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The rate laws for these reactions are:
,
,
,
,
,
where is the rate of reaction
(
),
is the rate constant (
),
is reaction temperature (K),
and
are the concentrations of
and
(
), the subscript
refers to the inlet,
,
and
are the molar flow rates of
,
and
(mol/s) and
is the total molar flow rate (mol/s).
The rate constants are calculated from the pre-exponential factors which are solved at :
,
,
where is a pre-exponential factor (1/s),
is the rate constant at 380 K,
is activation energy (kJ/mol) and
is the ideal gas constant (kJ/(mol K)),
Mole and energy balances are done around the reactor:
,
,
,
,
where is volume (
),
is the heat transfer coefficient times heat transfer area per volume (kJ/(m s K)),
is the coolant temperature (K),
is heat of reaction (kJ/mol), and
,
and
are the heat capacities of
,
and
(kJ/(mol K)).