Kinetic Studies on Saponification of Ethyl Acetate by the Conductance Method - Physical Chemistry

Propose

1.     To know the characteristics of a second-order reaction by a graphical method.

2.     To determine the effect of temperature on the reaction rate of ethyl acetate with dilute sodium hydroxide.

3.     To be familiarized with the operation of a digital conductometer.

Principles

        The saponification of ethyl acetate with sodium hydroxide is a second-order, irreversible reaction which can be represented by the following equation:

         If the initial concentration of the reactants are equal (both a) and that converted concentration is x at reaction time t, then the concentration of ethyl acetate and NaOH is C₀-x. Supposing that the reverse reaction can be ignored, the reactant and product concentrations at different time are

t = 0	C0	C0	0	0
t = t	C0 - x	C0 - x	x	X
t -> ∞	-> 0	-> 0	-> C0	-> C0

        The rate equation for the above second-order reaction can be expressed as

                                                     

Where k₂ is second-order rate constant,  mol^-1 L min^-1

        The equation can be integrated to give:

                                                        

        From the concentrations of the reactant and product in the reaction vessel and time of reaction, rate constant k₂ can be calculated.

        In this reaction, OH^- ion is the most highly conductive species therefore the conductivites of the ethyl acetate and ethyl alcohol may be ignored. Since the reaction solution is dilute aqueous, it can be assumed that sodium acetate is completely ionized. The concentration of Na⁺ remains invariable before and after reaction. As the reaction time increases, the number of OH^- ions decreases continuously, and the conductance of the system declines continuously.

t = 0	к0 = A1C0
t = t	кt = A1(C0 - x) + A2x
t = ∞	к∞ = A2a

Then         

Where к₀ and к_t are the conductivity at beginning and time t, respectly, к_∞ is the conductivity at the end of reaction, and A is the proportionality constant. Substituting the equation into below                                              

or

A plot of (к₀ - к_t)/(к_t – к_∞) against t sjould yield a straight line with a slpoe of k₂C₀ AND k₂ can be calculated from the slope. The rate of reaction as characterized by its rate constant k is strongly temperature dependent. This is generally express as the Arrhenius equation:

                                                        

Where  E_a : activation energy, kJ/mol

             T : the reaction temperature, K

             R : gas constant, J/(mol K)

        Therefore,

         Then                                                               

                                      

        From the equation E_a can be obtained based on the determination of k_T2 and k_T1.                                                                                                                            

Chemicals

1.     NaOH_(aq) (0.01852 M, standardized )

2.     NaOAc_(aq) (0.00926 M)

3.     Ethyl acetate (A.R.)

4.     Distilled water

Apparatus

1.     Digital conductometer and computer

2.     Platinum electrode

3.     Glass reactor

4.     Volumetric flask

5.     Thermostatic water bath

6.     50-mL test tube

7.     Pipette

8.     Washing ear ball

  

Procedures

Measurement of к₀ ~ к_t

        Add 20-mL NaOH_(aq) in the tube 1 and 20-mL ethyl acetate in tube 2. Set up the platinum electrode on the reactor and put the reactor in the thermostatic water bath for at least 10 minutes until the temperature is constant. Turn on the computer and the recorder. Use a washing ear ball to force the solution in tube 1 to remove to tube 2 and quickly mix for 3~5 times. Let the recorder works for about 20 minutes. Raise the temperature high for 3℃ and repeat the same steps above until the temperature is above 30℃.

Measurement of к_∞

        Also suck a 50-mL test tube in the thermostatic water bath and hold with 0.00926M NaOAc_(aq). After each temperature of measurement of к₀ ~ к_t , wash the platinum electrode with distilled water and then suck the electrode in to the sodium acetate solution. Record the reading on the conductometer.

