Kinetic Analysis and Optimum Conditions for Ethanol Formic Acid Esterification Reaction

Study Case Kinetic Analysis and Optimum Conditions for Ethanol– Formic Acid Esterification Reaction with Sulfuric Acid Catalyst Michael Kurniawan (2018123456) University of Cincinnati, 2600 Clifton Ave, Cincinnati, OH 45221, United States kurniaml@mail.uc.edu Abstract Ethyl formate is produced through esterification reaction between ethanol and formic acid using sulfuric acid as a catalyst. This study aims to analyze the effect of temperature and catalyst concentration on reaction conversion and reaction rate constant. The esterification process was carried out in a laboratory batch reactor under isothermal conditions and with a balanced amount of reactants. The catalyst concentration varied from 0.0923% w/w to 0.9231% w/w, while the reaction temperature varied from 30°C to 70°C. Quantitative analysis was performed by measuring the residual concentration of formic acid. The results showed that the optimum conditions were obtained at a sulfuric acid catalyst concentration of 0.3692% w/w and a temperature of 50°C. The empirical equations obtained are: 𝑘 = 6.51 × 10−3 𝑒 (−141.9868/𝑅𝑇) ln𝐶𝑘𝑎𝑡𝑎𝑙𝑖𝑠 with an error of 2.19% for catalyst concentration 1 variation, and 𝑘 = 3.1143𝑒 (−1079/𝑅) × 𝑇 with an error of 6.52% for temperature variation. When both variables are combined, the following equation is obtained: 𝑘 = 6.88 × 10−3 𝑒 (−100.1965/𝑅) × ln 𝐶𝑘𝑎𝑡𝑎𝑙𝑖𝑠 𝑇 with an error rate of 18.29%. Keywords: Esterification, Formic acid, Ethanol, Reaction kinetics INTRODUCTION Ethanol is widely produced in the United States, generally through the fermentation of biomass such as corn or sugar cane. This ethanol can be further processed into various derivative products, one of which is ethyl formate through the esterification MICHAEL KURNIAWAN 1 Study Case process. Ethyl formate has various industrial applications, including as a flavoring agent in flavoring and soft drinks, a solvent for nitrocellulose, and a raw material for the manufacture of fumigants and larvicides in tobacco plants, grains, and dried fruits [1]. To obtain optimal ethyl formate yield, testing of various variables that affect conversion and reaction rate is required. The kinetic data obtained from these tests can be used to determine the rate of ethyl formate formation and to design efficient reactor designs and operating conditions [2]. Esterification, which is the reaction of ester formation, is carried out by reacting organic acids and alcohols with the help of mineral acid catalysts—a method first described by E. Fischer. This reaction is reversible and reaches equilibrium accelerated by the presence of hydrogen ions [3]. THEORETICAL REVIEW Influence of Catalysts Catalysts play an important role in accelerating chemical reactions through the formation of intermediate compounds or surface adsorption processes. In esterification reactions, the reaction rate increases significantly with the addition of strong acids such as sulfuric acid (H₂SO₄) or hydrochloric acid (HCl) [4]. Although catalysts do not change the position of equilibrium, they increase the rate at which equilibrium is reached. In general, a small amount of concentrated acid catalyst is used in a mixture of alcohol and carboxylic acid. The addition of a small amount of catalyst (about 0.3–0.5% of the total reaction volume) is sufficient to activate the reaction. However, the use of excess sulfuric acid (5–10% of the reaction volume) can shift the equilibrium position due to its nature as a dehydrating agent, which binds the water produced by the reaction and drives the reaction towards ester formation. The main reaction can be written as follows: “Alcohol” + “Acid” ↔ ‘Ester’ + “Water” Although it increases ester yield, excessive use of sulfuric acid is economically inefficient and complicates the separation of the final product [5]. Conversely, base catalysts are ineffective because they can form carboxylate ions that shift the equilibrium towards the reactants, thereby inhibiting ester formation [6]. Effect of Reaction Temperature The rate of chemical reactions generally increases with rising temperatures. Based MICHAEL KURNIAWAN 2 Study Case on the principles of kinetics, a 10°C increase in temperature can double the speed of a chemical reaction [7]. This is due to the increase in molecular kinetic energy, which causes more frequent collisions between particles with greater energy. In the context of esterification, heating is used to accelerate the reaction and increase product yield. The higher the temperature, the more molecules have sufficient activation energy to react, resulting in a significant increase in conversion [8]. Several methods that can be used to shift the equilibrium