CRE7: Mass transfer aspects of a gas-solid non catalytic reaction

AIM: To determine the effective diffusion coefficient for the non-catalytic gas-solid reaction of
calcium carbonate decomposition.

APPARATUS:
 Furnace: Used to provide controlled high temperatures.
 Holders: Containers to hold the chalk pellets.
 Microbalance: Instrument to measure precise weights of samples.
 Stopwatch: Tool to measure reaction times.
 Crucibles: Containers to hold samples during the reaction.
 Vernier scale: Used for measuring dimensions accurately.
 Chemicals: Chalk (calcium carbonate).

CHEMICALS:
Calcium carbonate powder or chalk

PREPARATION:
 Cut the chalk into cylindrical shapes and weigh them to ensure precise weight measurement.
 Measure the diameter and thickness of the chalk pellets and note the readings.

PROCEDURE:
I. Number the pellets for identification.
II. Raise the furnace temperature to the desired reaction temperature (750°C and 800°C).
III. Place all the pellets in the furnace simultaneously. Ensure they have similar
dimensions and initial weights.
IV. Remove each pellet after different reaction times and transfer them to a desiccator for
cooling.
V. Measure the weight loss of the pellets corresponding to different reaction times.
VI. Perform the experiment at both 750°C and 800°C. Take four chalk samples at each
temperature.
VII. Maintain a time gap of 15 minutes between readings for both 750°C and 800°C.
THEORY:
In the context of gas-solid reactions, diffusion plays a
crucial role in transporting reactant molecules from the bulk gas phase to the solid
surface where the reaction occurs. Fick's Law of Diffusion can be used to describe this
process. The effective diffusion coefficient takes into account the complex nature of diffusion in
heterogeneous systems like gas-solid reactions. It considers factors such as pore
structure, surface area, and possible hindrances to diffusion due to interactions between
reactant molecules and the solid surface. The effective diffusion coefficient is not a
constant value, but rather a parameter that varies depending on the conditions and
characteristics of the system. The Arrhenius equation relates the rate constant of a reaction to
temperature. It's commonly used to describe the temperature dependence of reaction rates.

CaCO3 → CaO + CO2

The reaction is assumed to proceed according to the shrinking core model.

At the high temperature rate of reaction will be high but the mass transfer is controlling.

DERIVATION:
DATA AND CALCULATIONS
For 750°C

Initial
Initial D final D W Final W Initial L Final L Time
9.81 8.85 1.9587 1.5425 32.55 30.12 15
9.5 8.27 2.3807 1.8743 41.22 36.4 30
9.78 8.21 2.0988 1.6521 35.39 30.54 45
9.62 7.75 2.2413 1.7638 38.47 31.89 60

For 800°C

Initial
Initial D final D W Final W Initial L Final L Time
9.67 8.45 2.198 1.7298 36.42 32.93 10
9.76 7.98 2.4444 1.9235 39.21 32.82 20
9.72 7.46 2.1544 1.6953 36.56 29.77 30
9.56 7.32 2.1321 1.6776 36.89 29 40

Theoretical Effective Diffusivity Calculation:

For 750°C

Initial True Bulk

Volume Final Volume Density Density Porosity
2460.248009 1852.812151 2.711 0.81432877 0.699621
2921.763635 1955.249953 2.711 0.88670738 0.672922
2658.57033 1616.758781 2.711 0.90565308 0.665934
2796.161243 1504.346243 2.711 0.98701633 0.635922
0.89842639 0.6686
For 800°C

Initial True Bulk

Volume Final Volume Density Density Porosity
2674.747381 1846.69439 2.711 0.87923029 0.67568
2933.5018 1641.474879 2.711 1.00254117 0.630195
2712.867597 1301.20694 2.711 1.04850427 0.613241
2647.977686 1220.422038 2.711 1.08989347 0.597974
1.0050423 0.629272

Experimental Effective Diffusivity Calculation:

