Bomb Calorimetry of Sucrose Lab PDF

Preview

Summary

Lecture 6-8...

Description

BOMB CALORIMETRY: HEAT OF FORMATION OF SUCROSE (SK) Kuganesh Ketheesh Student ID # 100598968 Date: March 30th, 2021 T.A: Omer Yukseker

INTRODUCTION The purpose of this lab is focused on a very two very important objectives. The first objective is to determine the heat capacity of the calorimeter. The second objective is to determine the standard heat of formation of sucrose from its heat of combustion. In this experiment the standard heat of formation of a common organic compound such as naphthalene ( C10H8) , glucose (C6H12O6) , or sucrose (C112H22O11) will be determined but in this case it would be sucrose. This would essentially be determined through its measured heat of combustion.

In this lab , we use a calorimeter in order to obtain data , which can later be analyzed and used to perform necessary calculations. The type of calorimeter used is a bomb calorimeter .A bomb calorimeter is a type of constant-volume calorimeter used in measuring the heat of combustion of a particular reaction. . The bomb, with the known mass of the sample and oxygen, form a closed system ,no gases escape during the reaction. The weighed reactant put inside the steel container is then ignited. It is used to measure the energy produced by reactions that yield large amounts of heat and gaseous products, such as combustion reactions.

The compound being studied in this lab is sucrose;

Sucrose The formation reaction for sucrose is; 12C(s) + 11H 2 (g) + 11/2O 2 (g) ➝ C 12 H 22 O 11 (s) It is difficult to execute “cleanly” - other products would likely form. To circumvent this problem a reaction of sucrose is used where the products are well known and for which the standard enthalpies of formation of all the other products and reagents are known. The combustion reaction of sucrose is such a reaction: C 12 H 22 O 11 (s) + 12O 2 (g) ➝ 12CO 2 (g) + 11H 2 O(l) Once the standard enthalpy of combustion is measured, the standard enthalpy of formation of sucrose can be found from the tabulated standard enthalpies of formation for CO 2 (g) and H 2 O(l)

The heat of formation of sucrose is found using the following equation.

∆ H rxn=

∑

product

∆ n products ∆ H f , products−

∑

∆ nreactants ∆ H f , reactants

reactants

In a chemical reaction, delta H represents the sum of the heats of formation, commonly measured in kilojoules per mol (kJ/mol), of the products minus the sum of those of the reactants. The letter H in this form is equal to

a thermodynamic quantity called enthalpy, representing the total heat content of a system. The combustion reaction of sucrose is carried out with a large excess of O 2 to ensure complete combustion of the sucrose. It also allows the reaction to occur very rapidly. The high pressure requires a special reaction vessel: a “ bomb” that can withstand high pressures and which is chemically inert. By necessity, then, the reaction must be performed at constant volume.

In this experiment we will use calorimetry measurements which are based on;

q=C cal ∆T Where (q) is the given amount of heat , which produces a temperature change ( on the heat capacity (

C cal ¿

∆T

) which is dependent

of the calorimeter.The heat gained by the calorimeter, q cal, is determined from

the formula, qcal = Ccal×Δt, where Δt is the change in temperature undergone by the mixture.

Throughout this lab we determined heat capacity of the calorimeter and the standard enthalpy of formation of sucrose through a variety of calculations. When ensuring a constant C cal , you need to realize a bulk of the calorimeter heat capacity comes from the water in the bucket. However , the air is composed of particles of nitrogen and in order to get rid of it the reaction is purged. By purging the bomb, you essentially eliminate side reactions so that your q is accurately known. Once the bomb is purged and finally ignited , the data will be electronically recorded on the calorimeter. This can be used to determine the

∆T

, which can be used to

help determine the heat capacity of the calorimeter and the standard heat of formation of sucrose.

∆ T =T c −T a−r 1 (b−a)−r 2 (c−b) Once the ignition is complete calculations must take place in order to determine the heat of the ignition wire which also adds heat when it burns.

For both the calibration of the calorimeter and finding ΔU of sucrose, finding ΔT becomes essential. ΔT is found from a temperature versus time plot and the plot has three distinct areas: i) The pre-ignition region; where the temperature is “low” (before the fuel is ignited). The temperature should be almost invariant with the time. ii) The ignition or rise region; where the reaction has been initiated and the temperature is rising rapidly. iii) The post-ignition region where the temperature has reached a maximum and is steady (ideally) or falling very slightly with time.

