11.2 Energy Balances for Reactive Systems

Chemical reactions bring energy changes to systems. In reactive processes, we must account for heat released or absorbed during reactions, alongside heat transfer and work.

Energy balances for reactive systems extend basic principles to include reaction energetics. We'll explore how to calculate heats of reaction, understand temperature effects, and solve complex reactive system problems.

Energy Balances for Reactive Systems

Energy balance in reactive systems

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• General energy balance equation for reactive systems extends fundamental principles to chemical reactions
  • $\Delta H_{rxn} + Q - W = \Delta H_{out} - \Delta H_{in}$ accounts for energy changes during reaction
• Components of the energy balance incorporate reaction-specific terms
  • Heat of reaction ($\Delta H_{rxn}$) quantifies energy absorbed or released
  • Heat transfer (Q) represents thermal energy exchange with surroundings
  • Work (W) accounts for mechanical energy interactions
  • Enthalpy change of streams measures energy content differences between inlet and outlet
• Steady-state operation characteristics maintain constant system conditions
  • No accumulation of mass or energy ensures balanced input and output
  • Inlet and outlet flow rates remain constant preserving system stability
• Differences between reactive and non-reactive systems highlight unique considerations
  • Inclusion of heat of reaction term accounts for chemical energy changes
  • Potential changes in chemical composition affect stream properties and energy content

Enthalpy changes in chemical reactions

• Heat of reaction quantifies energy transfer during chemical transformations
  • Definition: enthalpy change during a chemical reaction measures energy absorbed or released
  • Standard heat of reaction ($\Delta H_{rxn}^°$) provides reference value at standard conditions
• Exothermic reactions release energy to surroundings
  • Release heat to surroundings warms the environment (combustion)
  • Negative heat of reaction indicates energy output
• Endothermic reactions absorb energy from surroundings
  • Absorb heat from surroundings cools the environment (photosynthesis)
  • Positive heat of reaction indicates energy input
• Hess's Law enables complex reaction energy calculations
  • Calculation of overall heat of reaction from individual reaction steps simplifies analysis
• Heat capacity effects influence reaction energetics
  • Temperature dependence of reactants and products impacts overall energy balance

Heat of reaction calculations

• Methods for calculating heat of reaction provide multiple approaches
  • Formation enthalpies utilize tabulated data for standard states
    • $\Delta H_{rxn} = \sum \Delta H_f^° \text{(products)} - \sum \Delta H_f^° \text{(reactants)}$ calculates overall energy change
  • Combustion enthalpies apply to fuel reactions
  • Bond enthalpies estimate energy changes based on molecular structure
• Temperature dependence of heat of reaction affects process conditions
  • Kirchhoff's equation relates heat capacity to reaction enthalpy change
    • $\frac{d(\Delta H_{rxn})}{dT} = \Delta C_p$ quantifies temperature effects
• Impact on overall energy balance influences process design
  • Heat generation or consumption affects temperature control requirements
  • Temperature changes in the system impact reaction rates and equilibrium
• Adiabatic temperature rise predicts maximum temperature change
  • Calculation for constant pressure processes estimates heating or cooling needs
    • $\Delta T_{ad} = -\frac{\Delta H_{rxn}}{C_p}$ determines temperature change without heat transfer

Reactive system energy balances

• Problem-solving approach ensures systematic analysis
  1. Identify the system boundaries
  2. Write out the chemical reaction equation
  3. Apply the general energy balance equation
• Common unknown variables include key process parameters
  • Reactor temperature affects reaction kinetics and equilibrium
  • Heat transfer requirements determine heating or cooling needs
  • Conversion or yield quantifies reaction progress and efficiency
• Assumptions and simplifications facilitate calculations
  • Ideal gas behavior simplifies gas-phase reactions (PV = nRT)
  • Constant heat capacities approximate temperature-dependent properties
• Reference states provide consistent basis for calculations
  • Standard temperature and pressure (STP) establishes common conditions (0℃, 1 atm)
  • Elements in their standard states serve as enthalpy reference points
• Conversion between molar and mass bases ensures consistent units
  • Use of molecular weights translates between mole and mass quantities
• Multiple reactions require comprehensive analysis
  • Applying energy balance to each reaction accounts for all energy changes
  • Summing the contributions yields overall system energy balance