Department of Chemical & Biomolecular Engineering
Chem. Eng. Process Laboratory I B.Tech CN 2116E
Experiment R3 Batch Reactor
Objectives:
To determine the stoichiometric, the heat of reaction, and the rate constant of the reaction between sodium thiosulphate and hydrogen peroxide in an aqueous medium. Apparatus:
Dewar flask, thermometer, thermocouple, and chart recorder Theory:
The oxidation of sodium thiosulphate with hydrogen peroxide can be written as: A Na2S2O3 + B H2O2 C Na2SO4 + D H2O + E Na2S3O6 1. Stoichiometry The stoichiometric coefficient is defined as the moles of hydrogen peroxide reacted per mole of sodium thiosulphate consumed. This can be determined from a series of runs in which the total volume of reactant solution is held constant and the volume of hydrogen peroxide is varied. Only the overall temperature rise (T) had to be measured. When T is plotted against the volume of hydrogen peroxide used, the temperature rise will go through a maximum when the reactants are mixed in their stoichiometric ratio. 2. Water Equivalent of Dewar flask
The water equivalent is the amount of water that will absorb the same amount of heat as the container (flask). From heat balance equation (i.e. M .Cp.T), the heat loss by hot water is equal to the heat gain by cold water and flask. 3. Heat of Reaction
In a chemical reaction, the total heat released can be calculated from the overall temperature rise (T), and the system heat capacity. In a solution, since reactant not in excess will react completely, the heat of reaction can be calculated if the stoichiometric coefficient is known. In this work the hydrogen peroxide is normally used in excess in order to suppress possible side reaction and, therefore, the heat of reaction ( H), is reported as calorie per mole of Na2S2O3. 4. Activation Energy The activation energy, essentially a measure of the effect of temperature on reaction rate, can be derived from data obtained in a series of runs in which the initial reactant concentrations are held constant and the initial temperature is varied. The initial concentrations being constant, it follows that the concentrations at a temperature midway between the initial and final temperatures will be the same for all runs, since at this point exactly half of the reactant not in excess will have reacted. This temperature is called the midpoint temperature (Tm). At the midpoint temperature, the reaction rate is directly proportional to the rate of temperature increase i.e., the slope of the temperature - time curve. Thus, if the logarithm of the midpoint slope is plotted against the reciprocal of the absolute temperature and a straight line results, the assumption of an activationenergy-like temperature dependence is justified and the slope of the line is equal to -E/R. 5. Reaction Rate Constant
For any point on the temperature vs. time curve, and in particular the midpoint, the slope of the curve is given by the expression:
dT A ( H ) ( M C P ) SYS 1 .e E / RT .C 1 .C 2 .V SYS dt From the stoichiometry and the initial reaction concentrations, C 1 [Na2S2O3] and C2 [H2O2] at the midpoint can be calculated. Since the activation energy, the heat of reaction and the system heat capacity are known, the value of the reaction rate constant k can be determined by multiplying A with e-E/RT. Experimental Procedures: (A) Determination of the Stoichiometry of the reaction
Mix 50 ml of H 2O2 and 250 ml of Na 2S2O3 in a Dewar flask. Take note of the initial and highest final temperature readings. With the total volume of reactant solution held constant at 300 ml, the experiment is repeated with five different sets of H2O2 and Na2S2O3 volumes. (B) Determination of the water equivalent of the Dewar flask
Pour 100 ml of cold water into the Dewar flask, and then record the temperature. Immediately, pour another 100 ml of hot water of known temperature into the flask to mix with the cold water. Take note of the highest temperature r eached. (C) Determination of the heat capacity of reaction mixture (M Cp) sys
100 ml of Na2S2O3 at room temperature is poured into the Dewar flask. Note the initial temperature .Start the chart recorder using a chart speed of 200mm/M. Next, 200 ml of H 2O2, also at room temperature is added. Look out for the highest temperature reached from the temperaturetime curve plotted on the chart recorder. When this happens, immediately add 150ml cold water of known temperature into the Dewar flask. Record the steady equilibrium temperature. Derive the energy balance equations to calculate (MCp) sys and the heat of reaction ( H). Repeat the run with different sets of initial reactant temperatures, say at 400C; 480C and 550C (separate flasks of Na2S2O3 and H2O2 heat up to 40 0C before mixing).
