Ramy Chaoul

BOMB CALORIMETRY: DETERMINATION OF THE HEAT OF COMBUSTION AND THE

STANDARD

ENTHALPY OF FORMATION OF GLUCOSE

Course: Chem 220

Name: Ramy Chaoul

Instructor: Dr. Samar Sadek

Group (C)

Date: 25/02/20131

Ramy Chaoul

Abstract:

The purpose of this experiment is to measure the heat of combustion of glucose using a constant–volume bomb calorimeter; where heat causes an increase or rise of the temperature by the calorimeter is which is evaluated and used to calculate the change of energy during combustion. Thus we can use this data to and apply thermodynamic relations to calculate the enthalpy of combustion and the enthalpy of formation of glucose. To determine the specific heat capacity (Cv) of the bomb calorimeter we standardize it by the use of benzoic acid pellets of which the heat capacity (Cv Benzoic acid) is known to and thus enables the determination of the calorimeter heat capacity. We also use the benzoic acid for spiking and triggering glucose combustion. After calibration, we add a certain defined mass of benzoic acid to glucose, and thus glucose combustion is studied. Two sources of heat that cause a rise in temperature are considered as an error to be corrected; the first is the fuse combustion while the second is due to the presence of N2 in the bomb calorimeter. We determine the increase in temperature due to the fuse combustion by weighing the fuse before and after each run; while the nitric oxide in the calorimeter is converted to nitric acid when it reacts with water, and thus to correct for N2 present as part of entrapped air, a titration with standardized base of sodium carbonate is conducted. Our obtained values for ΔHcombustion and ΔHo

formation are -3855.854 KJ/mol and -609.1805 KJ/mol respectively, with % errors of (13.45%) and (29.79%)respectively.

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Introduction (2) :

fig 1: bomb calorimeter(1)

During the combustion of glucose the heat transfer is monitored and measured using a constant volume bomb calorimeter. Each material has a specific enthalpy of combustion, which is the enthalpy change accompanying a complete oxidation of the material to form H2O and CO2

(1) .The combustion reaction is:C6H12O6 + 6O2→ 6CO2+ 6H2O

An enthalpy change that accompanies an isothermal process is not measured directly (i.e., the change of state is not carried out isothermally). Instead the process is carried out adiabatically, using a path composed of 2 steps (2):

To start, we measure the experimental process of enthalpy change isothermally by the formula:

R1(T0)+R2(T0)+S(T0)→P1(T0)+P2(T0)+S(T0)

Where Δ Uisothermal=Δ UT0

“Where S refers to all parts of the system that is in contact with the reaction medium other than the reactants and products by that we mean that S refers to the stirrer, the

calorimeter walls, the water bucket ...etc ”

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The determination step is not carried in a single isothermal step because the fall and rise of heat causes it variation, thus the determination is carried adiabatically by 2 steps,

where Δ U is a state function that is independent of the used path :

(1) Adiabatic Process: (from T0 to T1)

R1(T0) +R2 (T0) + S (T0) →P1(T1)+P2(T1)+S (T1) Δ Ucal

(2) Imaginary Process back to the initial temperature(from T1 to T0)

P1(T1)+P2(T1)+S(T1) → P1(T0)+P2(T0)+S(T0) Δ Uimag

with Δ Uisothermal = Δ Ucal +Δ Uimag

But Δ Ucal = qv + W = 0 where we have a constant volume: ∆V =0 then W=p∆V = 0

where the heat flow in an adiabatic process qv is also = 0.

Then, Δ Uisothermal = Δ Uimag = qv + w = Cv ∆T= Cv (T0- T1) = -Cv (T1-T0) where Cv = Cv (S) + Cv (H2O) + Cv (CO2)

To determine the heat capacity Cv (of the whole bomb), standardization is applied, where the known heat of combustion of benzoic acid is used in the standardization reaction. To calculate Cv, ∆T (the calorimeter measures the temperature rise), the following equation is used:

mbenzoic acid Ubenzoic acid + mfuse Ufuse + meq UN2= -Cv (S) T

with: mfuse = mass of fuse combusted (g)

meq = milliequivalence = mmol of N2 present at equivalence (mmol)= N(base) x V(base at eq.)

