Laboratory Experiment: Kinetics of Calcium Carbonate Decomposition

The aim of this laboratory experiment is to interpret decomposition-time data for the non-catalytic reaction of calcium carbonate particles and predict the rate-determining step from experimental data. The focus is on developing rate expressions for the decomposition of calcium carbonate using the unreacted core model.

Theory: The decomposition of calcium carbonate (CaCO3) is a fluid-solid reaction, and understanding such reactions is crucial for various industrial processes. Two idealized models for non-catalytic reactions of particles surrounded by fluid are considered: Progressive Conversion model and Unreacted Core Model.

The latter is particularly suitable for representing the decomposition of CaCO3. The reaction involves five sequential steps: diffusion of gaseous reactant through the fluid film, penetration and diffusion through the ash layer, reaction at the unreacted core surface, diffusion of gaseous product through ash film, and diffusion of gaseous product back into the fluid.

Experimental Procedure:

1. Preparation of Calcium Carbonate Samples:
   • Obtain calcium carbonate samples of identical size.
   • Ensure the uniformity of particle size for accurate results.
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2. Experimental Setup:
   • Set up a reaction chamber with controlled temperature and pressure.
   • Introduce gaseous reactant A into the chamber.
3. Data Collection:
   • Record the decomposition-time data for various fractional conversions (xB) of calcium carbonate.
   • Measure the time taken for complete conversion of solid ().

Calculations and Formulas:

1. Progressive Conversion Model:
   • No specific formula provided. Data interpretation involves analyzing the continuous and progressive conversion throughout the particles.
2. Unreacted Core Model:
   • Calculate the time for each of the five steps using the unreacted core model equations.
     • Step 1: Diffusion through gas film controls: t/=xB
     • Step 2: Diffusion through ash film controls: t/=1−3(1−xB)2/3+2(1−xB)
     • Step 3: Chemical reaction controls: 3t/=1−(1−xB)1/3
     • Steps 4 and 5 involve diffusion of gaseous product through ash film and fluid film, respectively, contributing to overall conversion time.
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Results and Analysis:

1. Experimental Data:
   • Present the recorded decomposition-time data for different fractional conversions of calcium carbonate.
2. Comparison with Models:
   • Compare the experimental data with predictions based on the Progressive Conversion and Unreacted Core models.
   • Analyze deviations and identify the controlling step for different conversion regimes.
3. Rate-Determining Step:
   • Use the calculated times for each step to identify the rate-determining step at different conversion levels.
   • Discuss the significance of each step in the overall reaction kinetics.

Discussion:

1. Mass Transfer and Heat Transfer Limitations:
   • Discuss the impact of mass transfer and heat transfer limitations between phases on the reaction kinetics.
2. Applicability of Models:
   • Evaluate the suitability of the Unreacted Core model for representing the decomposition of calcium carbonate.
3. Industrial Implications:
   • Discuss the relevance of the experiment in the context of industrial processes involving fluid-solid reactions.

Conclusion: In conclusion, this laboratory experiment provides valuable insights into the kinetics of calcium carbonate decomposition. The analysis of decomposition-time data using the Unreacted Core model allows for the identification of the rate-determining step, contributing to a deeper understanding of fluid-solid reactions.

Experimental Procedure:

1. Temperature Control:
   • The muffle furnace was set and maintained at a constant temperature of 750°C by adjusting the controls.
2. Sample Preparation:
   • 10 g of calcium carbonate was weighed and placed in each of the 5 trays, with known masses.
3. Furnace Treatment:
   • The trays were placed in the furnace for varying durations, corresponding to different reaction times.
4. Sampling Interval:
   • At intervals of 25 minutes, one tray was removed from the furnace for analysis.
5. Desiccation Process:
   • To prevent moisture absorption during cooling, trays were placed in desiccators after removal from the furnace.
6. Post-Cooling Weighing:
   • After approximately 60 minutes of cooling, each tray was weighed to calculate the loss in mass.
7. Conversion Calculation:
   • The conversion of solids was determined based on the loss in weight of the trays. The obtained data provided conversion vs. time information, with 100% conversion corresponding to a 44% loss in the mass of the sample.

Calculations:

The standard deviation (σ) for a set of N data points is given by the formula:

σ=N∑(xˉ−xi​)2​​

As τ is constant in all three models, a comparison was made by calculating the standard deviation of τ's obtained from these models. The values of τt​ for each model were utilized to calculate τ for each experimental reading.

Upon conducting a thorough statistical analysis of the experimental data, it has been determined that the rate-controlling step in the decomposition of calcium carbonate is diffusion through the gas film. This conclusion is supported by the observation that the standard deviation for this case is minimal.

The investigation has revealed that, in the decomposition process of calcium carbonate, the diffusion through the gas film emerges as the pivotal step influencing the overall reaction rate. Moreover, it is evident that the reaction temperature plays a crucial role in governing the rate of the reaction. To enhance the reaction rate, improvements in heat transfer systems can be implemented.

Precautions:

1. Assign a unique number to each steel tray to mitigate discrepancies, especially considering potential variations in the mass of steel trays.
2. Utilize gloves and tongs when placing trays into the furnace to ensure safety and proper handling.
3. Minimize the duration of keeping the furnace door open to maintain consistent experimental conditions.
4. Exercise caution while placing trays in desiccators to prevent any unintended loss of reaction products.
5. When measuring the mass of trays, use a mass balance with precision and care.