LEC 05 Chemical Kinetics Reaction rate and activation energy of the acid hydrolysis What you can learn about Reaction rate Rate law for first and second order reactions Reactions with pseudo-order Arrhenius equation Activation energy Principle and tasks Ethyl acetate is hydrolysed in an acid solution according to a pseudo-first order rate law to equivalent quantities of ethanol and acetic acid. Based on the alkalimetric determination of the acetic acid formed, conclusions can be made about the temporal concentration of ester. The reaction rate constant for this reaction is determined at different temperatures, and the activation energy is calculated. What you need: Graphic determination of the reaction rate constants for the acid hydrolysis at T x = 299.15 K and T o = 314.15 K. Wash bottle, 500 ml 33931.00 1 Ethyl acetate, 250 ml 30075.25 1 Hydrochloric acid, 1 M, 1000 ml 48454.70 1 Sodium hydroxide solution, 1 M, 1000 ml 48329.70 1 Phenolphthalein solution, 1%, 100 ml 31714.10 1 Water, distilled, 5 l 31246.81 1 Reaction rate and activation energy of the acid hydrolysis Immersion thermostat, 100 C 08492.93 1 Accessory set for immersion thermostat 08492.01 1 Bath for thermostat, 6 l, Makrolon 08487.02 1 Rubber tubing, d i = 6 mm 39282.00 2 Hose clip, d = 8 12 mm 40996.01 3 Digital thermometer 07050.00 1 Immersion probe NiCr-Ni 13615.03 1 Stopwatch, digital, 1/100 s 03071.01 1 Magnetic heating stirrer 35750.93 1 Magnetic stirrer bar, l = 15 mm 46299.01 1 Magnetic stirrer bar, l = 30 mm 46299.02 1 Support rod, l = 500 mm, M10 thread 02022.05 1 Retort stand, h = 750 mm 37694.00 2 Burette clamp, roller mounting 37720.00 1 Right angle clamp 37697.00 4 Universal clamp 37715.00 4 Burette, 50 ml, with Schellbach line 36513.01 1 Graduated cylinder, 100 ml 36629.00 1 Volumetric flask, 1000 ml 36552.00 1 Volumetric pipette, 5 ml 36577.00 2 Volumetric pipette, 100 ml 36582.00 1 Pipettor 36592.00 1 Pipette dish 36589.00 1 Pasteur pipettes 36590.00 1 Rubber bulbs 39275.03 1 Crystallisation dish, 1000 ml 46245.00 1 Erlenmeyer flask, 250 ml, wide neck 36134.00 2 Erlenmeyer flask, 100 ml, narrow neck, SB 19 36424.00 2 Rubber stopper, 17/22 mm 39258.00 2 Glass beaker, 250 ml, short 36013.00 1 Funnel, glass, d o = 55 mm 34457.00 1 PHYWE Systeme GmbH & Co. KG D- 37070 Göttingen Laboratory Experiments Chemistry 65
Reaction rate and activation energy of the acidolysis LEC Related concepts Reaction rate, reaction rate constant, rate law for first and second order reactions, reactions with pseudo order, Arrhenius equation, activation energy. Principle In acid solution, ethyl acetate is hydrolysed to equivalent quantities of ethanol and acetic acid according to a pseudo-first order rate law. The alkalimetric determination of the acetic acid formed enables conclusions to be drawn on the temporal concentration of ester. Tasks Determine the reaction rate constant for the acidolysis of ethyl acetate at two (or more) temperatures. Calculate the activation energy of the reaction from the temperature dependence of the measured rate constants. Equipment Immersion thermostat, 100 C 08492.93 1 Accessory set for immersion thermostat 08492.01 1 Bath for thermostat, 6 l, Makrolon 08487.02 1 Rubber tubing, d i = 6 mm 39282.00 2 Hose clip, d = 8 12 mm 40996.01 3 Digital thermometer 07050.00 1 Immersion probe NiCr-Ni 13615.03 1 Stopwatch, digital, 1/100 s 03071.01 1 Magnetic heating stirrer 35750.93 1 Magnetic stirrer bar, l = 15 mm 46299.01 1 Magnetic stirrer bar, l = 30 mm 46299.02 1 Support rod, l = 500 mm, M10 thread 02022.05 1 Retort stand, h = 750 mm 37694.00 2 Burette clamp, roller mounting 37720.00 1 Right angle clamp 37697.00 4 Universal clamp 37715.00 4 Burette, 50 ml, with Schellbach line 36513.01 1 Graduated cylinder, 100 ml 36629.00 1 Volumetric flask, 1000 ml 36552.00 1 Volumetric