Ufuse = -1400.0 cal/g UN2 = -14.1 cal/meq

Ubenzoic acid = -6318.0 cal/g

T = temperature rise measured by the calorimeter (°C)

Since the number of moles produced from the combustion of standard material of carbon dioxide and water is different from the number of moles produced upon the combustion of the material under study, we will encounter an error that we will consider as a minimal error, because of the very small mass of the sample used which is £ 1g, compared with the mass of water in the bucket which is 2000 g, where the masses of the bomb and bucket > 500 g. CV can thus be approximated as being equal to CV (S), and thus the equation becomes:

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Δ Uisothermal = -Cv (S) (T1-T0)

Ideally the situation would be when a change in temperature is solely due to a change in the energy of combustion of glucose. However, the ideal situation is not present in this experiment. A correction is needed for these errors.

The first correction we account for is the change in energy due to the combustion of the fuse used, where two measures of the fuse are conducted one before and one after a calorimeter run in order for us to calculate the mass of the burned wire. The heat correction for fuse combustion is given as –1400 cal/g.

The second correction is for the air that enters the bomb and causes a temperature rise, where the N2 present in air is converted to nitric oxide upon reacting with oxygen then into nitric acid upon reacting with the water inside the bomb. We calculate the concentration of nitric oxide by a base titration of the nitric acid HNO3 with standard sodium carbonate NaHCO3 (0.0709 M) and thus we will be able to know the amount of nitrogen gas trapped in the bomb. Methyl orange is used as an indicator. The heat released from this reaction of nitrogen and oxygen is –14.1 cal/meq of HNO3.

The third and final correction (1) is for the calculated standard enthalpy of formation from the enthalpy of the combustion reaction, where we neglect the pressure effect on the values of energy and enthalpy. In reality, the effect of pressure changing on the energy and enthalpy is very small relative to the accompanied chemical changes. Thus the equation for glucose becomes:

msugar Usugar + m BA ∆UBA + mfuse Ufuse + meq U(N2) = -Cv (s) T

where: mBA = mass of benzoic acid used as spiking material (g)

mfuse = mass of fuse combusted (g)

meq = milliequivalence = mmol of N2 present at equivalence (mmol)

Ufuse = -1400.0 cal/g

UN2 = -14.1 cal/meq

Ubenzoic acid = -6318.0 cal/g

T = the measured temperature rise by the calorimeter (°C)

After we determine Δ Uglucose, its enthalpy of combustion is calculated using the following thermodynamic relation:

ΔHglucose = ΔUglucose + Δ (PV)

ΔHglucose = ΔUglucose + ΔngasRT

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with: ngas= change in number of moles of gases (mol) = Σn

products - Σnreactants

R = gas constant 8.314 J/mol.K

T = T0 = temperature of the adiabatic process (°C)

The standard enthalpy of formation of glucose ΔH0f is determined using:

∆H reaction = Σ∆H formation of products - Σ∆H formation of reactants

ΔH glucose = 6ΔH0f (CO2) + 6 ΔH0

f (O2) - ΔH0f (glucose)

Experimental Plan:

1- The calorimeter should be warmed for 20 min until the jacket temperature is constant

and stabilized at 35 °C.

2- Cut a 10 cm of Ni alloy wire and weigh it on each run, the wire must be twisted it in a

bell-shaped loop with no sharp edges to avoid the cutting of the wire, so that we will

attach the loop to the openings at the end of the grip electrodes of the bomb.

3- Weigh a benzoic acid pellet to know its mass, and then transfer it to the sample capsule

on the electrode loop, where it is fixed in position using the Ni alloy fuse wire.

4- Add 1 mL of distilled water to the bomb, where it will act as an absorbing agent and thus

absorb nitric oxide entrapped in the air and convert it to nitric acid. The sealing ring must

be moistened.

