Reactive systems are where the magic happens in chemical engineering. They involve chemical reactions that change the composition of materials, unlike non-reactive systems. This topic dives into how these reactions affect material balances and process modeling.

Balancing chemical equations is key to understanding reactive systems. We'll explore techniques for writing and balancing equations, and learn about the extent of reaction and limiting reactants. These concepts are crucial for solving material balance problems in reactive systems.

Reactive vs Non-reactive Systems

Differences in Material Balances

• Reactive systems involve chemical reactions that change the chemical composition and identity of the species present, while non-reactive systems do not involve chemical reactions and maintain the same chemical species throughout the process
• In reactive systems, the molar flow rates and concentrations of species change due to the formation or consumption of chemical species during the reaction (reactants consumed, products formed), while non-reactive systems have constant molar flow rates and concentrations of species
• Reactive systems require the use of stoichiometric coefficients and reaction extents to relate the changes in molar flow rates and concentrations of species, while non-reactive systems do not require these considerations
• The material balance equations for reactive systems must account for the generation or consumption of species due to chemical reactions, while non-reactive systems only consider the input and output flow rates of species

Impact on Process Modeling

• Reactive systems require more complex mathematical models to describe the chemical kinetics, thermodynamics, and transport phenomena associated with the reactions
• Non-reactive systems can often be modeled using simpler mass and energy balance equations without considering reaction kinetics or equilibrium
• Reactive systems may involve multiple phases (gas, liquid, solid) and require phase equilibrium calculations, while non-reactive systems typically involve fewer phases and simpler phase interactions
• Reactive systems may exhibit heat generation or consumption due to exothermic or endothermic reactions, which must be accounted for in energy balance calculations

Balancing Chemical Equations

Writing Chemical Equations

• A chemical equation represents the reactants, products, and stoichiometry of a chemical reaction, with reactants written on the left side of the arrow and products written on the right side
• The law of conservation of mass dictates that the total mass of reactants must equal the total mass of products in a balanced chemical equation
• Chemical equations must include the correct chemical formulas for all species involved in the reaction (H2O for water, CH4 for methane)
• The physical states of the species (solid, liquid, gas, aqueous) are often indicated using parentheses (s), (l), (g), (aq) after the chemical formula

Balancing Techniques

• To balance a chemical equation, the stoichiometric coefficients (numbers preceding the chemical species) are adjusted to ensure an equal number of atoms of each element on both sides of the equation
• Start by balancing the most complex molecule or the element that appears in only one molecule on each side of the equation
• Balance elements that appear in multiple molecules on one side of the equation before balancing elements that appear on both sides
• Use the smallest whole number coefficients possible to balance the equation (avoid fractions)
• In systems with multiple reactions, each reaction must be balanced separately, and the overall material balance must account for the contributions of all reactions

Extent of Reaction and Limiting Reactant

Extent of Reaction

• The extent of reaction (ξ) is a measure of the progress of a chemical reaction and represents the amount of reactant consumed or product formed
• The extent of reaction is related to the stoichiometric coefficients and the change in the number of moles of each species during the reaction
• For a general reaction aA + bB → cC + dD, the change in the number of moles of each species is related to the extent of reaction by: $Δn_A = -aξ, Δn_B = -bξ, Δn_C = cξ, Δn_D = dξ$
• The extent of reaction has units of moles and is always a positive value

Limiting Reactant

• The limiting reactant is the reactant that is completely consumed first during a reaction and determines the maximum extent of reaction possible
• To identify the limiting reactant, calculate the extent of reaction for each reactant assuming it is the limiting reactant (divide the initial moles of reactant by its stoichiometric coefficient)
• The reactant with the smallest extent of reaction is the limiting reactant
• The limiting reactant determines the maximum amount of product that can be formed and the amounts of other reactants that will be consumed (excess reactants remain after the reaction)
• In industrial processes, it is often desirable to use a slight excess of one reactant to ensure complete consumption of the limiting reactant and maximize product yield

Material Balances with Reactions

General Material Balance Equation

• Material balance calculations for reactive systems involve accounting for the changes in molar flow rates and concentrations of species due to chemical reactions
• The general material balance equation for a reactive system is: Input + Generation - Output - Consumption = Accumulation
• The generation and consumption terms in the material balance equation are determined by the stoichiometry of the chemical reactions and the extent of reaction
• For steady-state reactive systems, the accumulation term is zero, and the material balance equation simplifies to: Input + Generation = Output + Consumption

Solving Material Balance Problems

• To solve material balance problems for reactive systems, use the balanced chemical equations, stoichiometric coefficients, and extent of reaction to relate the changes in molar flow rates and concentrations of species
• For a single reaction, the change in the molar flow rate of each species is related to the extent of reaction by: $ΔF_A = -aξ, ΔF_B = -bξ, ΔF_C = cξ, ΔF_D = dξ$
• When multiple reactions occur in a system, the material balance equations must account for the contributions of all reactions to the generation and consumption of species
• Use the limiting reactant to determine the maximum extent of reaction and the final molar flow rates and concentrations of all species
• Consider any additional constraints, such as reactor volume, pressure, or temperature, when setting up and solving the material balance equations