pipette, 5 ml 36577.00 2 Volumetric pipette, 100 ml 36582.00 1 Pipettor 36592.00 1 Pipette dish 36589.00 1 Pasteur pipettes 36590.00 1 Rubber bulbs 39275.03 1 Crystallisation dish, 1000 ml 46245.00 1 Erlenmeyer flask, 250 ml, wide neck 36134.00 2 Erlenmeyer flask, 250 ml, narrow neck, SB 29 36424.00 2 Rubber stopper, 17/22 mm 39258.00 2 Glass beaker, 250 ml, short 36013.00 1 Funnel, glass, d o = 55 mm 34457.00 1 Wash bottle, 500 ml 33931.00 1 Ethyl acetate, 250 ml 30075.25 1 Hydrochloric acid, 1 M, 1000 ml 48454.70 1 Sodium hydroxide solution, 1 M, 1000 ml 48329.70 1 Phenolphthalein solution, 1%, 100 ml 31714.10 1 Water, distilled, 5 l 31246.81 1 Fig. 1. Experimental set-up. PHYWE series of publications Laboratory Experiments Chemistry PHYWE SYSTEME GMBH & Co. KG D-37070 Göttingen 1
LEC Reaction rate and activation energy of the acidolysis Set-up and procedure Set up the experiment as shown in Fig. 1. Prepare 0.2 molar NaOH solution by pipetting 200 ml of 1.0 molar sodium hydroxide solution into a 1000 ml volumetric flask and filling up to the calibration mark with water. Fill the burette with 0.2 molar NaOH solution. Pipette 100 ml of 1.0 molar hydrochloric acid solution into an Erlenmeyer flask, seal it with a stopper, and temperature equilibrate it for approximately 15 minutes at 25 C (measure the exact temperature T 1 ). Start the reaction by adding 5 ml of ethyl acetate (room temperature). Shake the flask briefly, then replace it in the temperature controlled bath. After 10 minutes, and at further intervals of 10 minutes, take 5 ml samples and transfer them into a wide neck Erlenmeyer flask containing 100 ml of cold water. This will stop the reaction immediately. Titrate the solutions with as little delay as possible with the 0.2 molar sodium hydroxide solution, using phenolphthalein as indicator. Terminate the measurement series after a reaction time of 50 minutes. Repeat the above procedure at a temperature of 45 C (T 2 ). The volumes of NaOH at time t 0 (V NaOH; 0, neutralisation of the constant quantity of HCl) and subsequent to complete conversion (V NaOH; ) are required for the evaluation. They can either be calculated (see Theory and evaluation ) or be determined experimentally as follows. To determine V NaOH;, after concluding the first measurement series, heat the solution which was converted to the greatest extent to approximately 70 C (for app. 20 minutes) in a water bath on the magnetic stirrer. The reaction will go to completion at this temperature. Allow the solution to cool, then titrate it with 0.2 molar NaOH solution as described above. To determine the initial consumption V NaOH; 0 titrate 5 ml of the 1.0 molar hydrochloric acid solution used, by the volume must be corrected by a factor of 100/105 for the ester portion which is absent here. The ester concentrations c E; 0 and c E at time t 0 and t can be replaced by the volumes of NaOH required for neutralisation of the samples at the start (v NaOH; 0 ), during the reaction (V NaOH ) and after complete conversion (V NaOH; ): (1.3) The volumes V NaOH; 0 and V NaOH; can be experimentally determined (see Set-up and procedure ) or be calculated using relationships (2.1) and (2.2): c HCl c NaOH V 1 r E M E V E ln V NaOH,q V NaOH,0 V NaOH,q V NaOH Concentration of the HCl solution (= 1.0 mol/l) Concentration of the NaOH solution (= 0.2 mol/l) Sample volumes (= 5 ml) V NaOH,q r E V E V 1 M E V S c NaOH ln Q k' t V NaOH,0 c HCl V 1 100 c NaOH 105 V NaOH,0 (2.1) (2.2) Density at T = 298 K (= 0.895 g/ml) Molar mass (= 88.12 g/mol) Volumes contained in the volume of the total system V S = 105 ml at time t 0 (= 5 ml) In accordance with equation (1.3), the plot of the expression ln [(V NaOH; - V NaOH; 0 / V NaOH; - V NaOH )] as a function of time results in a rising straight line with a slope of