5- Use the pressurized oxygen gas to fill the bomb with oxygen at a pressure of 30 atm that

should be maintained, release the valve two consecutive times to expel unwanted N2

entrapped in the air.

6- Fill the bucket with 2000 grams of water (at constant temperature 300C) and then place

the bucket in the calorimeter so that the bomb calorimeter will be placed in the bucket.

7- Using the specific clamp, lower the bomb and place it in the bucket after attaching the

two ignition wires into the sockets on the bomb’s head and make sure of the complete

immersion of the bomb into the bucket.

8- Now we close the calorimeter and press “shift start” then enter “sample ID” # followed

by the “weight” of the sample under study.

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9- At the process end we press “DONE” bottom to store the results, where we open the

cover to disconnect, and remove the bomb be using the clamp once again.

10- More water is added to the 1 ml already present in order to wash the bomb where the

washings are titrated with 0.0709 N Sodium carbonate for acid correction.

11- The procedure is repeated twice for benzoic acid (standardization), and another two

times for glucose (determination), and finally a last time for the unknown sugar

determination.

Data:

ID number 7 8

Mass benzoic acid pellet ±0.0001g 1.0125 1.0119

Mass 10 cm wire ±0.0001g 0.0169 0.01603

Mass remaining fuse ±0.0001g 0.0034 0.0031

Volume Na2CO3 ±0.02 mL 3.80 5.10

Initial Temperature ±0.00001°C 27.7049 27.1285

ΔT temperature rise ±0.00001°C 2.65477 2.65087

Table 1: Standardization by combustion of Benzoic Acid pellets (sample 7 and 8)

ID number 9 10

Mass benzoic acid ±0.0001g 0.2946 0 .2985

Mass sugar in pellet ±0.0001g 0.6940 0.6965

Mass pellet ±0.0001g 0.9696 0.9874

Mass 10cm wire ±0.0001g 0.0165 0.0165

Mass remaining fuse ±0.0001g 0.0029 0.0039

Volume Na2CO3 ±0.02 mL 1.90 4.40

Initial Temperature ±0.00001°C 27.3024 28.7004

ΔT temperature rise ±0.00001oC 1.79823 1.84897

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Table 2: determination by combustion of Benzoic Acid in Mixed pellets (sample 9and 10)

Ramy Chaoul

ID number 11

Mass benzoic acid ±0.0001g 0.2957

Mass unknown powder ±0.0001g 0.6979

Mass pellet ±0.0001g 0.9656

Mass 10cm wire ±0.0001g 0.0162

Mass remaining fuse ±0.0001g 0.0014

Volume Na2CO3 ±0.02 mL 2.00

Initial Temperature ±0.00001°C 28.2060

ΔT temperature rise ±0.00001oC 1.78447

Table 3: combustion of unknown powder mixed with benzoic acid (sample11)

N.B.

UncertaintiesInstruments±0.02mlBurette±0.0001 gAnalytical balance±0.00001 0CBomb calorimeter

Table 4: uncertainty

Calculation:

CV of the calorimeter

−C v (S ) ∆T=mBA ∆ U BA+mfuse ∆ U fuse+meq ∆ U N2

C v ( S )=−mBA ∆ U BA−mfuse ∆ U fuse−meq ∆ U N2

∆ T

m fuse = m fuse before firing – m fuse after firing.

m eq (milliequivalence) = NHNO3 × VHNO3 = NNa2CO3 × VNa2CO3 = number of millimoles of HNO3 at equilibrium

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given:

∆Ubenzoic acid = -6318.0 cal/g

∆U wire = - 1400.0 cal/g

∆U (N2) = -14.1 cal/meq “ (reference 2)

Sample #7 (standardization):

Cv = (-1/ΔT) (mΔUbenzoic acid+mfuseΔUfuse+meqΔU(N2))

-) =1/2.65477)) (0.9985g*-6318cal/g) + (0.0135g*-1400cal/g)+(3.80*0.0709N*-14.1(

Then, Cv= 2421.20 cal/0C

Sample # 8:

Cv = (-1/ΔT) (mΔUbenzoic acid+mfuseΔUfuse+meqΔU(N2))

