Analyzing the Influence of Halogen Properties in Kinetics

Abstract

Due to their unique atomic and molecular properties, halogen gases play an important role in industrial and agricultural processes, including the production of pharmaceuticals, agrochemicals, and construction materials. This study investigates the reaction kinetics of hydrogen gas (H₂) with fluorine (F₂), bromine (Br₂), and iodine (I₂), focusing on how electronegativity, atomic size, and bond strength influence their reaction rates. In order to achieve this, trends in the reaction kinetics created, the correlation between reaction rates, and the halogenic properties quantified using computational methods will be analyzed. The data for the reaction rates in the three single-step balanced equations were sourced from experiments referenced in the NIST Chemical Kinetics Database. The temperature (100°C, 373.15 K) and the second reactant (H₂) were held constant throughout the experimentation process, ensuring less room for error and a sole focus on the halogen gases. The reaction rates were calculated in Wolfram Mathematica (MMA) algebraically using the Arrhenius equation and graphically using differential rate equations.  Finally, statistical analysis and correlation plots were generated in RStudio to evaluate the relationships between each halogen’s rate constants and their elemental and molecular properties. These diagrams proved that the three reaction rates followed periodic trends with a strong negative correlation between electronegativity and reaction rate (0.9819), a slightly weaker positive correlation with bond strength (0.9714), and a strong inverse correlation with atomic size (-0.9737). In conclusion, the figures demonstrated the theoretical predictions that fluorine’s small atomic size and high electronegativity result in faster reactions, while iodine’s larger size and lower electronegativity lead to slower reactions. Limitations in the study include the absence of chlorine data and potential rounding errors. In the future, research can expand upon this topic by exploring temperature variations and using advanced computational methods like density functional theory (DFT) to provide a more comprehensive understanding of halogen kinetics.

Key words: Halogenic gases, reaction kinetics, reaction rates, atomic size, electronegativity, bond strength, Arrhenius equation, hydrogen-halogen reactions, differential rate equations

Introduction

Halogen gases play a crucial role in industrial chemical processes and sustainable agricultural practices. Because of the unique properties of these gases and the variations in their atomic properties, the reaction behaviors between them are strikingly different (Chang, Yuan-Pin, et al.). Halogens like fluorine, bromine, and iodine are known for their high electronegativity and their ability to form strong oxidizing agents (Kleinberg, Jacob). Based on periodic trends, fluorine is the most electronegative element in Group 17 because it has only two electron shells, compared to chlorine, bromine, and iodine, which have three, four, and five shells respectively. As the number of electron shells increases, the distance between the nucleus and the valence electrons also increases, reducing the atom’s electronegativity or ability to attract additional electrons (Mastering Periodic Trends). Based on the atoms’ electronegativity, the bond strength, an important molecular characteristic, can tend to be higher in diatomic elements, which are elements that appear in pairs by nature. Fluorine's high electronegativity strengthens the bond with itself to make difluorine. This requires the most energy to break apart or bond dissociation energy (The Periodic Table and Periodic Trends). The bond strength of the predicted hydrogen-halogen compounds decreases in the order F₂ > Br₂ > I₂. This trend affects reaction rates, as weaker bonds (like I₂) require less energy to break, influencing the rate constant (k). Similar to the electronegativity trend, the distance between the valence electrons and protons in the nucleus is directly related to an atom’s atomic size. Since fluorine has the least number of electron shells compared to the rest of the halogens, it is the smallest atom, followed by chlorine, bromine, and iodine. These properties can affect  the speed and reactivity of chemical processes.  (22.3: Group 17: The Halogens). 

Molecules with a larger electronegativity difference between them and the second reactant tend to have strong reactions. In contrast, smaller atomic elements tend to react quickly because of steric hindrance: when a reaction is slowed due to the bulk or size of the atom (Ingold). It is typically used as a tool in organic chemistry to control the selectivity of a reaction by designing molecules with specific bulky groups to favor certain reaction pathways over others (Reactions of Main Group Elements With Halogens). Steric hindrance still plays a major role, however, even if an organic chemistry experiment is not occurring. One example is the current study, which analyzes the variation between the reaction kinetics of fluorine, bromine, and iodine. This study will also focus on the correlation between these variations and the estimated rate constants compared to their molecular and elemental properties. In order to make sure the differences in the reaction are solely because of the halogens and not because of any other factors in the reaction, hydrogen will be exercised as a constant for the second reactant. 

