Identifying the Kinetic Parameters of Crystal Violet Dye and Sodium Hydroxide

SUMMARY

The objective of this experiment was to determine the kinetic parameters for the reaction between crystal violet dye (CVD) and sodium hydroxide (NaOH). The reaction was investigated at temperatures of 25, 30, 35, and 40°C using a method of excess, which implies a 1000:1 ratio of CVD:NaOH concentrations. The completion of the reaction was monitored using a spectrophotometer to determine the absorbance of the reaction mixture at 590nm. The experimental data was used to calculate the concentrations of CVD during the reactions and generate plots for concentration versus time. The kinetic parameters (rate constants, Arrhenius factor, and activation energy) for the reaction were determined from the experimental data and plots.

The behavior of the reaction rate aligned with the expected behavior for reaction rate at increased temperatures under a method of excess. The first reaction at room temperature (25ᵒC) proceeded at the slowest rate and reached completion after approximately 40minutes; the subsequent reactions proceeded at a faster rate for each increase in temperature [Figure 1]. Although the overall reaction is considered third order, the process becomes pseudo-first-order under the method of excess, confirmed by the linear behavior of the integrated rate law [Figure 2]. From the experimental data, the activation energy of this experiment was determined to be Ea=62693.4 J/mol. This value is relatively close to other reported values of activation energy for this reaction. When the hydroxide ion is obtained from an acetone solvent, the activation energy at 25°C is approximately 63178 J/mol (Turgeon & LaMer, 1952). The pseudo-first-order rate laws were related to actual third order rate law assuming a constant concentration of NaOH. From the experimental data, the Arrhenius factor of the third order reaction was determined to be A = 6035.13 L2/mol2min. The high value was expected because the pre-exponential Arrhenius factor corresponds to the collision frequency of the gas kinetics. There were two primary sources of error during this experiment: lack of precision during temperature adjustments, plus lag-time between reaction sampling and absorbance measurements. Although these were considered the primary source of error, the impact of these errors was assumed to be relatively small because the problem was distributed throughout the experiment’s entirety. Additionally, throughout the entire experiment, the method of excess was used to assume that the concentration of sodium hydroxide was constant. The real behavior of the NaOH concentration likely includes a slight degree of change, causing the deviation from ideal behavior.

Understanding the process behind determining parameters or mechanisms of reactions is essential for a successful career in chemical reaction engineering. It is essential to study reaction kinetics on a small-scale to determine important conditions, factors, or parameters that have a large impact on the ability of the process to reach completion.

INTRODUCTION AND OBJECTIVE STATEMENTS

During this experiment, the reaction between crystal violet dye (CVD) and sodium hydroxide (NaOH) was carried out at four different temperatures. The underlying goal of this experiment was to determine the kinetic parameters for the reaction; including the rate constant as a function of temperature, the activation energy, and the Arrhenius factor. Due to the intense purple color of CVD, the reaction can be monitored through absorbance spectroscopy at a wavelength of 590nm. When CVD reacts with hydroxide ions, it turns from purple into a clear colorless liquid. At low concentrations, such as those used in this experiment, the concentration of CVD is proportional to the measured absorbance as defined by Beer’s Law. The reaction rate is a function of temperature that can be described by the Arrhenius equation. By combining these known behaviors plus a method of excess, the kinetics of the reaction can be studied relatively easily.

The material studied in chemical reaction engineering provides a fundamental skill set to the practicing chemical engineer. Understanding the process behind determining parameters or mechanisms of reactions is essential for a successful career in chemical reaction engineering. It is essential to study reaction kinetics on a small-scale to determine important conditions, factors, or parameters that have a large impact on the ability of the process to reach completion.

PROCEDURES

A complete detailed description of the methodology followed for the experiment was provided in the pre-lab report [Appendix-1]. The reaction of crystal violet dye (CVD) in the presence of sodium hydroxide (NaOH) was investigated at temperatures of 25, 30, 35, and 40°C under constant agitation of 200rpm. The reaction was conducting using the method of excess, which implies a 1000:1 ratio of CVD:NaOH concentrations. Appropriate reactant dilutions were made so that the initial concentrations in the reaction vessel are 10-2M and 10-5M for NaOH and CVD, respectively. The completion of the reaction was monitored using a spectrophotometer to determine the absorbance of the reaction mixture at 590nm. Samples of the reaction mixture were taken periodically and added to a cuvette to measure absorbance and subsequently returned to the reaction vessel. Samples were taken until the reaction was complete, indicated by an absorbance measurement below 0.1. The reactions at 35 and 40°C occurred much faster than the reaction at lower temperatures. For this reason, absorbance readings were taken more often. The experimental data was used to calculate the concentrations of CVD during the reactions and generate plots for concentration versus time. The kinetic parameters (rate constants, Arrhenius factor, and activation energy) for the reaction were determined from the experimental data. Exact values of reagents used for the experiment are summarized below.

