Rate Constant (k) Calculator
Zero Order (0)
First Order (1)
Second Order (2)
Calculated Rate Constant (k):
Understanding the Rate Constant (k)
In chemical kinetics, the rate constant (k) is a proportionality constant that links the molar concentration of reactants to the rate of a chemical reaction. Unlike the reaction rate itself, which changes as reactants are consumed, the rate constant remains fixed for a specific reaction at a constant temperature.
How to Calculate k for Different Reaction Orders
The method used to calculate the value of the rate constant depends entirely on the reaction's order. Below are the integrated rate laws used in the calculator above:
-
Zero-Order Reaction: The rate is independent of concentration.
Formula: k = ([A]₀ – [A]ₜ) / t
Units: M · s⁻¹ -
First-Order Reaction: The rate is proportional to the concentration of one reactant.
Formula: k = ln([A]₀ / [A]ₜ) / t
Units: s⁻¹ -
Second-Order Reaction: The rate is proportional to the square of the concentration.
Formula: k = (1/[A]ₜ – 1/[A]₀) / t
Units: M⁻¹ · s⁻¹
Step-by-Step Calculation Example
Suppose you have a first-order reaction where the initial concentration is 0.80 M. After 50 seconds, the concentration drops to 0.20 M. What is the rate constant?
- Identify the order: First Order.
- Identify variables: [A]₀ = 0.80, [A]ₜ = 0.20, t = 50.
- Apply the formula: k = ln(0.80 / 0.20) / 50.
- Solve: k = ln(4) / 50 ≈ 1.386 / 50 = 0.0277.
- Final Answer: k = 0.0277 s⁻¹.
Factors Affecting the Rate Constant
While concentration does not change the rate constant, other factors do:
- Temperature: According to the Arrhenius equation, k increases exponentially as temperature rises.
- Catalysts: Catalysts lower the activation energy, which increases the value of k.
- Surface Area: In heterogeneous reactions, increasing surface area can affect the effective rate constant.