### Abstract

The prevalence of apparently first-order kinetics of reactant disappearance in complex systems with many possible reaction pathways is usually attributed to the dominance of a single rate limiting step. Here, we investigate another possible explanation: that apparently first-order kinetics might arise because the aggregate behavior of many processes, with varying order of reaction and rate constant, approaches a "central limit" that is indistinguishable from first-order behavior. This hypothesis was investigated by simulating systems of increasing complexity and deriving relationships between the apparent reaction order of such systems and various measures of their complexity. Transformation of a chemical species by parallel irreversible reactions that are zero-, first-, or second-order is found to converge to a central limit as the number of parallel reactions becomes large. When all three reaction orders are represented, on average, in equal proportions, this central limit is experimentally indistinguishable from first-order. A measure of apparent reaction order was used to investigate the nature of the convergence both stochastically and by deriving theoretical limits. The range of systems that exhibit a central limit that is approximately first-order is found to be broad. First-order like behavior is also found to be favored when the distribution of material among the parallel processes (due to differences in rate constants for the individual reactions) is more complex. Our results show that a first-order central limit exists for the kinetics of chemical systems and that the variable controlling the convergence is the physical complexity of reaction systems.

Original language | English (US) |
---|---|

Pages (from-to) | 409-422 |

Number of pages | 14 |

Journal | Journal of Mathematical Chemistry |

Volume | 37 |

Issue number | 4 |

DOIs | |

State | Published - May 2005 |

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### Keywords

- Complexity
- First-order kinetics
- Reaction order

### ASJC Scopus subject areas

- Chemistry(all)
- Applied Mathematics

### Cite this

*Journal of Mathematical Chemistry*,

*37*(4), 409-422. https://doi.org/10.1007/s10910-004-1107-y

**Central limit theorem for chemical kinetics in complex systems.** / Bandstra, Joel Z.; Tratnyek, Paul.

Research output: Contribution to journal › Article

*Journal of Mathematical Chemistry*, vol. 37, no. 4, pp. 409-422. https://doi.org/10.1007/s10910-004-1107-y

}

TY - JOUR

T1 - Central limit theorem for chemical kinetics in complex systems

AU - Bandstra, Joel Z.

AU - Tratnyek, Paul

PY - 2005/5

Y1 - 2005/5

N2 - The prevalence of apparently first-order kinetics of reactant disappearance in complex systems with many possible reaction pathways is usually attributed to the dominance of a single rate limiting step. Here, we investigate another possible explanation: that apparently first-order kinetics might arise because the aggregate behavior of many processes, with varying order of reaction and rate constant, approaches a "central limit" that is indistinguishable from first-order behavior. This hypothesis was investigated by simulating systems of increasing complexity and deriving relationships between the apparent reaction order of such systems and various measures of their complexity. Transformation of a chemical species by parallel irreversible reactions that are zero-, first-, or second-order is found to converge to a central limit as the number of parallel reactions becomes large. When all three reaction orders are represented, on average, in equal proportions, this central limit is experimentally indistinguishable from first-order. A measure of apparent reaction order was used to investigate the nature of the convergence both stochastically and by deriving theoretical limits. The range of systems that exhibit a central limit that is approximately first-order is found to be broad. First-order like behavior is also found to be favored when the distribution of material among the parallel processes (due to differences in rate constants for the individual reactions) is more complex. Our results show that a first-order central limit exists for the kinetics of chemical systems and that the variable controlling the convergence is the physical complexity of reaction systems.

AB - The prevalence of apparently first-order kinetics of reactant disappearance in complex systems with many possible reaction pathways is usually attributed to the dominance of a single rate limiting step. Here, we investigate another possible explanation: that apparently first-order kinetics might arise because the aggregate behavior of many processes, with varying order of reaction and rate constant, approaches a "central limit" that is indistinguishable from first-order behavior. This hypothesis was investigated by simulating systems of increasing complexity and deriving relationships between the apparent reaction order of such systems and various measures of their complexity. Transformation of a chemical species by parallel irreversible reactions that are zero-, first-, or second-order is found to converge to a central limit as the number of parallel reactions becomes large. When all three reaction orders are represented, on average, in equal proportions, this central limit is experimentally indistinguishable from first-order. A measure of apparent reaction order was used to investigate the nature of the convergence both stochastically and by deriving theoretical limits. The range of systems that exhibit a central limit that is approximately first-order is found to be broad. First-order like behavior is also found to be favored when the distribution of material among the parallel processes (due to differences in rate constants for the individual reactions) is more complex. Our results show that a first-order central limit exists for the kinetics of chemical systems and that the variable controlling the convergence is the physical complexity of reaction systems.

KW - Complexity

KW - First-order kinetics

KW - Reaction order

UR - http://www.scopus.com/inward/record.url?scp=17744373461&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=17744373461&partnerID=8YFLogxK

U2 - 10.1007/s10910-004-1107-y

DO - 10.1007/s10910-004-1107-y

M3 - Article

AN - SCOPUS:17744373461

VL - 37

SP - 409

EP - 422

JO - Journal of Mathematical Chemistry

JF - Journal of Mathematical Chemistry

SN - 0259-9791

IS - 4

ER -