Reactive Mixtures

Reactive-mixture balances

Chemical reactions change species amounts while conserving each element. A reacting energy balance must include formation enthalpies and sensible enthalpy changes on one consistent basis. Temperature-dependent heat capacities and equilibrium dissociation matter in high-temperature combustion.

Stoichiometry

For an idealized dry-air model with 3.76 mol N₂ per mol O₂, complete stoichiometric methane combustion is:

CH₄ + 2(O₂ + 3.76N₂) → CO₂ + 2H₂O + 7.52N₂.

The nitrogen does not disappear: even if treated as chemically inert, it absorbs sensible energy. The equation is per mole of methane. Excess air would add oxygen and nitrogen to the products, changing their heat capacity and temperature.

Reaction enthalpy

At the reference temperature, Δ_rH° = sum(ν_i h_f,i°) for products minus reactants. Use molar quantities and include stoichiometric coefficients. For the supplied 298 K values h_f°(CH₄) = -74.8 kJ/mol, h_f°(CO₂) = -393.5 kJ/mol and h_f°(H₂O vapor) = -241.8 kJ/mol, with elemental O₂ and N₂ assigned zero:

Δ_rH° = -393.5 + 2(-241.8) - (-74.8) = -802.3 kJ per mol CH₄.

The negative sign denotes an exothermic reaction. The water phase matters: a liquid-water product would give a different heating value.

Adiabatic flame temperature

For steady adiabatic constant-pressure combustion with no shaft work and negligible kinetic/potential changes, total product enthalpy equals total reactant enthalpy. With reactants at 298 K and fixed complete-combustion products:

sum over products [ν_i integral from 298 to T_ad of c_p,i(T)dT] = -Δ_rH° = 802.3 kJ per mol fuel.

Solve for T_ad using consistent property data. Adiabatic means no heat crosses the boundary; chemical energy still becomes sensible energy in the products.

Worked simplified estimate

For an arithmetic exercise only, suppose the aggregate constant heat-capacity sum of ALL products, including nitrogen, is supplied as C_products = 0.400 kJ/(mol fuel K). Then:

T_ad = 298 + 802.3/0.400 = 2303.75 K.

This is a constant-heat-capacity, fixed-product estimate, not a validated methane–air flame temperature. Using one species' 29.1 J/(mol K) as the whole product heat capacity incorrectly omits product amounts and gives an unrealistic result. The sensible temperature rise uses the positive released-energy magnitude -Δ_rH°, not a negative rise for an exothermic reaction.

Refinements and pitfalls

• Evaluate each species’ sensible enthalpy over the temperature interval; a room-temperature heat capacity can be inaccurate over a large rise.
• Account for dissociation/equilibrium composition when needed rather than assuming only CO₂, H₂O and N₂ remain.
• A closed rigid adiabatic reactor uses internal-energy conservation instead of the steady constant-pressure enthalpy balance.
• Specific heat c_v = (∂u/∂T)_v has units J/(kg K), with u specific internal energy. (∂U/∂T)_V gives total heat capacity in J/K for fixed composition.

Quick check

Why include nitrogen in an air-combustion energy balance? It absorbs sensible energy even in the inert approximation. Does adiabatic combustion have zero temperature rise? No: zero boundary heat transfer does not mean zero chemical-energy conversion.