### Abstract

A continuous-time, discrete-state stochastic approach was used to study a simple, chiral autocatalytic model that was composed of the following three reactions: A → 0.5B_{R} + 0.5B_{S} (v_{1} = k _{u}[A]), A + B_{R} → 2B_{R} (v_{2} = k_{c}[A][B_{R}]), A + B_{S} → 2B_{S} (v_{3} = k_{c}[A][B_{S}]). It is shown that the final distribution of enantiomers B_{R} and B_{S} is described by the one-parameter probability function Cx^{δ}(1-x)^{δ}, where x is the molar fraction of B_{R}, δ = 0.5/α -1 (where α = k^{c}/(k_{u}N_{A}V), N_{A} is Avogadro's constant, and V is the volume of the sample), and C = Γ(1/α)/{Γ(0.5/α)}^{2} (where Γ is the gamma function). Comparison with two published examples shows that the probability function introduced here gives a reasonable interpretation of the experimental results.

Original language | English |
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Pages (from-to) | 9475-9478 |

Number of pages | 4 |

Journal | Journal of Physical Chemistry A |

Volume | 108 |

Issue number | 44 |

DOIs | |

Publication status | Published - Nov 4 2004 |

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### ASJC Scopus subject areas

- Physical and Theoretical Chemistry

### Cite this

**Homogeneous chiral autocatalysis : A simple, purely stochastic kinetic model.** / Lente, G.

Research output: Contribution to journal › Article

*Journal of Physical Chemistry A*, vol. 108, no. 44, pp. 9475-9478. https://doi.org/10.1021/jp046413u

}

TY - JOUR

T1 - Homogeneous chiral autocatalysis

T2 - A simple, purely stochastic kinetic model

AU - Lente, G.

PY - 2004/11/4

Y1 - 2004/11/4

N2 - A continuous-time, discrete-state stochastic approach was used to study a simple, chiral autocatalytic model that was composed of the following three reactions: A → 0.5BR + 0.5BS (v1 = k u[A]), A + BR → 2BR (v2 = kc[A][BR]), A + BS → 2BS (v3 = kc[A][BS]). It is shown that the final distribution of enantiomers BR and BS is described by the one-parameter probability function Cxδ(1-x)δ, where x is the molar fraction of BR, δ = 0.5/α -1 (where α = kc/(kuNAV), NA is Avogadro's constant, and V is the volume of the sample), and C = Γ(1/α)/{Γ(0.5/α)}2 (where Γ is the gamma function). Comparison with two published examples shows that the probability function introduced here gives a reasonable interpretation of the experimental results.

AB - A continuous-time, discrete-state stochastic approach was used to study a simple, chiral autocatalytic model that was composed of the following three reactions: A → 0.5BR + 0.5BS (v1 = k u[A]), A + BR → 2BR (v2 = kc[A][BR]), A + BS → 2BS (v3 = kc[A][BS]). It is shown that the final distribution of enantiomers BR and BS is described by the one-parameter probability function Cxδ(1-x)δ, where x is the molar fraction of BR, δ = 0.5/α -1 (where α = kc/(kuNAV), NA is Avogadro's constant, and V is the volume of the sample), and C = Γ(1/α)/{Γ(0.5/α)}2 (where Γ is the gamma function). Comparison with two published examples shows that the probability function introduced here gives a reasonable interpretation of the experimental results.

UR - http://www.scopus.com/inward/record.url?scp=9144272352&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=9144272352&partnerID=8YFLogxK

U2 - 10.1021/jp046413u

DO - 10.1021/jp046413u

M3 - Article

AN - SCOPUS:9144272352

VL - 108

SP - 9475

EP - 9478

JO - Journal of Physical Chemistry A

JF - Journal of Physical Chemistry A

SN - 1089-5639

IS - 44

ER -