Energy balance using heat of reaction (reference states are reactants and products at 25°C and 1 atm)

$$\xi \mathrm{\Delta }{\dot{H}}_{reaction}^{\circ }+\mathrm{\Sigma }{\dot{n}}_{i,out}{H}_{i,out}-\mathrm{\Sigma }{\dot{n}}_{i,in}{H}_{i,in}+\mathrm{\Delta }{\dot{E}}_{K.E.}+\mathrm{\Sigma }{\dot{E}}_{P.E.}=\dot{Q}+{\dot{W}}_S$$

where $\xi$ = extent of reaction (dimensionless) = $({\dot{n}}_{i,out}–{\dot{n}}_{i,in})/{\nu }_i$

${\nu }_i$ = stoichiometric coefficient (positive for products, negative for reactants)

$\mathrm{\Delta }{\dot{H}}_{reaction}^{\circ }$ = $\mathrm{\Sigma }{\nu }_i\mathrm{\Delta }{H}_{f,i}^{\circ }$

${\dot{n}}_{i,out}$ = molar flow rate of component $i$ out of system (mol/s)

${\dot{n}}_{i,in}$ = molar flow rate of component $i$ into system (mol/s)

$H_{i,out}$ = enthalpy of component $i$ exiting the system, relative to its enthalpy at a reference temperature (J/mol)

$H_{i,in}$ = enthalpy of component $i$ entering the system, relative to its enthalpy at a reference temperature (J/mol)

$\mathrm{\Delta }{\dot{E}}_{K.E.}$ = change in kinetic energy of system per time (J/s)

$\mathrm{\Delta }{\dot{E}}_{P.E.}$ = change in potential energy of system per time (J/s)

$\dot{Q}$ = heat added (J/s)

${\dot{W}}_S$ = shaft work added (J/s)

Energy balance using heats of formation (reference states are elements at 25°C and 1 atm)

$$\mathrm{\Sigma }{\dot{n}}_{i,out}{H}_{i,out}-\mathrm{\Sigma }{\dot{n}}_{i,in}{H}_{i,in}+\mathrm{\Delta }{\dot{E}}_{K.E.}+\mathrm{\Sigma }{\dot{E}}_{P.E.}=\dot{Q}+{\dot{W}}_S$$

Note that enthalpies are defined differently from above.

where $H_{i.out}$ = enthalpy of component $i$ exiting the system, relative to the enthalpy of its elements at a reference temperature (J/mol)

$H_{i,in}$ = enthalpy of component $i$ entering the system, relative to the enthalpy of its elements at a reference temperature (J/mol)