1. What is the First Order Rate Constant?

The first-order rate constant (k) is a proportionality constant that relates the rate of a first-order reaction to the concentration of the reactant. It is inversely related to the half-life of the reaction.

2. How Does the Calculator Work?

The calculator uses the first-order kinetics equation:

Where:

• \( k \) — First-order rate constant (s⁻¹)
• \( t_{1/2} \) — Half-life of the reaction (seconds)

Explanation: The equation shows that the rate constant is inversely proportional to the half-life of the reaction. The constant 0.693 is ln(2).

3. Importance of Rate Constant Calculation

Details: The rate constant is fundamental in chemical kinetics, used to predict reaction rates, determine reaction mechanisms, and calculate shelf life of pharmaceuticals.

4. Using the Calculator

Tips: Enter the half-life in seconds. The value must be positive (half-life > 0). The calculator will compute the first-order rate constant in reciprocal seconds (s⁻¹).

5. Frequently Asked Questions (FAQ)

Q1: What are typical units for first-order rate constants?
A: The units are reciprocal time (e.g., s⁻¹, min⁻¹, h⁻¹). The specific unit depends on the time unit used for half-life.

Q2: How does temperature affect the rate constant?
A: According to the Arrhenius equation, rate constants typically increase with temperature.

Q3: Can this equation be used for radioactive decay?
A: Yes, radioactive decay follows first-order kinetics, so this equation applies.

Q4: What's the relationship between rate constant and reaction speed?
A: Larger rate constants indicate faster reactions (shorter half-lives).

Q5: How accurate is this calculation?
A: The calculation is mathematically exact for ideal first-order reactions.