1.4 Chemical Reaction Engineering Principles

Chemical reaction kinetics and stoichiometry are crucial for understanding how reactions occur and predicting their outcomes. This knowledge helps engineers design efficient processes and optimize reactor conditions for desired products.

Ideal reactor performance and optimization are key to maximizing yield and selectivity in chemical processes. By understanding reactor types and their characteristics, engineers can choose the best setup and fine-tune conditions for optimal results.

Chemical Reaction Kinetics and Stoichiometry

Classification of chemical reactions

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• Reaction order describes how the reaction rate depends on reactant concentrations
  • Zero order reactions have rates independent of reactant concentration (decomposition of hydrogen peroxide)
  • First order reaction rates are proportional to reactant concentration (radioactive decay)
  • Second order reaction rates are proportional to the square of reactant concentration or the product of two reactant concentrations (dimerization of cyclopentadiene)
• Molecularity refers to the number of reactant molecules involved in an elementary reaction step
  • Unimolecular reactions involve one reactant molecule (isomerization of cyclopropane)
  • Bimolecular reactions involve two reactant molecules (formation of hydrogen iodide from hydrogen and iodine)
  • Termolecular reactions involve three reactant molecules (formation of ozone from oxygen atoms and molecules)
• Stoichiometry describes the quantitative relationships between reactants and products
  • Irreversible reactions convert reactants completely to products (combustion of methane)
  • Reversible reactions have both forward and reverse reactions occurring simultaneously (formation of ammonia from nitrogen and hydrogen)
  • Multiple reactions involve more than one reaction step or pathway (oxidation of sulfur dioxide to sulfur trioxide)

Rate equations for reactions

• Elementary reactions have rate laws determined by the molecularity of the reaction
  • For a generic reaction $aA + bB \rightarrow cC + dD$, the rate law is $r = k[A]^a[B]^b$ where $k$ is the rate constant and $[A]$ and $[B]$ are reactant concentrations
• Complex reactions consist of multiple elementary steps
  • The rate-determining step (RDS) is the slowest step in the reaction mechanism and controls the overall reaction rate (formation of nitrogen monoxide from nitrogen and oxygen)
  • The steady-state approximation (SSA) assumes the concentration of reactive intermediates remains constant (formation of hydrogen bromide from hydrogen and bromine)
  • Derive the overall rate law by applying SSA to the reaction mechanism (formation of nitrogen dioxide from nitric oxide and oxygen)

Ideal Reactor Performance and Optimization

Performance of ideal reactors

• Batch reactors have concentration and temperature varying with time
  • Mass balance: $\frac{dN_A}{dt} = -r_AV$ where $N_A$ is moles of species A, $r_A$ is the reaction rate, and $V$ is the reactor volume
• Continuous Stirred Tank Reactors (CSTRs) have uniform concentration and temperature throughout the reactor
  • Mass balance: $F_{A0} - F_A - r_AV = 0$ where $F_{A0}$ and $F_A$ are the inlet and outlet molar flow rates of species A
• Plug Flow Reactors (PFRs) have concentration and temperature varying with position
  • Mass balance: $F_A\frac{dX_A}{dV} = -r_A$ where $X_A$ is the conversion of species A
• Residence time ($\tau$) is the average time reactants spend in the reactor
  • Batch: $\tau = t$ where $t$ is the reaction time
  • CSTR: $\tau = \frac{V}{v_0}$ where $v_0$ is the volumetric flow rate
  • PFR: $\tau = \frac{V}{v_0}$

Optimization of reactor conditions

• Yield is the amount of desired product formed relative to the limiting reactant
  • Maximize yield by increasing conversion of the limiting reactant (production of ethylene oxide from ethylene and oxygen)
• Selectivity is the amount of desired product formed relative to the total amount of products
  • Maximize selectivity by suppressing side reactions and byproduct formation (production of para-xylene from mixed xylenes)
• Factors affecting yield and selectivity include:
  1. Temperature: higher temperatures generally increase reaction rates but may favor side reactions (production of acetone from isopropanol)
  2. Pressure: higher pressures can increase reactant concentrations and favor reactions with negative volume change (production of ammonia from nitrogen and hydrogen)
  3. Catalyst: can increase reaction rate and selectivity by lowering activation energy and providing an alternative reaction pathway (production of sulfuric acid from sulfur dioxide and oxygen)
• Optimize operating conditions by balancing the effects of temperature, pressure, and catalyst on yield and selectivity (production of methanol from carbon monoxide and hydrogen)