In an inlet-outlet framework, how are conversion and selectivity defined?

• A. Conversion X = (F_in − F_out)/F_in; Selectivity S = moles of desired product formed per moles of undesired byproduct formed.
• B. Conversion X = (F_out − F_in)/F_in; Selectivity S = moles of undesired per desired product formed.
• C. Conversion X = (F_in − F_out)/F_in; Selectivity S = moles of desired product formed per moles of undesired byproduct formed.
• D. Conversion X = (F_out − F_in)/F_out; Selectivity S = moles undesired per mole of desired.

Answer: (A)

In an inlet-outlet framework, the idea is to measure what happens to the feed as it passes through the reactor. Conversion is the fraction of the feed that actually reacts. That is the amount the feed loses to reaction, divided by the amount fed in: X = (F_in − F_out) / F_in. This makes intuitive sense because F_in is the total reactant you started with, F_out includes any unreacted feed, and their difference is what was consumed by the reaction.

Selectivity, on the other hand, tells you how preferentially the reaction makes the desired product compared to an undesired byproduct. It is defined as the moles of the desired product formed divided by the moles of the undesired byproduct formed: S = (moles of desired product formed) / (moles of undesired byproduct formed). A larger number means the system favors making the desired product over the byproduct.

For example, if you started with 100 moles of feed, ended up with 60 moles of the desired product and 15 moles of undesired byproduct, the conversion would be (100 − 60)/100 = 0.40, and the selectivity would be 60/15 = 4.

Other formulations would either misstate conversion (using F_out − F_in would give a negative or illogical value) or invert the ratio for selectivity (undesired per desired) or change the denominator, which would not consistently reflect the fraction converted or the preferential formation of the desired product.