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 activation-

energy-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:

SYS

RTE

SYSP VCCeCMHA ....)()(dt

dT21

/1

From the stoichiometry and the initial reaction concentrations, C1 [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 H2O2 and 250 ml of Na2S2O3 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 reached.

(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 H2O2, also

at room temperature is added. Look out for the highest temperature reached from the temperature-

time 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; 48

0C and 55

0C (separate flasks of

Na2S2O3 and H2O2 heat up to 400C before mixing).

Tabulation and Calculation: Determination of the Stoichiometry of the reaction

Concentration of Na2S2O3 CA= 1.0723M

Concentration of H2O2 CB= 1.0937M

Volume of Na2S2O3

VA(ml)

Volume of H2O2

VB(ml)

Initial

Ti (oC)

Final

Tf (oC)

T

(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

Plot T vs. volume of H2O2 used

Reading out from the graph plotted, the following volumes were obtained corresponding to

maximum ∆T

Volume of H2O2 occurred at maximum ∆T 190ml

Volume of Na2S2O3 occurred at maximum ∆T 110ml

Maximum ∆T 40oC

Therefore the stoichiometric coefficient can be determined by the following ratio:

7617.10723.1110

0937.1190

)(

)(

322

22

AA

BB

CV

CV

reactedOSNaAofMoles

reactedOHBofMoles

A

B

0

5

10

15

20

25

30

35

40

45

0 50 100 150 200 250 300

T

Volume of H2O2

Determination of the water equivalent of the Dewar flask

Mass of cold water mc = 100 g

Mass of hot water mh = 100 g

Temperature of cold water Tc = 24.3oC

Temperature of hot water Th = 60.0oC

Equilibrium Temperature Te = 40.3oC

The water equivalent of the Dewar flask

gmTT

TTmm c

ce

ehhe 125.23

3.243.40

3.400.60100

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)

(MCp)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:

*

waterpe

eh

cewaterpc

sysp CmTT

TTCmMC

1810.4125.23555.57

3.24551810.4

= 5037.582375 J/K

**

322 OSNaofmoles

TTMCH

ihsysp

0723.110001.0

245.57582.5037

= 322804.1573 OSNamolkJ

Average (MCp)sys = 2308.616(J/K)

Average -H ** = 756.78(kJ/mol Na2S2O3)

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 1.30×1013

3201.97

60 333.15 951.857 6.85841 0.003001651 3.63×10

12 3205.39

66.5 339.65 1358.6 7.21421 0.002944207 2.433×1012

3201.74

72 345.15 3451.5 8.14656 0.002897291 1.757×1012

3202.81

Plot ln [dTm/dt] vs. 1/Tm

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:

SYS

RTE

SYSP

VCCeCM

HA...

)(

)(

dt

dT21

/

y = -6945.4x + 27.919R² = 0.9032

0.00000

1.00000

2.00000

3.00000

4.00000

5.00000

6.00000

7.00000

8.00000

9.00000

0.00285 0.0029 0.00295 0.003 0.00305 0.0031 0.00315 0.0032 0.00325

ln [

dT m

/dt]

1/Tm

Taking the natural logarithm on both sides of the equation yields:

SYS

RTE

SYSP VCCeCMHA ....)()(lnlndt

dTln 21

/1

From experimental data, ln [dTm/dt] is evaluated to be:

91159.5dt

dTln

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:

3.00937.10723.1616.2308

78.756lnln91159.5 9.313314.8

06.57744

eA

1110836.2ln91159.5 eA

1310302.1

The rate constant K = A.e(-E/RT)

= 1.302×1013

× 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 (40oC) occurred at

the mixture of H2O2 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, H2O2 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 Th 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 RTEeA 1 .

Reference:

Cohen, W. C. and Spence, J. C., Chem. Eng. Prog.,Vol 58, No.12 December,

pg 40-41, 1962.