on a separate graph.

To determine if the overall reaction is first order or second order with respect to crystal violet, fit a straight line to the data, and obtain the equation of the line and the regression coefficient (R2). Label the axes of the graph and give it an informative title from which the reader can readily understand the relationship represented on the graph. Make two copies of the graphs. Hand in one copy with your notebook pages and report form, and tape the other one into the corresponding white pages of your lab notebook. In the spreadsheet, include the slope and R2 value for each solution (see example spreadsheet in Question 1).

3.) If the overall reaction is first order in CV+, all four curves of ln(A) vs. time will be linear; if the overall reaction is second order in CV+, all four curves of 1/A vs. time will be linear. Is the reaction first or second order in CV+ (what is the value of n)? Explain your answer

4.) Evaluate the pseudo-rate constant, k1, from the slope of each plot that is linear. Put this value, as well as the actual NaOH concentration into the Excel spreadsheet. This can be a new section of the spreadsheet. For example:

In which column, A, B, or C is the calculated value of k constant for all six NaOH solutions? (Which column has the lowest %RSD?)

6.) Is the reaction zero, first, or second order in NaOH (what is the value of m)?

7.) What is the overall rate constant value, k?

8.) What is the overall rate law expression for the reaction (Equation 1)?

Turn in stapled together:

1.) Your Excel spreadsheet including graphs, 

2.) All pages of this Report Form, and 

3.) A word-processed single paragraph summary of the experiment. Type a brief (5-10 sentences) summary of this experiment. The following should be included in the summary: 

1.      A topic sentence(s) describing the goal of the experiment.

2.     A description of the results/outcomes of the experiment – don’t include procedural details or intermediate calculations. Include uncertainties associated with numerical results. If literature values are available, include a comparison between the experimental results and literature values. Include % error if a literature value is available.

3.     A description of source(s) of error for this experiment. (This is usually the uncertainty associated with whichever instrument was used to record the data.) Do not cite human error.

4.     A conclusion sentence.