∆ T =Tf −Ti Ideally, the calorimeter should not lose (or gain) any heat in the pre-ignition or post- ignition regions - the temperature should be be constant. Therefore, T and t should have no linear relationship (more pedantically, the slope of the line should be zero). The existence (or non-existence) of a relationship should be tested

statistically (see the student notes and the Excel guide for how to test for a linear relationship). If no linear relationship exists, T i is found by averaging the temperatures in the pre-ignition region. Similarly, T f is found by averaging the T values in the post-ignition period.

´ Q tot ,cal =m benzoicacidQ´ benzoic acid +mwire Q wire

Where:

´ benzoic acid Q m benzoic acid

´ =¿ Q wire m wire

= heat released per gram of benzoic acid combusted (known) = mass of benzoic acid combusted (measured) heat released per gram of wire combusted (known)

= mass of wired combusted (measured)

For the combustion of sucrose, the calculation process is exactly “reversed”. ΔT must still be found (in the same way), for now our equation is:

Q tot =C cal ∆ T

Q tot =Q sucrose +Q wire Q tot =n sucrose ∆ H comb( sucrose ) +m wireQ´ wire ∆ H comb ( sucrose ) =

Q tot −mwire Q´ wire n sucrose

ΔH3 is the enthalpy change associated with changing a gas to its hypothetical ideal standard state. ΔH3 is calculated for each gas: °

°

∆ H 3=12 C p ,m ( O 2) μJT ( O 2) (0−30 ) +10 C p ,m ( CO2 ) μJT ( CO 2) ( 5−0 ) The total correction is the sum of the ΔH3 values for the individual gases. The correction to standard pressure for the gases should not be neglected.

Once the enthalpy of the combustion reaction has been determined then the heat of formation of sucrose may be obtained by applying Hess’s law to reaction (2b). For equation (2b)

C12 H 22 O 11 (s)=12 ∆ f H [CO 2 (g)]+11 ∆ f H [ H 2 O(l)]−∆c H , ∆f H ¿

∆ H f =12 ∆ H f [CO 2 (g ) ] +11 ∆ H f [ H 2 O ( l ) ]−∆ H comb ( average)

DATA/RESULTS

CALCULATIONS ENTROPY – RUN #1 Given: Benzoic Acid Heat of Combustion (kJ /g) :26.454 kJ/g Fuse Wire Heat of Combustion / (cal/g) : 1400 cal/g Mass of Bucket + Water /g : 2814.4g Mass of Empty Pan /g : 30.9629g Mass of Benzoic Acid + Pan /g : 31.9266g Initial Mass of Wire /g : 0.0151g Mass of Residual Wire : 0.0110g

Mass of Benzoic Acid = ( Mass of Benzoic Acid+ pan )−( Mass of Emptied Pan ) Mass of Benzoic Acid = ( 31.9266 g )− ( 30.9629)

Mass of Benzoic Acid =0.9637 g Benzoic Acid Heat of Combustion=26.454 kJ / g

Mass of Wire= ( Initial Mass of Wire / g )−( Mass of Residual Wire/g) Mass of Wire=(0.0151 g ) −( 0.0110 g ) Mass of Combusted Wire=0.0041 g

Fuse Wire Heat of Combustion 1400 1

kilocal cal =1.4 g g

J kcal =4184 g g

( calg )=:1400 cal/ g

J J 1.4 x 4184 =5857.6 g g Fuse Wire Heat of Combustion(

kJ kJ )=5.8576 g g

Q total =C cal ΔT

C cal=

Q tot ∆T

Entropy Data - Run 1 20.00

f(x) = 0 x + 17.16 19.50 R² = 0.76 Temperature (°C)

19.00 18.50 18.00 17.50 17.00 16.50 16.00 15.50 0

100

200

300

400

500 Time (s)

600

700

800

900

1000

Entropy Data - Run 1 : Pre-Ignition 17.08 17.06

Temperature (°C)

17.04 17.02

f(x) = 0 x + 17.02 R² = 0

17.00 16.98 16.96 16.94

0

50

100

150

200

Time (s)

