A plug flow reactor operates with a stoichiometric gas-phase mixture of A and B fed at 300 K. At a distance of 1 m along the reactor, the temperature reaches 360 K. Assuming negligible pressure drop and ideal gas behavior, identify the correct expression relating the inlet concentration (CA0), concentration at 1 m (CA), and conversion (X)?
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Answer: C. CA = 0.83 CA0 (1 – X)/(1 – 0.33X)
Explanation
Applying ideal gas laws and stoichiometric volume expansion accounts for both temperature changes and variable gas volume. Combining feed stoichiometry with temperature ratios of 360 to 300 Kelvin yields the correct numerical pre-multiplier. Mathematical simplification of the variable-volume plug flow equation produces this specific concentration-conversion relationship. Plug flow reactors operating with significant temperature gradients require simultaneous energy and mole balance equations. Ideal gas behavior links temperature, pressure, concentration, and volumetric expansion factors in gas-phase systems. Conversion variables track the progress of the reaction along the spatial coordinate of the tubular reactor.
Exothermic gas-phase tubular reactors experience severe temperature rises that alter fluid density and reaction kinetics. Accurate concentration-conversion relations are essential for predicting reactor performance and avoiding thermal runaways. Process control engineers use these advanced hydrodynamic models to maintain safe temperature profiles in industrial tubes. Option A uses an incorrect temperature ratio or expansion denominator that fails the rigorous gas law derivation. Option B incorporates a wrong stoichiometric expansion denominator that does not match the reaction stoichiometry. Option D features an incorrect pre-exponential temperature factor that violates ideal gas law expansion principles.
- Subject
- Engineering
- Category
- Chemical Engineering
- Topic
- —
- Difficulty
- medium
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