Hydrogen has a simple molecular structure and provides stable and consistent behavior in controlled environments, minimizing the complexities in the reactions. In addition, its reactivity with halogens and the reaction mechanisms within are well-studied and well-characterized, providing a clear foundation for comparing rate constants across different halogens (King). These mechanisms are commonly referred to as chain initiation, propagation, and termination or the steps of a reaction: (1) bonds are broken to create a free radical (initiation), (2) the free radical reacts with a stable molecule, generating another free radical, which can then continue the process by reacting with another molecule, attesting to the “chain” part of the name (propagation), and (3) once two free radicals encounter each other and react to form a stable molecule, the chain reaction stops (termination) (LumenLearning). By having accessible information to these steps, a deeper analysis can be done on the results of the study. 

Using existing research on hydrogen-halogen reactions, this paper can also better compare experimental results with theoretical predictions. Yet, there continue to be holes in the current research on this topic. For example, even though steric hindrance is recognized as a factor that influences reaction rates, the exact quantitative relationship between halogen size, bond strength, electronegativity, and rate constants is not fully understood. By analyzing the reaction rates, developing computational models to predict these effects, and correlating them with halogen properties, data-driven insights into steric hindrance can be provided to understand how factors quantitatively influence reaction kinetics. Additionally, this study uses a constant temperature in the experiments and models, establishing a controlled baseline for comprehending halogenic kinetics. 

Although Arrhenius equations are widely used, experimental validation of how temperature shifts affect individual hydrogen reactions across different halogens is incomplete. The activation energy for hydrogen-halogen reactions has also been studied unevenly; iodine reactions, specifically, are not well-analyzed. While the temperature variations are not directly explored, the study understands the effects and can act as groundwork for later studies that decide to use varying temperatures as an extra experimental condition. Furthermore, the models created in this study are not often found in ongoing papers: there is a lack of integration of advanced computational tools and experimental validation. Many kinetic theories and predictions rely heavily on computational models, but experimental validation remains limited, particularly for less common halogens or reaction conditions. Because the research focuses on experimental reaction rates for hydrogen with fluorine bromine and iodine, it further supports the theoretical models. Computational chemistry approaches like density functional theory (DFT) have been used for bond energy calculations but are underutilized in predicting full reaction kinetics for hydrogen-halogen systems. Through the use of tools like Wolfram Mathematica (MMA) and RStudio (R), the models combine computational simulations with experimental validation, bridging theoretical predictions with observed data.

Computational Approach

This study employs experimentally determined reaction rate data for the interactions between hydrogen gas (H₂) and the halogens fluorine (F₂), bromine (Br₂), and iodine (I₂). The atoms in all four of these gases are diatomic elements in their natural state, hence the subscript “2” for the chemical formulas. The reaction rate data was sourced from the National Institute of Standards and Technology (NIST) Chemical Kinetics Database. This platform is a governmental website that contains validated and peer-reviewed kinetic data under various conditions, ensuring reliability for computational modeling. The specifics are mentioned below:

• The hydrogen-fluorine (H₂ + F₂) rate constant was retrieved from a study that determined the rate expression between the two gases to observe differences between the rate constant for the reaction of unexcited and excited hydrogen molecules (Bokun and Chaikin). 

• The hydrogen-bromine (H₂ + Br₂) rate constant was sourced from a documented experiment that analyzed the synthesis reaction between the two elements and the correlation between the experimentally determined values and the classic rate law (Vidal). 

• The hydrogen-iodine (H₂ + I₂) rate constant was based on data from multiple experiments done by a scientist over the course of a decade dealing with hydrogen and iodine reactions (Sullivan). 