towards ester formation include: a. Adding excess alcohol or carboxylic acid. b. Removing the water produced by the reaction using drying agents such as sulfuric acid or zinc chloride (ZnCl₂). c. Distilling the ester product to remove it from the reaction mixture continuously [9]. RESEARCH METHODS Materials and Equipment This study used technical ethanol, technical formic acid, and concentrated sulfuric acid as catalysts as the main materials. Additional materials used included oxalic acid dihydrate, sodium hydroxide (NaOH), and phenolphthalein indicator for titration analysis. Figure 1. Experimental Equipment Setup Determination of Initial Material Concentration To determine the volume and concentration of ethanol, formic acid, and sulfuric acid to be used in the reaction, the density of each material was measured using a picnometer. The density values obtained from the measurements were used to calculate the purity of each material, which was then used as the basis for determining the MICHAEL KURNIAWAN 3 Study Case concentration and volume of the reaction mixture. Determination of Optimum Catalyst Concentration Preliminary experiments were conducted to determine the optimum catalyst concentration. A mixture of 121.8 mL of ethanol and 0.0923% w/w concentrated H₂SO₄ (0.1 mL) was heated to a temperature of 40°C. At the same time, 78.2 mL of formic acid was also heated to the same temperature. After reaching the desired temperature, the two solutions were mixed and stirred at 500 rpm for 90 minutes. Every 15 minutes, 1 mL of sample was taken to analyze the concentration of the remaining formic acid from the reaction. This procedure was repeated for various concentrations of H₂SO₄ catalyst, namely 0.1846% w/w, 0.3692% w/w, 0.6461% w/w, 0.7384% w/w, and 0.9231% w/w. Determination of Optimum Reaction Temperature The optimum temperature was determined using the catalyst concentration obtained from the previous experiment (optimum at 0.3692% w/w). A mixture of 121.8 mL ethanol + H₂SO₄ and 78.2 mL formic acid was heated at various temperatures—30°C, 40°C, 50°C, 60°C, and 70°C—under the same stirring conditions and duration (500 rpm for 90 minutes). Every 15 minutes, 1 mL of sample was taken for formic acid residue analysis. RESULTS AND DISCUSSION Effect of H₂SO₄ Catalyst Concentration on Reaction Rate Constant The relationship between catalyst concentration variation and reaction rate constant is shown in Table 1. Table 1. Experimental Results with Variations in Catalyst Concentration MICHAEL KURNIAWAN 4 Study Case The table above shows that an increase in catalyst concentration results in an increase in the reaction rate constant. However, at a concentration of 0.9231% w/w, there is a slight decrease in the reaction rate constant value. This phenomenon is likely caused by the interaction between alcohol and concentrated sulfuric acid, which forms a monosulfate compound, so that some of the ethanol is no longer available as the main reactant. Because the reaction rate is directly proportional to the reactant concentration, a decrease in alcohol content causes the rate constant to decrease [1]. The empirical relationship between the rate constant and catalyst concentration follows the equation: ln𝑘 = −0.2285ln𝐶 − 5.0339 with a coefficient of determination value of R^2=0.9837, indicating an excellent relationship between the two variables. Figure 2. Relationship between Reaction Rate Constant and Catalyst Concentration Conversion Analysis and Determination of Optimum Conditions Based on the observation results (Figure 3), at catalyst concentrations of 0.3692% w/w, 0.6461% w/w, and 0.7384% w/w, the initial conversion showed an almost similar trend. However, between 1 and 10 hours, the most significant increase in conversion occurred at a concentration of 0.3692% w/w, which was then set as the optimum condition for the next experiment. The equilibrium conversion for all catalyst variations at a temperature of 40°C reached approximately 98.7%, but the time to achieve this conversion varied. Estimates of the time to reach equilibrium and conversion were calculated using the Runge-Kutta method for numerical solution of reaction kinetics. MICHAEL KURNIAWAN 5 Study Case Figure 3. Prediction of Reaction Conversion over Time at Various Catalyst Concentrations Table 2. Predicted Equilibrium Constants and Time to Reach Equilibrium for Various Catalyst Concentrations From Table 2, it can be seen that the higher the catalyst concentration, the shorter the time required to reach equilibrium, while the equilibrium conversion value remains constant at 0.987. This phenomenon reinforces the principle that catalysts do not change the position of the reaction equilibrium, but only accelerate its achievement [1]. From the