Reactant Concentrations and Volumes Used

Reactant Stock Concentration Stock Volume Reaction Concentration Reaction Volume

Sodium Hydroxide (NaOH) 1 mol/L 5mL 10-2 mol/L 500mL

Crystal Violet Dye (CVD) 10-3 mol/L 5mL 10-5 mol/L

Table 1 – Reactant Concentrations and Volumes

PRESENTATION OF RESULTS

The measured absorbance of the reaction mixture at 590nm was used to calculate the corresponding concentration of CVD using Beer’s Law.

A_t=εl〖[CVD]〗_t

Equation 1 – Beer’s Law

Where: At = Absorbance at time t

ε = Molar Absorptivity of Crystal Violet = 5x102 (L/mol*cm)

l = Cell Path Length = 2.54cm

[CVD]t = Concentration of CVD at time t (mol/L)

Data for Reaction at Room Temperature (≈25°C)

Time (min) Absorbance @ 590nm Concentration (mol/L) ln(Concentration)

0 1.279 1.90E-05 -10.87

10 0.335 4.78E-06 -12.25

20 0.155 2.07E-06 -13.09

30 0.081 9.56E-07 -13.86

40 0.08 9.41E-07 -13.88

Table 2 – Table of Absorbance and Time for Reaction at 25ᵒ C

Data for Reaction at 30°C

Time (min) Absorbance @ 590nm Concentration (mol/L) ln(Concentration)

0 0.713 1.05E-05 -11.47

4 0.42 6.06E-06 -12.01

8 0.316 4.49E-06 -12.31

12 0.152 2.03E-06 -13.11

16 0.075 8.66E-07 -13.96

Table 3 – Table of Absorbance and Time for Reaction at 30ᵒ C

Data for Reaction at 35°C

Time (min) Absorbance @ 590nm Concentration (mol/L) ln(Concentration)

0 0.702 1.03E-05 -11.48

1 0.59 8.62E-06 -11.66

2 0.49 7.11E-06 -11.85

3 0.406 5.85E-06 -12.05

4 0.333 4.75E-06 -12.26

5 0.264 3.71E-06 -12.50

6 0.236 3.29E-06 -12.62

7 0.198 2.72E-06 -12.82

8 0.164 2.21E-06 -13.02

9 0.132 1.72E-06 -13.27

10 0.123 1.59E-06 -13.35

11 0.118 1.51E-06 -13.40

12 0.094 1.15E-06 -13.67

Table 4 – Table of Absorbance and Time for Reaction at 35ᵒ C

Data for Reaction at 40°C

Time (min) Absorbance @ 590nm Concentration (mol/L) ln(Concentration)

0 0.721 1.06E-05 -11.4553355

1 0.593 8.67E-06 -11.65616415

2 0.458 6.63E-06 -11.92349293

3 0.342 4.89E-06 -12.22911784

4 0.238 3.32E-06 -12.61550568

5 0.183 2.49E-06 -12.90243218

6 0.145 1.92E-06 -13.16328701

7 0.121 1.56E-06 -13.37183177

8 0.104 1.30E-06 -13.55125896

9 0.083 9.86E-07 -13.82935324

Table 5– Table of Absorbance and Time for Reaction at 40ᵒC

Figure 1 –Plot of Concentration vs. Time for Reaction at Various Temperatures

Although the known rate law is third order overall, the method of excess assumes the change in concentration of NaOH is negligible resulting in a pseudo first order reaction.

Rate=r=k〖[〖OH〗

-]〗

2 [CVD]

Equation 2 – Known Rate Law for Reaction of CVD and Hydroxide Ion

Rate=r=k

' [CVD]

Equation 3 – Pseudo-First-Order Rate Law for Reaction of CVD and Hydroxide Ion

k=k

'/〖〖[OH〗

-]〗

2

Equation 4 – Relationship Between Actual Rate Constant and Pseudo-Rate Constant

Where: k = Actual Rate Constant (L2/mol2min)

k’= Pseudo-Rate Constant (min-1)

[OH-] = Concentration of Hydroxide Ion (mol/L)

[CVD] = Concentration of CVD (mol/L)

By plotting the integrated pseudo-first-order rate law, the rate equation can be modeled as a linear equation where the pseudo-rate constant is equal to the slope of the line.

y=mx+b

Equation 5 – Generic Linear Equation

ln