Initial
Initial D final D W Final W Initial L Final L Time X t/X
9.81 8.85 1.9587 1.5425 32.55 30.12 15 0.482927 31.0606
9.5 8.27 2.3807 1.8743 41.22 36.4 30 0.483433 62.05616
9.78 8.21 2.0988 1.6521 35.39 30.54 45 0.483718 93.02942
9.62 7.75 2.2413 1.7638 38.47 31.89 60 0.484195 123.9169

t/X v/s X
140

120 y = 74892x - 36138

100
Chalk DAB
80
1 5.373059
min

60 2 0.851482
40 3 0.857101
4 0.832361
20
1.978501
0
0.4828 0.483 0.4832 0.4834 0.4836 0.4838 0.484 0.4842 0.4844
X

DAB = 0. 859114 cm2/s

Initial
Initial D final D W Final W Initial L Final L Time X t/X
9.67 8.45 2.198 1.7298 36.42 32.93 10 0.484118 20.65613
9.76 7.98 2.4444 1.9235 39.21 32.82 20 0.484317 41.2953
9.72 7.46 2.1544 1.6953 36.56 29.77 30 0.484315 61.94311
9.56 7.32 2.1321 1.6776 36.89 29 40 0.484478 82.56317
 t/X
90
80
Chalk DAB
y = 170997x - 82763
70 1 2.316319
60 2 0.39259
50 3 0.358822
min

40
30
4 0.359118
20 0.856712
10
0
0.48405 0.4841 0.48415 0.4842 0.48425 0.4843 0.48435 0.4844 0.48445 0.4845
X

DAB = 0. 374146 cm2/s

RESULTS AND CONCLUSION:

 Theoretical vs. Experimental Diffusion Coefficient: we used complex calculations

involving various process parameters to determine the theoretical diffusion coefficient
(Dtheo). However, there is a difference between the theoretical and experimental
diffusion coefficient (Dexp) values. This difference is attributed to variations between the
assumptions of the theoretical model and the actual experimental conditions.
 Shrinking Core Model: The Shrinking Core model, which assumes that the rate of mass
transfer within the unreacted core controls the rate of reaction, was selected to represent
the reaction mechanism. This choice was reasonable considering the observed
breakdown process characteristics in your experiment.
 Temperature Effects: Normally, higher temperatures lead to increased kinetic energy and
higher diffusion coefficients. However, our experiment's results did not entirely align with
this expectation.
 Internal Diffusion-Limiting Factors: The diffusion rate of carbon dioxide gas through the
unreacted core of the particles significantly affects the overall reaction rate.
 Complexity of Real-World Reactions: Despite the observed discrepancies between
theoretical predictions and practical results, our experiment sheds light on the complexity
of real-world reactions. This emphasizes the importance of accurate experimental
methods and the understanding that real reactions can be influenced by numerous
factors beyond theoretical considerations
PRECAUTION AND SOURCES OF ERROR:

 Temperature Control: Ensure accurate and consistent temperature control throughout

the experiment to avoid variations in reaction rates due to temperature fluctuations.
 Pellet Uniformity: Maintain uniform pellet dimensions and weights to minimize
discrepancies in mass transfer rates and reaction kinetics.
 Pellet Handling: Handle pellets carefully to avoid damage or irregularities that could
affect the experiment's results.
 Gas Flow: Ensure proper gas flow and distribution around the pellets to prevent localized
variations in gas concentration.
 Pressure Changes: Monitor and control pressure conditions to prevent deviations from
standard atmospheric pressure, which can impact gas-solid interactions.
 Data Collection: Accurately record weight and time data, minimizing human errors during
measurements and data logging.

SCOPE FOR IMPROVEMENT:

 Advanced Instrumentation: Employ advanced equipment for more precise

measurements, such as high-resolution thermocouples and advanced gas flow control
systems.
 Real-time Monitoring: Use real-time monitoring techniques to continuously track weight
changes and reactions, enhancing data accuracy and capturing dynamic behaviors.
 Variability Analysis: Investigate the effect of variations in pellet properties on
experimental outcomes through systematic studies.
 Gas Mixture Control: Experiment with different gas mixtures and compositions to
understand their impact on mass transfer and reaction kinetics.

INDUSTRIAL APPLICATION:

 Catalyst Development: Insights from these experiments can aid in the design and
optimization of catalysts and solid reactants for various industrial processes.
 Chemical Production: Understanding mass transfer and reaction kinetics is crucial for
optimizing chemical reactions and production processes, leading to improved yield and
efficiency.
 Environmental Control: Knowledge of gas-solid reactions can be applied to
environmental control technologies, such as air pollution control systems and carbon
capture processes.
 Material Synthesis: These principles are essential in industries involving material
synthesis, where controlling reactions between gases and solids leads to tailored
material property.