-) =1/2.65087)) (0.9941-*6318cal/g) + (0.0129g*-1400cal/g)+(5.10*0.0709N*-14.1(

Then, Cv= 2436.26 cal/0C

→Average Cv : Cvavg= (Cv71+ Cv74 )/2= 2428.73 cal/0C

Determining the ∆U combustion of glucose :

∆Uglucose = [ - Cv∆T – (mBA ∆UBA + mburned fuse ∆U fuse + meq ∆U(N2) ] / mglucose

Sample #9(determination):

Mass of glucose=0.6940g

Mass of benzoic acid=0.2946g

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Mass of the pellet= 0.9696 g

%glucose = (0.6940/(0.6940+0.2946))*100=70.20%

%benzoic acid = (0.2946/(0.2946+0.6940))*100=29.80%

Then, the mass of benzoic acid in the pellet is: mb= mpellet* percentage of benzoic acid= 0.9696*29.80%=0.2889g

And the mass of glucose in the pellet is: mg= mpellet* percentage of glucose= 0.9696*70.20%= 0.6807 g

using the equation:

ΔUglucose=(1/ mglucose) (-CvΔT - mΔUbenzoic acid-mfuseΔUfuse-meqΔU(N2) ) =(1/0.6807)(- 2422.905*1.79823 - 0.2889*-6318 – 0.0136*-1400 – 1.90*0.0709*14.1)= -3694.035cal/g

→ ΔUglucose( for sample 9 ) = -3694.035cal/g

Total mass ± 0.0001 g 0.9696

%glucose ± 0.8% 70.20%

%benzoic acid ± 1% 29.80%

M glucose 0.6807 g

M benzoic acid 0.2889g

∆U glucose -3694.035cal/g

Table 5: sample 9

Then using the formula:

ΔH=ΔU+Δ (pV)= ΔU+ RTΔn

but, Δn= 0 so ΔHcombustion=ΔUglucose

Thus ΔHcombustion=ΔUglucose= -3694.035cal/g

Then, conversion of the unit of the combustion into joule units:

ΔHm=ΔH ×M ×4.184= -3694.035×180.16 ×4.184= -2781.8626KJ/mol

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Moreover, we can calculate the standard enthalpy of combustion of glucose, the used formula:

ΔHcombustion= ∑(product)v Hf0- ∑(reactants) v Hi

0

Where v is the stochiometric coefficient of the reaction

And using the following given informations:

Δ Hf0( H2O)=-285.83KJ/mol

Δ Hf0(CO2)= -393.509KJ/mol

Thus, ΔHf0(glucose)=6 Δ Hf

0( H2O)+ 6 Δ Hf0(CO2)- 6 Δ Hf

0(O2)- ΔHcombustion

= -648.394 KJ/mol.

Sample #10:

Doing the same calculations for sample 10 we get:

Total mass ± 0.0001 g 0.9487

%glucose ± 0.8% 70.00%

%benzoic acid ± 1% 30.00%

M glucose 0.6641 g

M benzoic acid 0.2846g

∆U glucose -4017.6396cal/g

Table 6: sample 10

ΔUglucose=(1/ mglucose) (-CvΔT - mΔUbenzoic acid-mfuseΔUfuse-meqΔU(N2) ) =(1/0.6641)(- 2422.905*1.84897- 0.2846*-6318 – 0.0129*-1400 – 4.40*0.0709*14.1)=-4017.6396cal/g

→ΔUglucose( for sample 10) = -4017.6396cal/g

Then, ΔHcombustion=ΔUglucose=-4017.6396cal/g

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ΔHm(76)= ΔH ×M ×4.184= -4017.6396cal/g ×180.16 ×4.184= -3028.454 KJ/mol

Next, the standard enthalpy of combustion of glucose is calculated:

ΔHf0(glucose)=6 Δ Hf

0( H2O)+ 6 Δ Hf0(CO2)- 6 Δ Hf

0(O2)- ΔHcombustion

= -568.667 KJ/mol

The average value of ΔHm and ΔHf0 of glucose :

The average value of enthalpy of combustion: ΔHm= -3855.854 KJ/mol

The average value of standard enthalpy of combustion of glucose:

ΔHf0= -609.1805 KJ/mol.