Initial Temperature = (17.02°C +17.02°C)/2 = 17.02

℃

Temperature (°C)

Entropy Data - Run 1 : Ignition 20.00 19.50 19.00 18.50 18.00 17.50 17.00 16.50 16.00 15.50 200

f(x) = 0.02 x + 14.06 R² = 0.93

220

240

260

280

Time (s)

300

320

340

Entropy Data - Run 1 : Post-Ignition 19.80 19.70 f(x) = 0 x + 19.17 R² = 0.53

Temperature (°C)

19.60 19.50 19.40 19.30 19.20 19.10 19.00 18.90 300

400

500

600

700

800

Time (s)

Final Temperature = (19.37°C + 19.64°C) /2 = 19.51

ΔT=∆ T f −∆ T i ΔT=19.51 ℃−17.02℃ ΔT=2.49℃

Q total =m benzoic acid∗Q benzoicacid +m wire∗Q wire

Q total = (0.9637 g ) ( 26.454 kJ / g ) +( 0.0041 g )( 5.8576 kJ / g ) Q total =25.4937198 kJ +0.02401616 kJ Q tot =25.51773596 kJ

C cal=

Qtot 25.51773596 kJ = 2.49 ℃ ∆T

C cal=10.2480867309

kJ ℃

℃

900

C cal=10.248

kJ ℃

ENTROPY – RUN #2 Given: Benzoic Acid Heat of Combustion (kJ /g) :26.454 kJ/g Fuse Wire Heat of Combustion / (cal/g) : 1400 cal/g Mass of Bucket + Water /g : 2817.5g Mass of Empty Pan /g : 30.9634 Mass of Benzoic Acid + Pan /g : 31.9376g Initial Mass of Wire /g : 0.0152g Mass of Residual Wire : 0.0000g

Mass of Benzoic Acid = ( Mass of Benzoic Acid + pan )−( Mass of Emptied Pan ) Mass of Benzoic Acid = (31.9376 g )− ( 30.9634) Mass of Benzoic Acid =0.9742 g

Benzoic Acid Heat of Combustion=26.454 kJ / g Mass of Wire= ( Initial Mass of Wire / g )−( Mass of Residual Wire/g) Mass of Wire=(0.0152 g ) −( 0.000 g )

Mass of Combusted Wire=0.0152 g

Fuse Wire Heat of Combustion 1400 1

( calg )=:1400 cal/ g

cal kilocal =1.4 g g

kcal J =4184 g g

J J 1.4 x 4184 =5857.6 g g Fuse Wire Heat of Combustion(

kJ kJ )=5.8576 g g

Q total =C cal ΔT

Qtot ∆T

Entropy Data - Run #2 21.00 f(x) = 0 x + 17.18 R² = 0.75

20.00

Temperature (°C)

C cal=

19.00 18.00 17.00 16.00 15.00

0

200

400

600

Time (s)

800

1000

Entropy Data - Run 2 : Pre-Ignition 17.30

Temperature (°C)

17.25 f(x) = 0 x + 17.16 R² = 0.56

17.20 17.15 17.10 17.05

0

50

100

150

200

250

300

350

Time (s)

Initial Temperature = (17.17°C+17.23°C)/2 =17.20°C

Entropy Data - Run 2 : Ignition 20.00 19.50

f(x) = 0.01 x + 15 R² = 0.8

Temperature (°C)

19.00 18.50 18.00 17.50 17.00 16.50 16.00 15.50 280

330

380

430

Time (s)

480

530

580

Entropy Data - Run 2 : Post-Ignition 19.86

Temperature (°C)

19.84 19.82 19.80 19.78

f(x) = − 0 x + 19.82 R² = 0.06

19.76 19.74 19.72 560

660

760

860

960

Time (s)

Final Temperature = (19.79°C + 19.77°C)/2 = 19.78°C

ΔT =∆ T f −∆ T i

ΔT=19.78 ℃−17.20 ℃ ΔT =2.58℃

Q total =mbenzoic acid∗Q benzoicacid +m wire∗Q wire Q total = (0.9742 g ) ( 26.454 kJ / g ) +( 0.0152 g ) (5.8576 kJ / g ) Q total =25.7714868 kJ +0.08903552 kJ Q tot =25.8605223 kJ