Tabulation and Calculation: Determination of the Stoichiometry of the reaction
Concentration of Na2S2O3 Concentration of H 2O2
CA= 1.0723M CB= 1.0937M
Volume of Na2S2O3 VA(ml)
Volume of H2O2 VB(ml)
Initial Ti (oC)
Final Tf (oC)
(oC)
50
250
22.5
42.2
19.7
100
200
22.5
62
39.5
150
150
22.5
58.2
35.7
200
100
22.5
48.3
25.8
250
50
22.5
35.7
13.2
T
Plot T vs. volume of H 2O2 used 45 40 35 30 25 T 20 15 10 5 0 0
50
100
150
200
250
300
Volume of H2O2 Reading out from the graph plotted, the following volumes were obtained corresponding to maximum ∆T Volume of H2O2 occurred at maximum ∆T Volume of Na2S2O3 occurred at maximum ∆T Maximum ∆T
190ml 110ml 40oC
Therefore the stoichiometric coefficient can be determined by the following ratio:
B A
Moles of B ( H 2O2 ) reacted Moles of A ( Na2 S 2O3 ) reacted
V B C B V A C A
190 1.0937 110 1.0723
1.7617
Determination of the water equivalent of the Dewar flask
Mass of cold water Mass of hot water Temperature of cold water Temperature of hot water Equilibrium Temperature
mc = 100 g mh = 100 g Tc = 24.3oC Th = 60.0oC Te = 40.3oC
The water equivalent of the Dewar flask
me
mh T h T e
T e T c
mc
10060.0 40.3
40.3 24.3
23.125g
Determination of the heat capacity of reaction mixture (MCp) SYS
Volume of Na2S2O3 = 100 ml Volume of H2O2 = 200 ml Volume of cold water = 150 ml Initial Ti (oC)
Highest Th (oC)
Equilibrium Te (oC)
Cold water Tc (oC)
(MC p)sys * (J/K)
-H ** (kJ/mol Na2S2O3)
24
57.5
55
24.3
5037.582
1573.804
40
80
69
24.3
1602.321
597.714
48
85
70
24.3
1177.126
406.170
55
89
75
24.3
1417.434
449.433
Sample calculation: *
MC
p sys
mcC p water T e T c
T h T e
meC p water
4.181055 24.3 57.5 55
23.125 4.1810
= 5037.582375 J/K
**
H
MC p sys T h T i moles of Na2 S 2O3 5037.582 57.5 24 0.1 1000 1.0723
= 1573.804kJ mol Na2 S 2O3
Average (MC p)sys = 2308.616(J/K) Average -H ** = 756.78(kJ/mol Na 2S2O3) Determination of the activation energy and rate constant
Midpoint Tm =0.5 (Ti +Th) (oC)
Tm (k)
dTm/dt
ln [dTm/dt]
1/Tm
A
Rate Constant (k)
40.75
313.9
369.296
5.91159
0.003185728
1.30×10
3201.97
60
333.15
951.857
6.85841
0.003001651
3.63×10
3205.39
66.5
339.65
1358.6
7.21421
0.002944207
2.433×10
3201.74
72
345.15
3451.5
8.14656
0.002897291
1.757×10
3202.81
Plot ln [dTm/dt] vs. 1/Tm 9.00000 8.00000 7.00000
] t d 6.00000 / 5.00000 m T 4.00000 d [ n 3.00000 l
y = -6945.4x + 27.919 R² = 0.9032
2.00000 1.00000 0.00000 0.00285
0.0029
0.00295
0.003
0.00305
1/Tm
0.0031
0.00315
0.0032
0.00325
Sample calculation
The slop of the curve = -E/R = -6945.4 Thus E = 57744.0556J/mol Based on the intercept of the curve, the value of the frequency factor is determined:
dT dt
A ( H ) ( M C P ) SYS
e E / RT .C 1 .C 2 .V SYS
Taking the natural logarithm on both sides of the equation yields:
dT 1 E / RT .C 1 .C 2 .V SYS ln A ln( H ) ( M C P ) SYS .e dt
ln
From experimental data, ln [dT m/dt] is evaluated to be:
dT 5.91159 dt
ln
It is also cautioned that the concentration of sodium thiosulphate and hydrogen peroxide is evaluated with respect to initial concentration and stoichiometric ratio, thus the concentrations of these two reactants are as follows: C1 (Concentration of Na2S2O3 at midpoint) = 1.0723 M C2 (Concentration of hydrogen peroxide at midpoint) = 1.0937 M Thus, the frequency factor is calculated: 57744.06 756.78 8 5.91159 ln A ln e .314313.9 1.07231.0937 0.3 2308.616
A
e 5.91159ln2.83610 11
1.302 1013 The rate constant K = A.e (-E/RT) = 1.302×10 13 × e(-6945.4/313.9) = 3201.97
