The Le Châtelier Principle is one of the most important concepts in chemistry, and it has been the topic of many publications over the years. However, its meaning and application are often fraught with misunderstanding and confusion. As a suggested replacement, we present herein a precise general statement that we call the Basic Le Châtelier Principle (BLCP), which is in keeping with a common thread in Le Châtelier’s original statements. The BLCP is formulated as a consequence of well-known properties of a simple but general optimization problem, which elevates its range of application beyond chemistry to any phenomenon governed by such an optimization principle. We show applications of the BLCP to simple example problems in economics and in physics, in addition to the usual chemistry problems,. Following a brief outline of Le Châtelier’s original statements, we formulate the BLCP, which incorporates the notion of “de signe contraire” (of opposite sign), common to all his statements. It arises by abstracting the chemical reaction equilibrium problem (CREP) in the single-reaction case to the general problem of minimizing a differentiable function f(x;{pj})\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f(x;\{p_j\})$$\end{document}, where x is the single independent variable and {pj}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\{p_j\}$$\end{document} is a set of parameters. The BLCP arises from an exact expression for the dependence of the sign of the incremental change in the optimal solution x∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x^*$$\end{document} on the sign of the incremental change in a parameter, which is derived using techniques taught in an early undergraduate calculus course. When translated back to the CREP, this yields unambiguous expressions for the sign of the incremental change in the equilibrium reaction extent, ξ∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\xi ^*$$\end{document}, arising from an incremental change in each of T, P, the initial species amounts, {ni0}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\{n_i^0\}$$\end{document}, and the standard reaction free energy change, ΔG□\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varDelta G^{\Box }$$\end{document}. Special emphasis is placed on the requirement that f must satisfy a positive definite second derivative condition, for which we present a proof in the case of multiple reactions in an ideal solution model system. We also briefly consider the extension of the single-variable BLCP derived herein to the case of multiple independent variables and to finite parameter perturbations.

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基于初等微积分的精确、简单和通用的基本 Le Châtelier 原理：Le Châtelier 的想法是什么？

勒夏特列原理是化学中最重要的概念之一，多年来一直是许多出版物的主题。然而，它的含义和应用往往充满了误解和混乱。作为建议的替代，我们在此提出了一个精确的一般性陈述，我们称之为基本 Le Châtelier 原则 (BLCP)，这与 Le Châtelier 原始陈述中的一个共同主线保持一致。BLCP 被公式化为一个简单但通用的优化问题的众所周知的性质的结果，这将其应用范围从化学提升到任何受这种优化原理支配的现象。除了通常的化学问题外，我们还展示了 BLCP 在经济学和物理学中的简单示例问题中的应用。在简要概述 Le Châtelier 的原始陈述之后，我们制定了 BLCP，其中包含了他的所有陈述所共有的“de signe contraaire”（相反符号）的概念。它是通过将单反应情况下的化学反应平衡问题 (CREP) 抽象为最小化可微函数 f(x;{pj})\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage 的一般问题而产生的{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f(x;\ {p_j\})$$\end{document}, 其中 x 是单个自变量， {pj}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \ usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\{p_j\}$$\end{document} 是一组参数。BLCP 源于最优解 x∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb } \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x^*$$\end{document} 关于增量变化的标志在一个参数中，该参数是使用在早期本科微积分课程中教授的技术得出的。ΔG□\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin }{-69pt} \begin{document}$$\varDelta G^{\Box }$$\end{document}。特别强调 f 必须满足正定二阶导数条件的要求，对此我们给出了理想溶液模型系统中多反应情况下的证明。我们还简要地考虑了在此导出的单变量 BLCP 对多个自变量的情况和有限参数扰动的扩展。特别强调 f 必须满足正定二阶导数条件的要求，对此我们给出了理想溶液模型系统中多反应情况下的证明。我们还简要地考虑了在此导出的单变量 BLCP 对多个自变量的情况和有限参数扰动的扩展。特别强调 f 必须满足正定二阶导数条件的要求，对此我们给出了理想溶液模型系统中多反应情况下的证明。我们还简要地考虑了在此导出的单变量 BLCP 对多个自变量的情况和有限参数扰动的扩展。