This simulation models an A → B → C consecutive reaction, tracking how the concentrations of reactant A, intermediate B and product C evolve over a 120-second window. It integrates the coupled rate equations dA/dt = −k₁A + k₋₁B, dB/dt = k₁A − k₋₁B − k₂B and dC/dt = k₂B using a simple explicit Euler scheme. The rate constants come from the Arrhenius equation, k = A·e−Ea/RT, with R = 8.314 J/mol·K.
The temperature slider (273–700 K) and the two activation-energy sliders (Ea₁ and Ea₂, 10–120 kJ/mol) set the rate constants k₁ and k₂. A catalyst toggle lowers both activation energies by 30%, and a reversibility toggle adds a back-reaction B → A. Consecutive kinetics like these govern everything from industrial synthesis and drug metabolism to atmospheric chemistry, where a fleeting intermediate builds up and then decays.
What does this simulation actually show?
It plots the concentrations of three species in a consecutive reaction A turns into B, which then turns into C. The reactant A (red) falls, the intermediate B (yellow) rises to a peak and then falls, and the product C (green) accumulates. You watch the whole curve and a live time marker sweeps across it as the reaction proceeds.
What is the Arrhenius equation used here?
The Arrhenius equation k = A times e to the power of minus Ea over RT relates a rate constant to temperature and activation energy. Here A is a fixed pre-exponential factor of 1 times 10 to the 8 per second, R is the gas constant 8.314 joules per mole per kelvin, T is temperature in kelvin and Ea is the activation energy. The simulation evaluates it separately for each step.
What do the temperature and activation-energy sliders do?
Temperature (273 to 700 kelvin) and the two activation energies Ea1 and Ea2 (10 to 120 kilojoules per mole) feed directly into the Arrhenius equation to set the rate constants k1 and k2. Raising temperature or lowering activation energy increases the rate constants, speeding the reaction. The panel shows the resulting k1, k2 and the half-life of A.
In a consecutive reaction B is formed from A but also consumed to make C. Early on A is plentiful so B builds up faster than it decays, giving a rising curve. Once A is depleted, formation slows while consumption continues, so B passes through a maximum and then declines. The height and timing of that peak depend on the ratio of k1 to k2.
The catalyst checkbox multiplies both activation energies by 0.7, lowering them by 30%. Because activation energy sits in the exponent of the Arrhenius equation, even this modest reduction can raise the rate constants substantially and dramatically speed the reaction. Crucially a catalyst changes the kinetics, not the thermodynamics, so it does not alter the overall free-energy change or the final products.
Enabling the reversible toggle adds a back-reaction B turns into A with its own rate constant. This means A is no longer fully consumed, because some B continually returns to A. The system tends towards a dynamic equilibrium rather than complete conversion, so the A and B curves level off at non-zero values instead of A falling all the way to nothing.
It integrates the three coupled ordinary differential equations with the forward (explicit) Euler method, using a small fixed time step of 0.02 seconds to precompute the full curve and 20 substeps per animation frame for the live run. Concentrations are clamped at zero to avoid small negative values from rounding. Euler is simple and fast but only first-order accurate.
The displayed half-life is the time for A to fall to half its starting value, computed as the natural logarithm of 2 divided by k1, roughly 0.693 over k1. This is the standard first-order half-life and is exact only for the simple loss of A by the first step; the back-reaction and downstream steps mean the real decay can differ slightly when those are active.
The reaction scheme and the Arrhenius temperature dependence are physically correct, but the pre-exponential factor and concentrations are illustrative defaults rather than data for a specific real reaction. The simplified Euler integration and the fixed catalyst factor are teaching idealisations. It faithfully reproduces the qualitative behaviour of consecutive first-order kinetics rather than a calibrated industrial process.
Sequential A to B to C kinetics appear throughout chemistry and biology: pharmaceutical drugs are metabolised through intermediate compounds, polymers form in stages, and atmospheric pollutants degrade via reactive intermediates. Understanding when the intermediate peaks helps chemists time a reaction to maximise yield of B before it is lost to C, a common goal in synthesis.