Discussion: Determination of the Stoichiometry of the reaction From the experiment one has observed that the maximum temperature (40 oC) occurred at the mixture of H 2O2 and Na2S2O3 reacting at a range of 190 to 110 ml. From this lab experiment, one has also made a conclusion that the stoichiometric ratio is 1.761. This indicates that approximately 2 moles of hydrogen peroxide is needed to react with 1 mole of sodium thiosulphate to form products. Since the amount of reactant, H 2O2 in this experiment is found to be in excess, the heat of reaction expressed in terms KJ/mol of Na2S2O3, and the value is 756.78KJ/mol. Determination of the heat capacity of reaction mixture (MCp) SYS and Heat of Reaction It was observed that the enthalpy relative to 1 mole of sodium thiosulphate decreases with the increase in temperature Th. Reason being, the deviation of T h from equilibrium temperature of the system causes the denominator of the expression to increase, thus the value of (MCp)SYS increases. As a result, the change in enthalpy of the system decreases. It was also noted that, an average heat capacity and heat of reaction was taken instead of individually. This is to ensure ease of calculation for the frequency factor. Determination of the activation energy and rate constant During the reaction, heat is liberated due to exothermic reaction and. This will cause the temperature of the system to increase. If a desired temperature of the system is to be maintained so as to meet the product specification, it is crucial that excess heat must be removed, in order to maintain the reaction temperature. One solution is the addition of cooling coils to remove the excess heat. Based on the calculation of the activation energy, it is known that the activation energy of this reaction is 57744.0556 J/mol. This indicates that this is the amount of energy needed for product to be formed as sufficient energy is needed to overcome this energy barrier. From the Arrhenius equation it is suggested that the value of rate constant depends on the temperature of the system. This means that if the temperature of the system is high, the exponent term will become bigger, hence result in a higher rate constant. This is however not true, based on the calculations increasing the temperature of the system does not have any effect on the rate constant. Reason being, the exponential constant, which is also known as a frequency factor, is also proportionally inversed to the exponential term seen in the Arrhenius equation. This indicates that when the temperature increases, the value of frequency factor increases thus balancing the equation in the Arrhenius equation. Thus, the following statement made in the literature does not coincide with this experimental findings that, “Reactions with high activation energies are very temperature-sensitive; reactions with low activation energies are relatively temperature-insensitive”. Also, as one has noted, the order of the reaction of sodium thiosulphate and hydrogen peroxide is second order. This indicates that the rate constant has a unit of mole/min. Conclusion Based on this lab experiment, one has calculated the mole ratio of the reactants to be 1.7617, which is 2 moles of hydrogen peroxide is needed to react with 1 mole of sodium thiosulphate to form product. Also, based on the calculation of heat capacity, it is known that the heat capacity of the system tends to decrease in with the increase of the midpoint temperature. With the value of the heat capacity and enthalpy change known, the activation of energy is evaluated to be 57744.066 J/mol. This means, at least 57744.066 J/mol of energy is needed in order for reactants to form products. It was discovered later on that the temperature does not affect the rate constant as the
frequency factor is increased so that the Arrhenius equation is balanced. From this, one can conclude that the frequency factor related to the exponential term as follows A 1 e E RT .
Reference:
Cohen, W. C. and Spence, J. C., Chem. Eng. Prog.,Vol 58, No.12 December, pg 40-41, 1962.