C cal=

Qtot 25.51773596 kJ = 2.49 ℃ ∆T

C cal=10.3857519

kJ ℃

1060

C cal=10.386

kJ ℃

Run #1 & Run #2

∑¿ ¿

kJ ℃ cal ¿ C¿

10.386

+

10.248

kJ ℃

)

∑¿

¿ cal ¿ C¿

Sucrose Entropy Run #1: Given: Benzoic Acid Heat of Combustion (kJ /g) :26.454 kJ/g Fuse Wire Heat of Combustion / (cal/g) : 1400 cal/g Mass of Bucket + Water /g : 2816.4g Mass of Empty Pan /g : N/A Mass of Sucrose: 1.0888g Molar Mass of Sucrose: 342.3 g/mol Initial Mass of Wire /g : 0.0165g Mass of Residual Wire : 0.00029g Ccal (sum) = 10.317 kJ/

℃

Mass of Sucrose :1.0888 g nsucrose =

Mass of Sucrose Molar Mass of Sucrose

nsucrose =

m sucrose M sucrose

nsucrose =

1.0888 g 342.3 g /mol

nsucrose =0.00318084 mols

nsucrose =3.181 x 10−3 Benzoic Acid Heat of Combustion=26.454 kJ / g Mass of Wire= ( Initial Mass of Wire / g )−( Mass of Residual Wire/g) Mass of Wire=( 0.0165 g ) −( 0.00029 g)

Mass of Wire =0.01621 g

Fuse Wire Heat of Combustion 1400 1

( calg )=:1400 cal/ g

cal kilocal =1.4 g g

J kcal =4184 g g

J J 1.4 x 4184 =5857.6 g g Fuse Wire Heat of Combustion(

kJ kJ )=5.8576 g g

Sucrose - Entropy - Run #1 19.50

Temperature (°C)

f(x) = 0 x + 17.41 19.00 R² = 0.68 18.50 18.00 17.50 17.00 16.50 16.00 0.0

200.0

400.0

600.0

Time (s)

800.0

1000.0

1200.0

Temperature (°C)

Sucrose (Entropy) - Pre-Ignition :Run #1 17.50 17.45 17.40 17.35

f(x) = 0 x + 17.31 17.30 R² = 0.24 17.25 17.20 17.15 0.0

50.0

100.0

150.0

200.0

250.0

300.0

350.0

Time (s) Initial Temperature = (17.31°C+17.36°C)/2 =17.335°C

Sucrose (Entropy) - Ignition :Run #1 Temperature (°C)

19.00

f(x) = 0.01 x + 13.85 R² = 0.91

18.50 18.00 17.50 17.00 16.50 300.0

320.0

340.0

360.0

380.0

Time (s)

400.0

420.0

440.0

Sucrose (Entropy) - Post-Ignition :Run #1 Temperature (°C)

19.15 19.10 19.05 19.00

f(x) = − 0 x + 19.1 R² = 0.18

18.95 18.90 18.85 18.80 18.75 18.70 400.0

500.0

600.0

700.0

800.0

900.0 1000.0 1100.0 1200.0

Time (s)

Final Temperature = (19.03°C + 18.99°C)/2 = 19.01°C

ΔT =∆ T f −∆ T i

ΔT =19.01 ℃−17.355℃ ΔT =1.655 ℃

C cal=

Qtot ∆T

∑¿

¿ cal ¿ Q total =C ¿

Q total =(10.317

kJ )(1.655℃) ℃

Q total =17.074635 kJ Q total =17.07 kJ

∆ H comb (sucrose)=

Q total−m wire •Q wire nsucrose

(

17.07 kJ−[ ( 0.01621 g ) 5.8576 ∆ H comb (sucrose)=

)

