8.2 Material Balances with Chemical Reactions

Chemical reactions are the heart of many processes. We'll explore how to balance materials in reactive systems, considering equilibrium, limiting reactants, and reaction yields.

Understanding these concepts is crucial for predicting and optimizing chemical processes. We'll learn to calculate theoretical and actual yields, which are key for assessing reaction efficiency and economics.

Reactive Systems and Material Balances

Material balance equations for reactive systems

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• Chemical equilibrium concept governs reversible reactions reaching dynamic balance between forward and reverse rates
• Components in reactive system include reactants, products, and inert species not participating in reaction
• Write balanced chemical equations showing stoichiometric relationships between reactants and products
• Law of conservation of mass applied ensures total mass remains constant throughout reaction
• Develop material balance equations incorporating overall balance for entire system and component balances for individual species
• Stoichiometric coefficients indicate relative amounts of reactants consumed and products formed
• Reaction extent or degree of conversion quantifies progress of reaction from initial to final state
• Equilibrium constant relates to concentration ratios of products to reactants at equilibrium (gas-phase reactions use partial pressures)

Single reaction equilibrium calculations

• Equilibrium constant $K_c$ (concentration-based) or $K_p$ (pressure-based) expresses relationship between reactants and products at equilibrium
• Reaction quotient compares to equilibrium constant determines direction of reaction progress
• Material balance calculations use equilibrium constant to express concentrations in terms of reaction extent
• Set up equations based on equilibrium relationships and solve using iterative methods (Newton-Raphson, successive substitution)
• Software tools aid in complex equilibrium calculations involving multiple components or reactions
• Interpret results by checking for consistency with mass balance principles and thermodynamic constraints

Limiting and excess reactant quantities

• Limiting reactant determines maximum extent of reaction while excess reactants remain partially unreacted
• Determine limiting reactant using stoichiometric ratios method or percent excess method
• Calculate excess reactant amount by subtracting reacted amount from initial quantity
• Limiting reactant impacts reaction progress and final equilibrium composition
• Multi-component systems may have multiple excess reactants requiring careful analysis
• Incomplete reactions leave some limiting reactant unreacted affecting overall conversion
• Reactant ratios influence product yield and selectivity in complex reaction networks

Theoretical vs actual reaction yields

• Theoretical yield represents maximum possible product amount based on limiting reactant and reaction stoichiometry
• Calculate theoretical yield using stoichiometric relationships and accounting for reaction stoichiometry
• Actual yield refers to experimentally obtained product amount often lower than theoretical due to various factors
• Percent yield calculated as $\text{Percent Yield} = \frac{\text{Actual Yield}}{\text{Theoretical Yield}} \times 100\%$ quantifies reaction efficiency
• Factors affecting actual yield include side reactions, incomplete conversion, and processing losses
• Selectivity in multi-product reactions measures preferential formation of desired product
• Economic implications of yield involve process efficiency and cost considerations (raw material utilization, energy consumption)