Sample #11 (unknown):

Mass of the unknown=0.6979g

Mass of benzoic acid= 0.2957 g

Mass of pellet= 0.9656 g

% unknown = (0.6979/ (0.6979+0.2957))*100=70.24%

%benzoic acid = (0.2957/ (0.6979+0.2957))*100=29.76%

→mass of benzoic acid in the pellet = 0.9656×29.76%= 0.2873g

→mass of unknown in the pellet= 0.6782g

ΔUunknown =(1/ munknown) (-CvΔT - mΔUbenzoic acid-mfuseΔUfuse-meqΔU(N2) )

= -3656.628 cal/g

→ΔUunkown( for unknown sample) = -3656.628 cal/g

Total mass ± 0.0001 g 0.9656

%glucose ± 0.8% 70.24%

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%benzoic acid ± 1% 29.76%

M glucose 0.6782 g

M benzoic acid 0.2873 g

∆U glucose -3656.628cal/g

Table 7:sample 11 (unknown)

Discussion :

Comparison to literature value

A constant volume oxygen bomb calorimeter was used for the determinantion of the

enthalpy of combustion of glucose of an unknown sugar.

% error=|T heoretical−Experimental|

|T h eoretical|X 100

Function Experimental Theoretical [1] % error

ΔHcombustion -3855.854 -3508.00 13.45%

ΔHoformation -609.1805 -1068.04 29.79%

Table 8: experimental and theoretical values

There are errors obtained in our result due to many factors:

1. The titration of nitric acid where the added volume of Na2CO3 could hold an error in addition from the burette and an error in reading the value obtained, where the change in color of the methyl orange as indicator from orange to yellow is hard to be noticed directly which might contribute to an excess addition of Na2CO3.

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2. Errors due to the uncertainty of instruments used like the analytical balance (±0.0001 g) and thermostat uncertainty ((±0.000010C), where we might also encounter reading errors.

3. The fact that we neglect the pressure effect on the values of energy and enthalpy, where in reality the effect of pressure changing on the energy and enthalpy is very small relative to the accompanied chemical changes, which causes a certain error(2).

4. Another value neglected was the contribution of Water and carbon dioxide on the

heat of combustion because we used the same Cv for calculations for benzoic

acid and for glucose and the unknown sugar.

5. Still there would be certain errors encountered that would affect our readings and

values.

6. Other problems may occur in transferring material and various substance from a

place to another or from a vessel to another which may lead to some loss of our

substance.

Aerobic and Anaerobic Respiration: (3)

“Aerobic respiration is the process in which glucose is converted into CO2 and H2O in the presence of oxygen, releasing large amounts of ATP (3)”. The process of an aerobic respiration is represented in this equation:

Glucose + Oxygen →Energy + Carbon dioxide + Water

During the process of aerobic respiration 38 molecules of ATP are produced for every molecule of glucose that is utilized (3) .

“Anaerobic respiration is the cellular respiration which takes place in the absence of oxygen. The process of anaerobic respiration is relatively less energy yielding as compared to the aerobic respiration process.” The process of anaerobic respiration for

production of energy can occur in either of the ways represented below:

Glucose →Energy (ATP) + Ethanol + Carbon dioxide

Glucose →Energy (ATP) + Lactic acid

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The enthalpy of the combustion of glucose is -2808.00KJ/mol via aerobic respiration while the enthalpy of combustion of anaerobic fermentation is -1344.00KJ/mol then the total will be 2688.00KJ/mol. The difference between the aerobic respiration and anaerobic fermentation is around 120KJ/mol.

Calculation of the strain energy of cyclopropane :

“ Strain energy is the energy associated with every compound, corresponding to the bending or stretching of bond from their normal state as a result of geometric requirement. (4)”

The standard enthalpy difference of the dissociation of cyclopropane is only as a function of strain energy S. The standard enthalpy of dissociation ΔHdis is the sum of the bond energies B. B values are positive and for stable compounds, ΔHdis is positive 3.

