Rate of Reaction & Catalyst | Interactive Chemistry model

Change the reaction conditions

Temperature (°C) Reactant concentration (mol L⁻¹) Uncatalysed Ea (kJ mol⁻¹) Catalysed Ea (kJ mol⁻¹) Reaction enthalpy ΔH (kJ mol⁻¹) Catalyst used?

Uncatalysed pathwayCatalysed pathway

Pathway being used—

Activation energy—

Relative rate constant—

Catalyst rate increase—

Reaction ΔH—

Effect of concentration—

Approximate energetic-collision comparison

Uncatalysed

With catalyst

Collision theory: increasing concentration increases how often particles collide. Increasing temperature both increases collision frequency and increases the fraction of particles with sufficient energy. A catalyst mainly works by lowering the activation-energy requirement. The simple numerical model here isolates these ideas for comparison; real reaction rates also depend on mechanism, orientation, reaction order and the pre-exponential factor.

Reaction Rate with a Catalyst

The Arrhenius equation provides a simple quantitative way to see why lowering activation energy can greatly increase a reaction's rate constant.

import math

# Reaction conditions
temperature_C = 25
concentration = 1.0

# Activation energies
# kJ mol^-1
Ea_uncatalysed = 80
Ea_catalysed = 50

# Gas constant
# J mol^-1 K^-1
R = 8.314

temperature_K = (
    temperature_C + 273.15
)

# Convert kJ/mol to J/mol
Ea0 = Ea_uncatalysed * 1000
Ea1 = Ea_catalysed * 1000

# For comparison, use A = 1.
# Real reactions have a specific
# pre-exponential factor A.

A = 1.0

k_uncatalysed = (
    A * math.exp(
        -Ea0 / (R * temperature_K)
    )
)

k_catalysed = (
    A * math.exp(
        -Ea1 / (R * temperature_K)
    )
)

rate_increase = (
    k_catalysed / k_uncatalysed
)

print(
    "Temperature:",
    temperature_K,
    "K"
)

print(
    "Uncatalysed relative k:",
    k_uncatalysed
)

print(
    "Catalysed relative k:",
    k_catalysed
)

print(
    "Rate constant increase:",
    rate_increase,
    "times"
)

# Simple concentration illustration
#
# If the model is first order:
#
# rate = k[A]

rate_without_catalyst = (
    k_uncatalysed * concentration
)

rate_with_catalyst = (
    k_catalysed * concentration
)

print(
    "Relative rate without catalyst:",
    rate_without_catalyst
)

print(
    "Relative rate with catalyst:",
    rate_with_catalyst
)

# A catalyst lowers activation energy.
#
# It does NOT change:
# - reaction enthalpy (Delta H)
# - reactant energy
# - product energy
# - equilibrium constant
#
# It accelerates both forward and
# reverse reactions.

Why a Small Ea Change Can Matter

Activation energy appears in the exponential term of the Arrhenius equation. Therefore, even a moderate reduction in E_a can produce a large increase in the rate constant.

The energy diagram also makes an important connection to the previous experiment: the catalyst lowers the peak of the pathway, while the vertical difference between reactants and products — ΔH — remains unchanged.