  

Experimental Record

     Raw Data

NaOH(aq): 0.01852M ; Room Temperature.：20.0℃ ; EtOAc_(aq): 0.181 mL

Temperature 1： 20.08℃ ; Conductivity of 0.00926M NaOAc(aq): 420 uS/cm

Temperature 2： 22.90℃; Conductivity of 0.00926M NaOAc(aq): 448 uS/cm

Temperature 3： 26.30℃ ; Conductivity of 0.00926M NaOAc(aq): 478 uS/cm

Analysis

   Take the points after the 100^th point：

According to the slope of these three diagrams, the k₂ can be easily figured out as follow:

Temperature(℃)	slope	k2
20.08	-5.8324 x10-4	6.2984 x10-2
22.90	-6.8120 x10-4	7.3564 x10-2
26.30	-8.2301 x10-4	8.8878 x10-2

            

Draw a ln(k₂)-(1/T) figure and do a linear fitting with these points. The slope of the diagram could be expressed as: slope = -E_a /R

    For the slope = -4863.73, R = 8.314, and then the is E_a： 40.52 kJ/mol

To compare with the literature value^[6]： 39.9 kJ/mol , it is very close.

Ea (experimental)	40.52 kJ/mol
Ea (literature)	39.9  kJ/mol
Percentage error	1.6%

References

[1]  傅獻彩, 沈文霞, 姚天揚. 物理化學, 上冊歐4 版. 北京:高等教育出版社, 1990:144.

[2]  清華大學化學系物理化學實驗編寫組. 物理化學實驗. 北京：清華大學出版社, 1991.

[3]  Robert C. Wcast Handbook of Chemistry and Physics. Physics. 58^th ed. Ohio: CRC Press, 1977.

[4]  朱文濤. 物理化學. 北京：清華大學出版社，1995.

[5]  W. T. Gooch, J. Am. Chem. Soc., 1927, 49 (9), pp 2257–2257

[6]  ADELIO M. MENDES, LUIS M. MADEIRA, FERNAo D. MAGALHAES, J 0513 M. SOUSA. Universidade do Porto - Porto, Portugal

Solid-Liquid Phase Diagram - Physical Chemistry - Lu Le Laboratory

Purpose

1.     To investigate the heterogeneous equilibrium between solid and liquid phases of a two-component system.

2.     To construct the phase diagram by measuring the cooling curves.

3.     To determine the eutectic temperature and composition of the mixture.

Principles

        Solid-liquid phase diagrams are of great value in the technical study of alloys, ceramics and in the recovery of a salt by crystallization from a mixture of salts. The binary solid-liquid phase diagram in Figure 1 shows the stability of different phases as a function of temperature at a given pressure. This example shows a case where the two substances are miscible in the liquid state and insoluble in the solid state. In this diagram we are plotting temperature versus the mole fraction of substance B. At the left, the curve intersects at the melting point of pure A or pure B. This is a phenomenon of freezing point depression. The minimum in the freezing-point curve is called the eutectic, and a horizontal line has been draw along the eutectic temperature.

Figure 1.

        To construct a phase diagram for a binary mixture, phase transition temperature data for mixtures of different compositions of the two components must be collected. This can be achieved by recording cooling curves for the different mixtures as shown in Figure 1. Samples containing known amounts of both components are places in containers and heated until completely melting. Then allow it to cool slowly and measure the temperature at regular time intervals. Cooling curve 1 in figure 1 is for pure A. The sample cools at an approximately constant rate. Once the temperature is reached melting point of A, a “halt” is observed in the cooling curve. The temperature of the substance remains constant until all of the sample freezes. Then the temperature drops rapidly again. The same thing happens at the composition of a eutectic (curve 3) and pure B (cooling curve 5). Cooling curve 2 is for a mixture with composition between pure A and the eutectic. On this cooling curve we have a changing point where solid A is crystallizing out. Because the heat evolved by solidification partly offsets the heat lost by radiation and conduction to the cold surroundings, a slow rate of cooling is observed. The melt becomes richer in component B as component A is separating out, and the freezing point of the melting decreases along the curve. When we rich point “b” the liquid has reached the eutectic composition and a “halt” is observed in the cooling curve (line b-c). At this temperature, both pure A and pure B will crystallize together. Since three phases are in equilibrium at constant pressure, the number of degrees of freedom falls to f’ = C- Φ+1 = 2-3+1 = 0. If we continue to remove heat from the mixture the system will remain at eutectic temperature until all of the remaining liquid has solidified. Cooling curve 3 is for a mixture with composition between the eutectic and cooling curve 4 is for a mixture with composition between the eutectic and pure B. For each mixture studied, the cooling curve is examined to determine the temperatures at which changes in slope or plateau occur. A phase diagram is prepared by plotting the points of the corresponding breaks and halts in the cooling curves and connecting these points by smooth curves.

