Chemical Reaction Kinetics: Rate Laws & Arrhenius Equation

simulator intermediate ~10 min
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Equilibrium conversion: 90.9% at 450K, Ea=80 kJ/mol

At 450K with activation energy 80 kJ/mol, the forward rate constant is 0.47/s giving a half-life of 1.5s. The equilibrium constant of 10 yields 90.9% conversion, producing 0.91 mol/L of product from 1.0 mol/L feed.

Formula

k = A * exp(-Ea / (R * T))
r = k * C_A - k_r * C_B
X_eq = K_eq / (1 + K_eq)

The Speed of Chemistry

Chemical kinetics is the study of reaction rates - how fast reactants transform into products. While thermodynamics determines whether a reaction is possible and where equilibrium lies, kinetics determines how quickly that equilibrium is reached. This distinction is crucial: many thermodynamically favorable reactions (like rusting iron or burning wood) proceed at vastly different rates depending on temperature, catalysts, and concentration.

The Arrhenius Revolution

In 1889, Svante Arrhenius proposed that the rate constant depends exponentially on temperature through k = A * exp(-Ea/RT). This beautifully simple equation explains why chemical plants carefully control temperature: a 10K increase can double the reaction rate. The activation energy Ea represents the energy barrier that molecules must overcome, while the pre-exponential factor A captures the frequency and geometry of molecular collisions.

Reversible Reactions and Equilibrium

Most industrial reactions are reversible: A converts to B, but B also converts back to A. The equilibrium constant K_eq = k_forward/k_reverse determines the final ratio of products to reactants. This simulation shows how the concentration profiles of reactant and product evolve over time, approaching equilibrium from below. The rate of approach depends on kinetics; the final position depends on thermodynamics.

From Lab to Plant

Scaling a reaction from a laboratory flask to an industrial reactor is one of chemical engineering's greatest challenges. Heat removal, mixing uniformity, residence time distribution, and catalyst deactivation all affect performance at scale. The kinetic parameters measured in this simulation form the foundation of reactor design, but successful scale-up requires careful attention to transport phenomena.

FAQ

What is the Arrhenius equation?

The Arrhenius equation k = A * exp(-Ea/RT) describes how the rate constant k depends on temperature T. A is the pre-exponential factor (collision frequency), Ea is activation energy (energy barrier), and R is the gas constant. It shows that even small temperature increases can dramatically accelerate reactions.

What is the difference between kinetics and thermodynamics?

Thermodynamics tells you where the reaction will end up (equilibrium position), while kinetics tells you how fast it will get there. A reaction can be thermodynamically favorable but kinetically slow (like diamond converting to graphite at room temperature). Catalysts affect kinetics but not thermodynamics.

What is activation energy?

Activation energy Ea is the minimum energy that reactant molecules must possess to undergo a chemical reaction. It represents the height of the energy barrier between reactants and products. Catalysts work by providing an alternative reaction pathway with a lower activation energy.

How does temperature affect reaction rate?

A rough rule of thumb is that reaction rate doubles for every 10K temperature increase. More precisely, the Arrhenius equation shows the rate constant increases exponentially with temperature. However, for reversible reactions, higher temperature may shift equilibrium unfavorably.

Sources

Embed

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