Consecutive Reaction

Concentration vs Time

Reactant A Intermediate B Product C

Reaction Rate vs Time

Rate v₁ = k₁[A] Rate v₂ = k₂[B]

Reaction State Diagram

Reaction Time: 0.00 s

⟶ A → B → C

Reaction Parameters

Current [A] 0.00 M

Current [B] 0.00 M

Current [C] 0.00 M

Max [B] 0.00 M

t at Max [B] 0.00 s

Rate v₁ = k₁[A] 0.00 M/s

Rate v₂ = k₂[B] 0.00 M/s

k₁/k₂ Ratio 0.00

Reaction Parameters

Kinetic Parameters

Rate Constant k₁ (A→B): 0.50 s⁻¹ Rate Constant k₂ (B→C): 0.20 s⁻¹

Initial Concentration

Initial Concentration [A]₀: 1.00 M

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Consecutive Reaction Equations

Consecutive Reaction: A → B → C

Rate Law (A): d[A]/dt = -k₁[A]

Rate Law (B): d[B]/dt = k₁[A] - k₂[B]

Rate Law (C): d[C]/dt = k₂[B]

Solution [A](t): [A] = [A]₀·e^(-k₁·t)

Solution [B](t): [B] = [A]₀·(k₁/(k₂-k₁))·(e^(-k₁·t) - e^(-k₂·t))

Time at Max [B]: t_max = ln(k₂/k₁)/(k₂ - k₁)

What is a Consecutive Reaction?

A consecutive reaction is a multi-step reaction where the product of the first step becomes the reactant of the second step, represented as A → B → C. In this system, A is gradually converted to intermediate B, which is then converted to final product C. The intermediate B exhibits characteristic behavior: it first increases as A converts to B, reaches a maximum concentration, then decreases as B converts to C. This type of reaction is fundamental to understanding reaction mechanisms, rate-determining steps, and intermediate stability in chemical kinetics.

Consecutive Reaction Kinetics

Rate Equations: The system is described by three coupled differential equations: d[A]/dt = -k₁[A], d[B]/dt = k₁[A] - k₂[B], and d[C]/dt = k₂[B].
Concentration Solutions: [A] = [A]₀·e^(-k₁·t) (exponential decay). For [B] and [C], when k₁ ≠ k₂: [B] = [A]₀·(k₁/(k₂-k₁))·(e^(-k₁·t) - e^(-k₂·t)).
Intermediate Maximum: [B] reaches maximum at t_max = ln(k₂/k₁)/(k₂ - k₁).
Material Balance: [A] + [B] + [C] = [A]₀ (constant).

Rate-Determining Step

Concept: The slowest step controls the overall reaction rate. When k₁ << k₂, the first step (A→B) is rate-determining; B is consumed rapidly after formation. When k₁ >> k₂, the second step (B→C) is rate-determining; B accumulates to high levels.
Intermediate Behavior: When k₁ << k₂, [B]max is small and occurs early. When k₁ >> k₂, [B]max approaches [A]₀ and occurs later.
Steady-State Approximation: When k₂ >> k₁, d[B]/dt ≈ 0, [B] ≈ (k₁/k₂)[A].

Intermediate Species Behavior

Characteristic Shape: [B] vs time shows a peak: starts at 0, rises as A→B dominates, falls as B→C dominates. The peak height and timing depend on k₁/k₂ ratio.
Peak Analysis: Higher k₁/k₂ ratio gives higher [B]max and later t_max.
Practical Implications: In synthesis, desired intermediates require careful control of relative rates.

Real-World Applications

Radioactive Decay Series: U-238 → Th-234 → Pa-234 → ... → Pb-206.
Industrial Chemical Synthesis: Multi-step processes like NH₃ oxidation to NO then to NO₂.
Biochemical Pathways: Metabolic pathways where A → B → C represents sequential enzyme-catalyzed transformations.
Atmospheric Chemistry: CH₄ → CH₃O₂ → HCHO in methane oxidation.
Polymerization: Initiator → Radical → Polymer chain growth.

Factors Affecting Reaction Progress

Rate Constant Ratio (k₁/k₂): Determines whether B accumulates (k₁ >> k₂) or remains minimal (k₁ << k₂).
Initial Concentration: Affects absolute concentrations but not normalized shapes or t_max.
Temperature: Changes k₁ and k₂ via Arrhenius equation.
Catalysts: Can selectively accelerate one step.