A recycle reactor with very high recycle ratio is used to study the kinetics of a particular irreversible catalytic reaction, A → R. For a constant flow rate of feed (τ' = 2 kg · sec/liter) the following data are obtained:

The progressive drop in conversion suggests that the catalyst deactivates with use. Find rate equations for the reaction and for the deactivation which fit these data.

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Time after start of operation, hr XA 1 2 0.889 0.865 4 0.804