regression results of the relationship between the rate constant and catalyst concentration (Figure 2), the following empirical equation is obtained: 𝑘 = 6.51 × 10−3 𝑒 (−141.9868/𝑅𝑇) × ln𝐶catalyst (1) Equation (1) shows that the activation energy is directly related to the catalyst concentration through the term ln Ccatalyst〗. The collision frequency obtained was 6.51 × 10⁻³ min⁻¹, with an experimental temperature of T = 313 K (40°C). The average MICHAEL KURNIAWAN 6 Study Case deviation between the experimental results and the calculated results was 2.19%, indicating excellent agreement between the model and the experimental data. Effect of Temperature on Reaction Rate Constant The data from observations of the effect of temperature on reaction rate are shown in Table 3. Table 3. Experimental Results for Reaction Temperature Variations at a Catalyst Concentration of 0.3692% w/w An increase in temperature from 30°C to 60°C significantly increased the reaction rate constant value. However, at 70°C, the k value decreased, possibly due to the evaporation of some of the alcohol that did not recondense and therefore did not react with the formic acid. This shows that the reaction rate increased with temperature up to an optimum point before being limited by the loss of volatile reactants [2]. Within this temperature range, no dehydration or formic acid decomposition reactions were observed, as dehydration reactions only occur above 80°C, and formic acid decomposition generally occurs at 100.7°C [3]. From the regression results between temperature and reaction rate constant (Figure 4), a linear relationship was obtained that satisfies the following Arrhenius equation: 1 ln 𝑘 = 2143.2( ) + 1.1357 𝑇 or can be rewritten as: 𝑘 = 3.1143 𝑒 (−1079/𝑅) × 1 𝑇 (2) From equation (2), the activation energy (Eₐ) = 1079 cal/mol, and the frequency factor (A) = 3.1143 min⁻¹. The temperature range tested was 303 K, 313 K, 323 K, 333 K, and 343 K. The average error between the experimental results and the calculations was 6.52%. MICHAEL KURNIAWAN 7 Study Case Figure 4. Relationship between Reaction Rate Constant and Reaction Temperature Equilibrium Prediction Based on Temperature Variation Table 4. Prediction of Equilibrium Constant and Time to Reach Equilibrium for Various Temperatures The prediction results show that equilibrium conversion decreases with increasing temperature, indicating that this reaction is exothermic—the higher the temperature, the smaller the conversion at equilibrium [4]. Figure 5. Prediction of Conversion over Time at Various Temperatures MICHAEL KURNIAWAN 8 Study Case From Figure 5, it can be concluded that the optimum reaction temperature for ethanol–formic acid esterification is 50°C, because at that temperature the conversion increases significantly with a relatively short reaction time. Combining the Effects of Temperature and Catalyst Concentration The combined relationship between the reaction rate constant (k), catalyst concentration (Cₖ), and temperature (T) is approached with the following empirical model: ln 𝑘 = −50.426 ln 𝐶catalyst − 4.9789 𝑇 or can be rewritten as: 𝑘 = 6.88 × 10−3 𝑒 (−100.1965/𝑅) × ln 𝐶catalyst 𝑇 (3) The average deviation value of the calculation is 18.29%, indicating that this model adequately represents the combination of both variables, although with lower accuracy than the single temperature or catalyst model. Figure 6. Relationship between Reaction Rate Constant and Temperature and Catalyst Concentration From equation (3), the collision frequency (A) = 6.88 × 10⁻³ min⁻¹ is obtained. The effective activation energy for each catalyst variation can be calculated by multiplying the constant 100.1965 by the value of ln〖Ccatalyst〗. The temperature range in this model covers 303 K to 343 K (30–70°C). MICHAEL KURNIAWAN 9 Study Case CONCLUSION 1. Catalyst Effect: Increasing the concentration of sulfuric acid catalyst accelerates the reaction rate of ethanol and formic acid esterification. The empirical relationship is expressed as. 𝑘 = 6.51 × 10−3 𝑒 (−141.9868/𝑅𝑇) × ln 𝐶catalyst with an average error of 2.19%. 2. Effect of Temperature: The reaction rate constant increases with increasing temperature, in accordance with the following Arrhenius equation: 𝑘 = 3.1143𝑒 (−1079/𝑅) × 1 𝑇 with an average error of 6.52%. 3. Combination of Temperature and Catalyst: The combined relationship follows the equation: 𝑘 = 6.88 × 10−3 𝑒 (−100.1965/𝑅) × ln 𝐶catalyst 𝑇 with an average error of 18.29%. 4. Optimum Reaction Conditions: The best operating conditions are achieved at a catalyst concentration of 0.3692% w/w and a reaction temperature of 50°C, resulting in a maximum conversion of 98.7% in a relatively short time. REFERENCE MICHAEL KURNIAWAN 10 Study Case MICHAEL KURNIAWAN 11