Along with consistently having hydrogen as a reactant, the order of the reactions was kept as second-order overall as it is the type of reaction most likely to occur in a natural and industrial setting. The temperature was also kept consistent, by manipulating the rate expression to take into account the experimental temperature. Through the use of Wolfram Mathematica Version 14.1, the new rate constants were solved for, assuming the temperature of all the reactions would be 100 degrees Celsius or 373.15 Kelvin, by employing the Arrhenius equation: k(T) = A*e^-Ea/RT (Zumdahl and Zumdahl). The new constants were then used in sets of differential rate equations, which were solved and plotted in concentration vs. time graphs, using commands such as NDSolve (solving equations) and Plot (graphing change in concentration and change in time). Figure 1 shows an example of what the code for the H₂ + F₂ reaction would look like.

Figure 1: Code for H₂ + F₂ reaction

These equations are known as rate law equations. They are defined by the inclusion of the rate constant and the concentration of the reactant(s) used in the experiment in order to determine the instantaneous rate of the reaction. The rate law equations used in this study are assumed to be first order for each reactant with a second-order overall: rate = k[H2][F2], rate = k[H2][Br2]}, rate = k[H2][I2], in which k is the rate constant that was calculated. Creating these graphs helps visualize the reaction rate curves and can be utilized to check whether the theoretical predictions about the reaction's behavior made based on the atomic properties of each of the halogenic gases are reflected in the experimental trial. Afterward, the correlations between the rate constant determined previously and the atomic properties of the three halogen gases were evaluated using R, an open-source programming language and software environment designed for statistical computing, data analysis, and visualization. The data used for the calculations and graphics were from various sources, including universities, governmental organizations, and scientific journals. Individually, the atomic sizes were taken directly from the National Library of Medicine and truncated to a whole number (National Center for Biotechnology Information); the electronegativity of each element was collected from a chart provided by the University of California, Los Angeles’s chemistry department, which rounds the data to the nearest tenth (Illustrated Glossary of Organic Chemistry - Electronegativity); and finally, the bonds’ strength between the halides were gathered from information found in the Atkins' Physical Chemistry (11th Edition) textbook (Atkins et al.). Figure 2 below displays the data in an organized manner.

	Rate Constant (cm3/molecule*s)	Atomic Size (pm)	Electronegativity (Pauling Scale)	Bond Strength (kJ/mol)
F2	1.46085*10-23	135	4.0	570
Br2	1.11756*10-32	183	2.8	366
I2	1.92316*10-34	198	2.5	299

Figure 2: Data used for correlation analysis

The strength and type of relation between any two of the variables can be discovered by applying the “cor,” short for correlation, command: if the value given is close to 1, it indicates a strong positive correlation between the two variables; if the value given is close to -1, it suggests a strong negative correlation; and if the value is close to 0, it implies a weak or no correlation with the type of relation depending on whether the value is negative or positive. To create the linear regression graphs, the ggplot2 package was installed from the library because of its popularity as a data visualization package that allows users to build customizable graphs layer by layer. Overall, this study utilizes reliable datasets and computational modeling to achieve a detailed and accurate representation of reaction behaviors without physical experimentation.

Results and Discussion

The reaction rate constants for hydrogen gas (H₂) with fluorine (F₂), bromine (Br₂), and iodine (I₂) were assessed using experimentally validated data from the NIST Chemical Kinetics Database. Differential equations were solved in MMA at 100°C (373.15 K), and the results were plotted to visualize reaction kinetics. In Figure 2, there is an apparent decrease in the reaction constants, starting with the hydrofluoric reaction and ending with the hydroiodic reaction. Considering the gas constant (R) and the temperature (T) stay the same throughout the three elements, the calculated k values reflect the hypothesis that fluorine would require more energy to break the bond present because of its high electronegativity difference with hydrogen. In Figure 3, the graph created by MMA shows the comparison between the reactions of H₂ + F₂, H₂ + Br₂, and H₂ + I₂.

Figure 3: Reaction kinetics for all 3 reactions

It proves that compared to the reactions of bromine and iodine with hydrogen, fluorine with hydrogen took the shortest amount of time to have an effective collision occur, therefore having the quickest reaction, which exhibits the theory that fluorine’s smaller atomic radius and larger electronegativity difference between H₂ and F₂ correlate to the fast reaction. Likewise, H₂ and Br₂’s reaction is the next to occur because of bromine’s larger atomic size and smaller electronegativity difference between hydrogen and itself. In contrast, H₂ and I₂’s reaction is the last to occur because it is the biggest atom out of the three halogen gases but has the smallest electronegativity difference. Together, both the rate constants and the reaction graphs depict the idea that fluorine’s strong and fast reaction may be related to its properties similar to iodine’s weak and slow reaction. 