k (Fig. 2). Theory and evaluation The acid ester hydrolysis is described by the equilibrium CH 3 COOC 2 H 5 + H 2 O [H 3 O + ] CH 3 COOH + C 2 H 5 OH Under the given experimental conditions, equilibrium is shifted quantitatively towards the reaction products. The reaction velocity (rate) v R of this reaction is given by the rate law: v R dc E dt k c E c W c K (1) Fig. 2: Graphic determination of the reaction rate constants for the acid hydrolysis at two temperatures (x: T 1 = 299.5 K, o: T 2 = 314,15 K; c(h 3 O + ) = 1.0 mol l -1 ; ln Q = ln[(v NaOH; - V NaOH; 0 )]) k c E, c W, c K Reaction rate constant Concentration of ester, water and catalyst at time t The rate of the reaction investigated is a function of the acid concentration and can be controlled by it. As a result of the practical constancy of the concentrations of H 2 O (stoichiometric excess) and H 3 O + (catalyst), this reduces to dc E dt k' c E (1.1) The rate of hydrolysis thus conforms to a pseudo-first-order time rule whose integration results in the following : ln c E,0 c E k' t (1.2) 2 PHYWE series of publications Laboratory Experiments Chemistry PHYWE SYSTEME GMBH & Co. KG D-37070 Göttingen
Reaction rate and activation energy of the acidolysis LEC The constant k includes the dependence of the reaction velocity on the binding conditions of the participating molecules, the type of reaction and the temperature. For two molecules to react, they must not only collide, but also have a sufficient energy content. The activation energy E A is the difference between the average energy content prior to reaction and the energy required for reaction. The molecules obtain the energy that is needed for activation from heat supplied, from light and from the exchange of energy when collisions occur. Such take-up of energy activates the molecules (loosens bonds, polarisation etc.) so that they can react. The portion of molecules with this increased energy content increases with increasing temperature. The greater the portion of the molecules capable of reaction, the more molecules that will react, and so the higher the reaction velocity. The activation energy can be determined using the empirical Arrhenius equation: E A k = k max e RT (3) R Universal gas constant ( = 8.31441 J K -1 mol -1) k max Maximum rate constant at infinite temperature (frequency factor) k max is the velocity constant which would be given when every every collision resulted in reaction, i.e. when the activation energy was 0. For two known pairs of values having the rate constants k 1 and k 2 and the temperatures T 1 and T 2, using the following concrete relationships result: ln k' 1 ln k' 2 from which, by subtraction E A R E A R T 1 ln k max E A R T 2 ln k max T 1 T 2 T 2 T 1 ln k' 2 k' 1 (3.11) (3.12) (3.2) If further data regarding k and T are available (i.e., measurements at a number of temperatures), then the activation energy can alternatively be determined from the slope of the linear relation between ln k and 1/T according to equation (3.1). Data and results The linear relationships presented in Fig.2 confirm the validity of a pseudo-first-order time rule. The slopes of the straight lines, which are determined by regression analysis correspond to the rate constants of k 1 = 7.80 10-3 min -1 at T 1 = 299.15 K and k 2 = 2.86 10-2 min -1 at T 2 = 314.15 K. From these values, using equation (3.2), an activation energy of E A = 67.7 kj mol -1 is obtained. Literature values: k = 6.3 10-3 min -1 (T = 293.15 K) ; E A = 67.7 kj mol -1. ln k' E A R T ln k max (3.1) PHYWE series of publications Laboratory Experiments Chemistry PHYWE SYSTEME GMBH & Co. KG D-37070 Göttingen 3
LEC Reaction rate and activation energy of the acidolysis 4 PHYWE series of publications Laboratory Experiments Chemistry PHYWE SYSTEME GMBH & Co. KG D-37070 Göttingen