Gas-phase stoichiometry — fractional volume change For the isothermal gas-phase reaction A → 3B, what is the fractional volume change of the reacting system between zero conversion and complete conversion (assume ideal-gas behavior and constant T, P)?

Introduction / Context:
Fractional volume change is a key parameter in gas-phase reactor design because it affects concentrations and thus rates. For ideal gases at constant temperature and pressure, volume is proportional to total moles.

Given Data / Assumptions:

• Reaction: A → 3B (gas phase).
• Isothermal, isobaric, ideal-gas behavior.
• Fractional volume change ε is defined between zero and complete conversion.

Concept / Approach:
At constant T and P for an ideal gas, V ∝ n(total). For the reaction νr = 1 mole of A to νp = 3 moles of B, the change in total moles per initial mole of A is (3 − 1) = +2. The fractional volume change ε (relative to initial) equals the fractional change in total moles.

Step-by-Step Solution:
Initial moles per mole A fed at zero conversion: n0 = 1 (taking a 1-mole basis).Final moles at complete conversion: n = 3.Fractional change in moles (and hence volume) = (n − n0)/n0 = (3 − 1)/1 = 2.

Verification / Alternative check:
General formula for isothermal, isobaric gas reactions: ε = (Σνproducts − Σνreactants)/Σνreactants. Here, ε = (3 − 1)/1 = 2.

Why Other Options Are Wrong:

• 0.5, 1, 3 are not consistent with stoichiometric mole change for A → 3B.

Common Pitfalls:

• Forgetting the constant T, P assumption; under those conditions, volume tracks total moles.

Final Answer:
2