关键词: 分析化学, 气相色谱, 定量分析, 跨学科教学, 物理建模, 教材编写

Abstract: Analytical Chemistry is a core foundational course in science and engineering, placing equal emphasis on rigorous theoretical principles and practical operational skills. Modern analytical techniques demand both deep mechanistic understanding and rigorous logical reasoning. However, current textbooks often lean toward empirical statements to save page space, thereby frequently omitting fundamental physical insights and step-by-step mathematical derivations. This "conclusion-heavy, derivation-light" paradigm causes cognitive discontinuities during student self-study, as students often struggle to connect new chemical concepts with their prior knowledge. Gas chromatographic quantitative analysis in textbooks clearly illustrates this cognitive discontinuity problem. Students frequently memorize complex correction factors without understanding their physical origins, while also confusing concentration-sensitive detectors with mass-sensitive detectors under varying flow rates. To address these issues, this paper proposes a comprehensive pedagogical strategy that integrates conceptual clarification with interdisciplinary mathematical and physical tools. First, definition tracing and algebraic derivation are applied to quantitative calibration methods. This study clarifies the definitions of absolute and relative correction factors, revealing that normalization is a dimensionless mathematical transformation independent of relative correction factors. Second, a simplified three-dimensional physical model of solute transport is constructed, applying fundamental calculus and physical transport laws to the column element and accounting for solute micro-elements passing through the detector, from which equations for detector signal response are rigorously derived from first principles. The influence of carrier gas flow velocity on peak height is derived, and the effect of flow velocity on peak area is also thoroughly analyzed. Concentration-sensitive detectors show flow-rate dependence in peak area but not height, whereas mass-sensitive detectors exhibit flow-rate dependence in peak height but not area. Beyond theoretical derivation, this paper focuses on practical classroom implementation by establishing a teaching path termed "textbook reconstruction and classroom dimensionality reduction" that transforms static textbook knowledge into dynamic classroom inquiry. A comprehensive process-based evaluation framework, spanning both theoretical lectures and practical laboratory sessions, is designed to measure teaching effectiveness. In theoretical classes, derivations are converted into structured, inquiry-based questions that instructors use to diagnose students' real-time conceptual understanding. In laboratory sessions, where traditional grading relies heavily on numerical accuracy, this study expands assessment to include students' mechanistic reasoning, requiring them to explain anomalous peak shapes using solute transport micro-elements. For example, they explain peak broadening caused by carrier gas flow fluctuations. Furthermore, inverse annotations on lab reports address common conceptual confusion, guiding students to distinguish internal standard operations from relative response calculations. Subjective cognitive load surveys are incorporated into the evaluation, and interdisciplinary knowledge transfer tests are planned to measure cognitive gains. This multidimensional evaluation enhances feasibility and provides a reliable framework for classroom validation. This study explicitly adopts a multidimensional target audience orientation, establishing self-study as the primary cognitive baseline, while capping math depth at college calculus and general physics, so that students achieve logical consistency without advanced fluid mechanics backgrounds. Simultaneously, the study offers insights for instructors to use models as prompts, and references for authors to insert interdisciplinary interfaces into textbooks. Incorporating simple mathematical derivations does not increase cognitive burden but bridges students' existing reserves in calculus and introductory physics, transforming isolated conclusions into a self-consistent logical framework. This approach lowers the threshold for mastering complex analytical techniques, eliminating reliance on mechanical rote memorization among undergraduate chemistry students. Ultimately, it cultivates students' core competencies in building interdisciplinary knowledge systems and strengthens their abilities to solve complex scientific and engineering problems.

Key words: analytical chemistry, gas chromatography, quantitative analysis, interdisciplinary teaching, physical modeling, textbook compilation