                                             

Chemicals

1.     Tin (metal basis, A.R.)

2.     Bismuth (metal basis, A.R.)

Apparatus

1.     Electronic furnace

2.     Thermocouple

3.     Crucibles

4.     Ebulliometer (use to adjust the thermocouple)

5.     Barometer

6.     Computer and data receiver

7.     Hardened test tube

Procedure

Preparation of Samples

1.     Prepare 0%、30%、57%、80%、100%(Bi w/w) Bi-Sn alloy 50g with an analytical balance to nearest 0.0001g.

2.     Add some rosin in the test tube to prevent the sample been oxidized at high temperature.

Drawing Cooling Curves

1.     Set up the apparatus as Figure 2.

2.     Turn the heater on and adjust he voltage until all solids melt. Transfer the crucible out from a hotter furnace to a steel rank to cool down and start recording the temperature.

3.     Repeat these steps for different samples.

Experimental Record

Sample	d.d. H2O	Tin	Bismuth
Melting Point (Literature) (/℃)	100	232	271
Experimental (/℃)	99.58	224.44	247.65

Table 1.

Cooling Curve of Samples：

Sample Bi/Sn x 100%(w/w)	Bi 0%(w/w)	Bi 29.97%(w/w)	Bi 56.96%(w/w)	Bi 80.00% (w/w)	Bi 99.99% (w/w)
T1 (℃)	224.44	173.01	131.06	193.47	265.05
T2 (℃)	-	125.86	-	125.67	-

Table 1. Raw Data

Analysis

    Draw a calibration curve for the thermocouple set:

Calibration curve

y = -3.01901 + 1.03902*x

Sample Bi/Sn x 100%(w/w)	Bi 0%(w/w)	Bi 29.97%(w/w)	Bi 56.96%(w/w)	Bi 80.00% (w/w)	Bi 99.99% (w/w)
T1 (℃)	230.18	176.74	130.14	198.00	254.29
T2 (℃)	-	127.75	-	127.55	-

Table 2. Calibration data

Complete the phase diagram with other known data^[1]：

Add some colors and sign：

      

        Finally, analysis the phase diagram with Gibbs' phase rule: F = C - P + n

 here n=1 because it is at a constant pressure. Then we can get the degrees of freedom of each phase.

Item	Phase (P)	Degrees of Freedom
α	1	1
β	1	1
α+β	1	2
α+L	2	1
β+L	2	1
Liquid phase	1	2
Melting Curve	2	1
Minimum Melting Eutectic Point	3	0

References

[1]   虞覺奇, 易文質. 二元合金狀態圖集. 上海: 上海科學技術出版社, 1995: 250-251

[2]  傅献彩, 沈文霞, 姚天扬. 物理化学, 上册欧4 版. 北京:高等教育出版社, 1990:144.

[3]  清华大学化学系物理化学实验编写组. 物理化学实验. 北京：清华大学出版社, 1991.

[4]  Robert C. Wcast Handbook of Chemistry and Physics. Physics. 58th ed. Ohio: CRC Press, 1977.

[5]  朱文涛. 物理化学. 北京：清华大学出版社，1995.

[6] http://www.materials.ucsb.edu/~matclass/101/pdffiles/Lecture_13.pdf