Introduction
The kinetic characteristics are important for the design of chemical engineering processes. They allow assessing the time required for the reaction and choosing the temperature range suitable for the reaction.
The reaction path is observed by measurments the transmittance of the Crystal Violet solution that reacts with sodium hydroxide. The concentration, and the color of the solution changes with the reaction flow, and this is measured by the spectrophotometer.
The data are plotted as concentration - time and logarithm concentration time, and the reaction rate is:
Rate = [Crystal Violet] [Sodium Hydroxide].
Using the excess concentration of one of the reagents, the reaction rate with respect to the other reagent is found from logarithmic plot (Rahul & Chakrabarti 195):
ln [Ct] = ln [C0] – kt,
where Ct and C0 an is the concentration and t and the initial concentration, k - is the reaction rate coefficient, and t is time. The reaction rate constant is found as slope of the regression line of logarithmic plot.
The activation energy is determined from the reaction rate constant at various temperatures (kT) plotted versus the reverse temperature (1/T):
ln [kT] = ln A – Ea/R∙ 1/T.
The slope of the line is – Ea/R, and this the activation energy can be calculated (Kelter, Mosher, and Scott 653).
Experimental Methods
Part A. Calibration Line
Stock solutions (25 µM, 2.5∙10-5 M) of Crystal Violet were used. 10 ml of calibrations solutions were prepared by adding distilled water to the stock solution.
The spectrophotometer was set to the wavelength 570 nm, the absorbance and transmittance were set at 0 and 100%, respectively.
The stock solutions were measured for transmittance, and the values were recorded. The absorbance was calculated from the transmittance values and used to plot the calibration line.
Part B. Reaction Order by Crystal Violet
0.1 M NaOH was diluted to obtain 10 mL of 0.05 M. 1 mL of the solution was added to a small test tube.
The solution of crystal Violet was prepared by adding 30 mL of 2.5∙10-5 M Crystal Violet to 20 ml of water. The solution with 15 µM concentration was prepared. 9 mL of the prepared above solution was added into the dry screw tube.
1 ml of 0.05 M NaOH was mixed with 9 mL of Crystal Violet solution. The test tube was capped and mixed, then quickly poured into the cuvette.
The cuvette was wiped with Kim wipe and put into the spectrometer. Once it was done, the stopwatch was started. The transmittance was measured every 30 seconds for 15 minutes and recorded. The transmittance was converted into absorbance, and the concentration determined using the calibration line.
The concentration versus time, logarithm of concentration versus time were plotted.
Part C. Kinetic Analysis: Reaction Order with Respect to Sodium Hydroxide
1 mL of 0.0250 M NaOH and 9 mL of 15 µM Crystal Violet solution were prepared. The solutions were mixed: NaOH (1mL, 0.025 M) with Crystal Violet (9 mL, 15 µM). The test tube was capped and mixed, then poured into a cuvette; the cuvette was wiped with Kim wipe and put into the spectrometer. The time was measured with a stopwatch.
The transmittance was measured with 30 seconds interval for 15 minutes. The data were recorded and processed as described in Part B.
The same procedure was repeated with 0.0125 M NaOH. Basing on the data, the reaction order was determined, and k-value was calculated for both reagents studied in Part A and B.
Part D. Temperature Analysis: Activation Energy
The room temperature was recorded. The hot plate was set, and 250 mL beaker with water was put on it. The test tubes with Crystal Violet (9 mL, 15 µM) and NaOH (1mL, 0.025 M) were installed and heated until water temperature is 45ºC.
Another 250 mL beaker was filled with ice and water was added. The test tubes with the same amounts of NaOH and Crystal Violet were placed.
The beaker was removed from hotplate, and when the temperature reached 40ºC, the solutions were mixed, capped, wiped (as in Parts B and C) and placed into the cuvette. The measurements were performed as in previous sections.
The temperature of the ice beaker was measured. The test tubes with Crystal Violet and NaOH were mixed, and then the procetures were repeated.
The rates were determined, k-values as well. The graphs of log k versus 1/T were plotted, and the activation energy was determined.
Results
Part A. Calibration Line
Preparation of calibration solutions
Spectrometry of the calibration solutions
Part B. Reaction Order by Crystal Violet
Experimental data for reaction order by crystal violet
Figs. 2 and 3 present the graphical interpretation of kinetic of Crystal Violet.
The summary of the kinetic plots
Basing on the highest R2 value, the reaction of Crystal Violet follows second order mechanism.
