Concentration of Intermediate B in First Order Consecutive Reaction Calculator

Concentration Formula:

\[ [B] = A_0 \times \left(\frac{k_1}{k_2 - k_1}\right) \times \left(e^{-k_1 t} - e^{-k_2 t}\right) \]

Initial Concentration of Reactant A (A₀):

mol/m³

Reaction Rate Constant 1 (k₁):

s⁻¹

Rate Constant of Reaction 2 (k₂):

s⁻¹

Time (t):

seconds

Concentration of B at Time t [B]: mol/m³

Definition: This calculator determines the concentration of intermediate product B in a consecutive first-order reaction A → B → C.

Purpose: It helps chemists and chemical engineers analyze reaction kinetics and predict intermediate concentrations over time.

The calculator uses the formula:

\[ [B] = A_0 \times \left(\frac{k_1}{k_2 - k_1}\right) \times \left(e^{-k_1 t} - e^{-k_2 t}\right) \]

Where:

Explanation: The formula accounts for both the formation of B from A and the subsequent decay of B into C.

Details: Understanding intermediate concentrations helps optimize reaction conditions, control product yields, and design chemical processes.

Tips: Enter the initial concentration of A, both rate constants (k₁ must not equal k₂), and the reaction time. All values must be positive.

Q1: What if k₁ equals k₂?
A: The formula becomes indeterminate. In practice, use a limiting case formula when rate constants are nearly equal.

Q2: What units should I use?
A: Use consistent units - concentration in mol/m³, time in seconds, rate constants in s⁻¹.

Q3: How does time affect the concentration of B?
A: B concentration initially increases as A converts to B, then decreases as B converts to C.

Q4: Can this be used for other reaction orders?
A: No, this formula is specific for consecutive first-order reactions.

Q5: What's the maximum concentration of B?
A: The maximum occurs at time t_max = ln(k₂/k₁)/(k₂ - k₁).