Consecutive reactions A → B → C: If the activation energy for the first step (E1) is much greater than for the second step (E2), how does the yield of intermediate B change with temperature?

Introduction / Context:In consecutive reaction networks, optimizing selectivity to the intermediate product B is a classic design problem. Temperature alters relative rates via Arrhenius sensitivities, especially when activation energies differ markedly.

Given Data / Assumptions:

• Scheme: A → B → C (consecutive, irreversible steps).
• Activation energies: E1 ≫ E2.
• Other effects (mass transfer, deactivation) are negligible.

Concept / Approach:Rate constants: k1 ∝ exp(-E1/RT), k2 ∝ exp(-E2/RT). The selectivity toward B depends on the ratio k1/k2 and on residence time. Because E1 is much larger, increasing temperature amplifies k1 more strongly than k2. Thus k1/k2 increases with T, favoring formation of B relative to its consumption to C and improving achievable yield/selectivity of B for a given space time.

Step-by-Step Solution:Consider ratio: k1/k2 = exp(-(E1 - E2)/(RT)).With E1 > E2, the exponent increases (becomes less negative) as T rises.Therefore, k1/k2 increases with T, improving B formation relative to loss.Hence, yield of B increases with temperature (up to constraints like side reactions or thermal limits).

Verification / Alternative check:Optimal temperature-residence time strategies show higher selectivity windows at elevated T when the desired step has higher activation energy than the undesired subsequent step.

Why Other Options Are Wrong:

• Lower temperature: would reduce k1 disproportionately, lowering B formation.
• Dependence solely on initial concentration: incomplete; temperature is a primary lever here.
• Independence from temperature: contradicts Arrhenius behavior.

Common Pitfalls:Ignoring the need to limit residence time to prevent over-conversion of B to C at very high temperatures; selectivity involves both kinetics and contact time.

Final Answer:Yield of B increases as temperature increases