Part C. Kinetic Analysis: Reaction Order with Respect to Sodium Hydroxide
Experimental data for reaction order by sodium hydroxide
Figs. 5 and 6 present the graphical interpretation of kinetic with respect to sodium hydroxide.
Part D. Temperature Analysis: Activation Energy
Experimental data and calculations for activation energy graphs
Discussion
All of the measurements are obtained as transmittance values and have to be converted in to absorbance. This is realized using formula:
Absorbance (%) = 100% - Transmittance (%).
For example, 63.7% transmittance is: 100% - 63.7% = 36.3% absorbance.
The calibration line (fig. 1) indicates a good fit of absorbance data with the regression line. The determination coefficient value (R2) is 0.8865, and this is close to 1, which indicates that the concentration describes about 89% of variation of absorbance (Miller & Miller 126). Therefore, the line can be used for analytical measurements. The equation of the regression line is:
Absorbance = 6.1143 ∙ Concentration + 15.176
Therefore, the concentration calculates:
Concentration = (Absorbance – 15.176) / 6.1143.
For 75.4% absorbance, the concentration is:
Concentration = (75.4 – 15.176) / 6.1143 = 9.850 µM.
This technique was used to calculate the concentrations at all stages of the experiment.
The concentration – time plots (figs. 2 and 4) indicate the gradual decrease of concentration with time. There are no outliers in the data, which indicates that the experiments were performed accurately, and there are no systematic errors. The observed discrepancies in the data are explained by the random errors (Miller & Miller 8). The concentration decrease profiles are fitted well with the logarithmic lines (R2 > 0.9).
What effect does changing the concentration of OH- have on the reaction?
The increase of OH- concentration, which is the reagent, causes the increase of the reaction rate. The reaction rate constant increases from 0.0001 to 0.0002 1/s, when the concentration increases from 0.0125 to 0.0250 M.
What is the rate of the reaction which is consistent with the data?
ln [Ct] = ln [C0] – kt,
The reaction rates used for activation energy determination are presented in Table 7.
The reaction rate constants at different temperatures
The reaction rate constants at 5 and 22.4ºC are the same, which is explained by the random errors that appeared during the experiment. The random errors are inevitable and occur at all the experiments (Miller & Miller 8).
The reaction rate constants were plotted versus 1/T (fig. 7), and the slope of the reaction equals -Ea/R (Kelter, Mosher, and Scott 653). Although the plot does not indicate the perfect fit (R2 ≈ 0.66), yet the data can be used for calculation of the activation energy. Therefore, Slope = -Ea/R = -0.3881; Ea/R = 0. 3881, and Ea = 3.225 J/mol.
Inhibition questions
i) Yes, it is possible to determine the effect of citric acid on activation energy. First, the experiments for reaction rates at different temperatures have to be performed and the activation energy determined. Then, the cytric acid should be introduced in the system, and the same experiments performed. Therefore, two values of activation energy are available: with and without citric acid.
ii) The data on the oxidation reaction rate and/or activation energy should be available prior to the experiments with citric acid.
iii) The activation energy in presence of citric acid should be higher than without it. Since the citric acid causes inhibition, then the reaction is slowed down, and therefore the activation energy is higher.
Conclusions
The lab assignment aimed at measuring the kinetic characteristics of the reaction between the Crystal Violet and sodium hydroxide. The reacton is first-order reaction. The kinetic profiles of the reagents were plotted, and the reaction rate constants were found from the plots, and they were 0.0002 1/s for Crystal Violet and sodium hydroxide (0.025M), and 0.0001 1/s for sodium hydroxide (0.0125M). The reaction rate constants obtained at warmer and colder conditions were used to calculate the activation energy, which was 0.0017 J/mol.
The experimental data fitted the theoretical lines well; the coefficients of determination were high for concentration - time experiments, and moderate for activation energy plot. The goodness-of-fit indicates that the experiments were accurately performed, and there were no systematic errors.
Works Cited
Banerjee, Rahul, and B K. Chakrabarti. Models of Brain and Mind: Physical, Computational, and Psychological Approaches. Amsterdam: Elsevier, 2008. Print.
Kelter, Paul B, Michael D. Mosher, and Andrew Scott. Chemistry: The Practical Science. Boston: Houghton Mifflin, 2009. Print.
Miller, James, and Jane Miller. Statistics and Chemometrics for Analytical Chemistry. México: Pearson Educación, 2011. Print.