Nevertheless, to compute the specifics of which elemental and molecular property was more likely to influence the value for the rate constant, three correlation graphs were plotted: one for atomic size, one for electronegativity, and one for bond strength. Figure 3 shows the general relation between the atomic size of the halogens and their rate constant. 

Figure 4: Correlation between atomic size and rate constant

As seen in the plot, there is an inverse relationship between the atomic size and the rate constant. Even though the data point for bromine does not touch the linear graph, the overall correlation was evaluated to be -0.9736842, signifying a strong positive correlation between the two. Comparably, the dependence between the rate constant and electronegativity was also very high, though directly related; the correlation value was 0.9819805, slightly closer to a perfect fit compared to that of the atomic size. The general trend between these two traits is depicted below in Figure 4.

Figure 5: Correlation between electronegativity and rate constant

The weakest correlation observed was between  the rate constant and the bond strength, as it was calculated to be 0.9714291, closer to 0 compared to the other two plots. Nonetheless, the value is still close to a perfect fit, and it denotes a positive trend (direct relationship) between the two variables. This trend is conveyed in Figure 5 below. 

Figure 6: Correlation between atomic size and rate constant

This is surprising as bond strength is based on electronegativity difference, so the expected result would be for the value gauged for the correlation with bond strength to be very close to the value estimated for the correlation with electronegativity, but it is the opposite. Unexpected trends or errors like these can be attributed to discrepancies in experimental data as well as rounding errors on behalf of the computer. For instance, the data collected from NIST to evaluate the rate constant had large margin errors, justifying any inaccuracies in the graphed differential equations. The rounded and truncated data for the elemental properties could also have thrown off the points plotted on the graphs, causing an incorrect correlation value to be assessed. Moreover, assumptions made about the gas constant using the ideal gas behavior, negligible side reactions, and the uniformity of the data sources could have contributed to miscalculations made in this study. One of the biggest limitations is the lack of data for the chlorine gas. While this experiment is only between fluorine, bromine, and iodine, having data on the reaction between H₂ + Cl₂ may have provided more information about the linearization for correlation and could have offered a deeper insight into the step by step changes in these single-step reactions. 

In summary, the experiment confirms that reaction rate constants for H₂ with the halogens are influenced primarily by bond strength and electronegativity, decreasing in the order of fluorine, bromine, and iodine. The data aligns well with theoretical expectations, but minor deviations are likely due to experimental conditions or data variability.

Conclusions

This study examined  the reaction kinetics of hydrogen gas (H₂) with the halogens fluorine (F₂), bromine (Br₂), and iodine (I₂) to understand how molecular and elemental properties, like electronegativity, atomic size, and bond strength, influence reaction rates. Using data from the NIST Chemical Kinetics Database, reaction rate constants were calculated and visualized through differential equations in MMA. Statistical analysis in R quantified correlations between molecular properties and reaction rates and graphed their general trend, providing insights into how these factors impact reaction kinetics. 

The results confirmed  the reaction rates for H₂ + F₂ > H₂ + Br₂ > H₂ + I₂, aligning with trends in electronegativity and bond strength. The correlation analysis in R revealed a strong positive correlation between electronegativity and reaction rate (0.9819), a strong inverse correlation between atomic size and reaction rate (-0.9737), and a slightly weaker positive correlation with bond strength (0.9714). These findings support the hypothesis that fluorine’s small atomic size and high electronegativity lead to faster reactions, while iodine’s larger size and lower electronegativity result in slower reactions.

Unfortunately, the absence of chlorine data limited a complete periodic trend analysis, and data variability, rounding errors, and assumptions about ideal gas behavior may have influenced the results.  Future research should include H₂ + Cl₂ reactions, explore temperature variations using the Arrhenius equation, and employ advanced computational models like Density Functional Theory (DFT) to fill in the gaps of the current research in this field. These efforts can provide an understanding of halogen reaction kinetics and their applications in industry and agriculture.

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