Consecutive Reactions Simulation

About this experiment

Follow generic species A through intermediate B into product C. Measure the intermediate peak, compare production and removal rates and explore equal rate constants without a numerical singularity.

Learning goals

Explain why an intermediate can rise and then fall.
Predict how the two rate constants shift the peak.
Verify conservation of the tracked species total.

How to use it

1Run the default sequence and inspect the intermediate gauge.
2Sample the intermediate peak and compare the formation and removal rates.
3Make the rate constants equal and repeat.
4Increase the second rate constant and compare how much intermediate accumulates.

The model

A = A_{0} e^{- k_{1} t}, B = \frac{A _{0} k _{1}}{k _{2} - k _{1}} (e^{- k_{1} t} - e^{- k_{2} t})

This form applies when the two rates differ.

B = A_{0} k t e^{- k t} (k_{1} = k_{2} = k)

The equal-rate limit stays finite.

t_{m a x} = \frac{ln ( k _{2} / k _{1} )}{k _{2} - k _{1}}

The peak occurs where k one times A equals k two times B.

Assumptions

The reactor has constant volume and irreversible first-order A to B and B to C steps. Initially only A is present.
A, B and C are generic species with one-to-one conversion, so their concentration sum is conserved.
Particle colours and three sensor bars represent continuous concentrations rather than counted molecules or separate physical reactors.
The equal-rate expression is evaluated with its analytic removable-singularity limit.

Try this in class

Q1Why does equal production and removal rate identify the intermediate peak?
Q2Can C decrease in this irreversible model?

Frequently asked questions

Does a sensor bar show liquid moving into a different beaker?

No. The three bars are concentration gauges for the same closed reactor.

What happens when the rate constants are almost equal?

The implementation uses a stable exponential-relative expression that approaches the exact equal-rate solution continuously.