ΔHdis= ∑Bi-S+R; Bi is the bond energy, S strain energy, R is resonance energy, result from aromatic character .

“Cyclohexane carboxylate has a lower strain energy than n-butyl cyclopropane because the angle of cyclohexane is around 1090 while n-butylcyclopropane is approximately 600. Bomb calorimetry experiment is done for the two compounds so ΔHcombustion will be measured and the strain energy can be deduced.” In this case the strain energy of the cyclopropane is 112.887KJ/mol (4).

cyclopropanecarboxylic acid cyclohexanecarboxylic acid

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Resonance energy of benzene:

The resonance energy of a compound is a measure of the extra stability of the conjugated system compared to the corresponding number of isolated double bonds (5).

In order to identify the resonance energy of benzene a comparaison must be done between its enthalpy of combustion and that of its conjugated system .

Benzene has two resonance structures. its stabilization energy(resonance energy) is determined by the bomb calorimetry. we consider the energy change for the following reaction as the resonance energy:

B * (g) → B (g) [5]

B* represents the Kekule form of benzene (cyclohexatriene, not resonance stabilized) and B represents the actual benzene (resonance stabilized). The combustion of Kekule benzene and actual benzene, the difference in the combustion energies corresponds to the resonance energy:

∆Uresonance = ∆UcombB *( g ) - ∆Ucomb

B ( g ) [5]

We need to combust a molecule that has similar structure as a Kekule benzene structure (i.e. something with 3 C=C, 3 C-C, and 6 C-H bonds), in condition that the molecule does not have any contributions to its internal energy (such as steric strain). We use a combination of molecules that are combined equal to a Kekule benzene structure (there is no one molecules equal to Kekule structure):

TTCC CHX B*

3 C=C 0 C=C 3 C=C

9 C–C 6 C–C 3 C–C

18 C–H 12 C–H 6 C–H

where:

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TTCC = 1,5,9-trans,trans,cis-cyclododecatriene and CHX = cyclohexane, both strain-free.

Accordingly, ∆UcombB* ( g ) = ∆Ucomb

TTCC ( g ) - ∆UcombCHX ( g )

The enthalpy: ∆ H =∆U +∆ (PV ) = ∆U +RT∆ngas

the reaction of combustion of benzene:

C6H6 (g) +15/2O2 (g) 6 CO2 (g) + 3 H2O (g)

that ∆ngas= (9-17/2) = 1/2.

Substituting ∆U=∆H-RT∆ngas into

∆Uresonance = (∆HcombB *( g) - 1/2RT)- (∆Hcomb

B ( g )- 1/2RT)

∆Uresonance = ∆HcombB *( g ) - ∆Hcomb

B ( g )

where: ∆HcombB *( g ) = ∆Hcomb

TTCC ( g ) - ∆HcombCHX ( g ) [3]

∆Uresonance = ∆HcombTTCC ( g ) - ∆Hcomb

CHX ( g ) - ∆HcombB ( g )

This equation gives the resonance energy of Benzene (3).

Conclusion : To accomplish this experiment, we used a constant volume bomb calorimeter, to measure the heat of combustion of glucose. In order to calculate the energy change associated with the combustion of glucose we observe and calculate the temperature change. Thus we will be able to calculate and determine the enthalpy of combustion and the enthalpy of formation of glucose using some thermodynamic functions. We standardize the calorimeter two times by the use of a benzoic acid of known heat of combustion, and thus we can obtain Cv of the bomb. We apply the necessary calculations to determine the relative enthalpies of glucose and of the unknown sugar (ID#78). Our results contain an error which is 13.45 % and 29.79% for enthalpy of combustion and formation relatively. This error is due to many factors explained above.

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References:

1- Bomb Calorimetry Handout.Dr. Halaoui (spring 2013)

2- Wikipedia: http://en.wikipedia.org/wiki/Benzene

3- http://www.chemistryguide.org/

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