Time Interval for First Order Reaction in First Order followed by Zero Order Reaction Calculator

Time Interval Formula:

\[ \Delta t = \frac{1}{k_I} \times \ln\left(\frac{C_{A0}}{C_{k0}}\right) \]

Rate Constant for First Step First Order Reaction (k_I):

1/s

Initial Reactant Concentration (C_A0):

mol/m³

Reactant Concentration for Zero Order Reaction (C_k0):

mol/m³

Time Interval (Δt):

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1. What is Time Interval for First Order Reaction in Series?

Definition: This calculator determines the time interval required for the reactant concentration to change from initial to final value in a first order reaction followed by a zero order reaction.

Purpose: It helps chemical engineers and researchers analyze reaction kinetics in multi-step reaction systems.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \Delta t = \frac{1}{k_I} \times \ln\left(\frac{C_{A0}}{C_{k0}}\right) \]

Where:

\( \Delta t \) — Time interval (seconds)
\( k_I \) — Rate constant for first step first order reaction (1/s)
\( C_{A0} \) — Initial reactant concentration (mol/m³)
\( C_{k0} \) — Reactant concentration for zero order reaction (mol/m³)

Explanation: The natural log of the concentration ratio is divided by the rate constant to determine the time interval.

3. Importance of Time Interval Calculation

Details: Accurate time interval calculation is crucial for reaction optimization, process design, and safety analysis in chemical engineering.

4. Using the Calculator

Tips: Enter the rate constant (default 0.42 1/s), initial concentration (default 80 mol/m³), and final concentration (default 24 mol/m³). All values must be > 0 and initial concentration > final concentration.

5. Frequently Asked Questions (FAQ)

Q1: What does the rate constant represent?
A: The rate constant (k_I) indicates how fast the first order reaction proceeds.

Q2: Why must initial concentration be greater than final?
A: The reaction proceeds from higher to lower concentration; otherwise the calculation would give negative time.

Q3: What units should be used?
A: Use consistent units - seconds for time, mol/m³ for concentration, and 1/s for rate constant.

Q4: Can this be used for other reaction orders?
A: No, this formula is specific for first order followed by zero order reactions in series.

Q5: How does temperature affect the calculation?
A: Temperature affects the rate constant (k_I), which should be determined at the relevant temperature.