Average Life-Time for Set of Three Parallel Reactions Calculator

Formula Used:

\[ t_{1/2av} = \frac{0.693}{k_1 + k_2 + k_3} \]

Reaction Rate Constant 1 (k₁):

s⁻¹

Reaction Rate Constant 2 (k₂):

s⁻¹

Rate Constant of Reaction 3 (k₃):

s⁻¹

Average Life-Time (t₁/₂av):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Average Life-Time for Parallel Reactions?

Definition: The average life-time for a set of parallel reactions is the characteristic time period during which the concentration of reactants decreases to half its initial value through multiple simultaneous reaction pathways.

Purpose: This calculation is essential in chemical kinetics to understand the overall behavior of systems where multiple reaction pathways compete.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ t_{1/2av} = \frac{0.693}{k_1 + k_2 + k_3} \]

Where:

\( t_{1/2av} \) — Average half-life (seconds)
\( k_1 \) — Rate constant for reaction pathway 1 (s⁻¹)
\( k_2 \) — Rate constant for reaction pathway 2 (s⁻¹)
\( k_3 \) — Rate constant for reaction pathway 3 (s⁻¹)

Explanation: The natural logarithm of 2 (0.693) is divided by the sum of all parallel reaction rate constants to determine the average lifetime.

3. Importance of Average Life-Time Calculation

Details: Understanding the average life-time helps chemists predict reaction durations, design industrial processes, and analyze complex reaction mechanisms.

4. Using the Calculator

Tips: Enter the rate constants for all three parallel reactions in reciprocal seconds (s⁻¹). At least one rate constant must be greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What does the 0.693 represent in the formula?
A: This is the natural logarithm of 2 (ln(2)), which appears in all half-life calculations for first-order kinetics.

Q2: Can I use this for more than three parallel reactions?
A: Yes, simply extend the formula by adding additional rate constants to the denominator.

Q3: What if one rate constant is much larger than the others?
A: The fastest reaction will dominate, and the average lifetime will approach the lifetime of that single reaction.

Q4: How do I obtain the individual rate constants?
A: They are typically determined experimentally through kinetic studies of each isolated reaction pathway.

Q5: Does this apply to non-first-order reactions?
A: No, this specific formula only applies to parallel first-order reactions or elementary steps.