kJ ] g

0.00318084 mols

∆ H comb (sucrose)=

17.07 kJ −[ 0.0949517 kJ ] 0.00318084 mols

∆ H comb (sucrose)=

17.07 kJ −[ 0.0949517 kJ ] 0.00318084 mols

∆ H comb (sucrose)=

16.9750483 kJ 0.00318084 mols

∆ H comb (sucrose)=

16.9750483 kJ 0.00318084 mols

∆ H comb ( sucrose )=5336.65582 kJ /mol ∴ ∆ H comb( sucrose )=5336.66 kJ /mol

Sucrose Entropy Run #2: Given: Benzoic Acid Heat of Combustion (kJ /g) :26.454 kJ/g Fuse Wire Heat of Combustion / (cal/g) : 1400 cal/g Mass of Bucket + Water /g : 2816.4g Mass of Empty Pan /g : N/A Mass of Sucrose: 1.0820g Molar Mass of Sucrose: 342.3 g/mol Initial Mass of Wire /g : 0.0159g Mass of Residual Wire : IGNITION FAILED Ccal (sum) = 10.317 kJ/

℃

CANNOT PROCEED FOR ENTROPY RUN #2 : IGNITION FAILED

STANDARD CONDITIONS Given: °

O 2 , C p ,m

(

−1

J mol K

−1

) = 29.36

°

J mol−1 K−1 ) = 37.11 ¯−1 ( K ¿ ) = 0.31 ¿ ¯−1 ( K¿ ) = 1.10 ¿

CO2 , C p , m O 2 , μJT CO2 , μ JT

(

P2

∆ H 3=∫ ( −C p μJT ) dP=(P1− P2 )C p μ JT P1

∆ H 3=12 C p ,m ( O 2) μJT (O 2 ) (0−30 ) +10 C p ,m ( CO2 ) μJT ( CO 2) ( 5−0 ) °

°

¯ ¿ K 0.31 ¿ ¿ −30 ¯¿ ¿ ¯ ¿ 5¿¯ K 1.10 ¿ ¿

(

)

∆ H 3=12 29.36

kJ ¿ mol

(

)

∆ H 3= 352.32

)(

)

kJ kJ (−9.3 k ) + 311.1 ( 5.5 k) mol mol

)

∆ H 3=(−3276.576 )+ ( 1711.05) ∆ H 3=−1565.526

kJ mol

HEAT OF FORMATION OF SUCROSE

∆ H f =12 ∆ H f [CO 2 (g ) ] +11 ∆ H f [ H 2 O ( l ) ]−∆ H comb ( average) kJ kJ kJ ( mol )+ 11( −285.8 mol ) −5336.66 mol kJ kJ kJ ∆ H =12 (−393.5 + 11 ( −285.8 −5336.66 ) ) mol mol mol kJ kJ kJ ∆ H =(−4722 + (−3143.8 −5336.66 ) ) mol mol mol ∆ H f =12 −393.5

f

f

∆ H f =−13202.46

kJ mol

DISCUSSION

The objective of this experiment was to determine both the heat capacity of the calorimeter and to determine the standard heat of formation of sucrose from its heat of combustion. In the bomb calorimeter 's volume is constant, so there is no pressure-volume work and the heat measured relates to the change in internal energy The heat capacity of the bomb and calorimeter, C,cal, was found by determining the near isolated temperature change obtained from the specific enthalpy of combustion of benzoic acid and fuse wire , yielding a value of 26.454 kJ/g with an associated error of ±3 J /g . The combustion of the fuse wire was found to be 1400 cal/g. The midpoint temperature, Td, is necessary to find for a bomb calorimeter because a realistic combustion does not follow the ideal situation in which the slopes from t=0 to tfinal and tmax to the end of the run are not zero. From the trendlines constructed from these temperatures. The initial temperature is determined from the tangent lines of the pre-ignition plot provided in both the benzoic and sucrose section .and post ignition and used to calculate the enthalpy of combustion. The final temperature is determined from the tangent lines of the post-ignition plot provided in both the benzoic and sucrose section To start, both of the first two calibration runs the combusted mass of the benzoic acid and wire were determined first , and the values for the combustion of benzoic acid were given. Using these values along with the wire combusted , which were converted into the appropriate units ,and the temperature determined from the ignition graphs, we are able to determine the Q total. Essentially , the change in temperature was determined by taking the final temperature from the tangent lines of the post-ignition graph and subtracted it from the initial temperature , which was taken from the pre-ignition graph. The resulting temperature for run #1 was about 2.49 ℃ and for run #2 the change in temperature was 2.58 ℃ . U...