Development and practice of an interactive chromatography learning tool for beginners based on GeoGebra： a case study of plate theory

doi:10.3724/SP.J.1123.2025.03008

Abstract

Abstract:

This study developed a GeoGebra platform-based interactive pedagogical tool focusing on plate theory to address challenges associated with abstract theory transmission， unidirectional knowledge delivery， and low student engagement in chromatography teaching in instrumental analysis courses. This study introduced an innovative methodology that encompasses theoretical model reconstruction， tool development， and teaching-chain integration that addresses the limitations of existing teaching tools， including the complex operation of professional software， restricted accessibility to web-based tools， and insufficient parameter-adjustment flexibility. An improved mathematical plate-theory model was established by incorporating mobile-phase flow rate， dead time， and phase ratio parameters. A three-tier progressive learning system （single-component simulation， multi-component simulation， and retention-time-equation derivation modules） was developed on a cloud-based computing platform. An integrated teaching chain that combined athematical modeling （AI-assisted “Doubao” derivation）， interactive-parameter adjustment （multiple adjustable chromatographic parameters）， and visual verification （chromatographic elution-curve simulation） was implemented. Teaching practice demonstrated that：（1） The developed tool transcends the dimensional limitations of traditional instruction， elevating the classroom task completion rate to 94% and improving the student accuracy rate for solving advanced problems to 76%. （2） The dynamic-parameter-adjustment feature significantly enhances learning engagement by enabling 85% of the students to independently use the tool in subsequent studies and experiments. （3） The AI-powered derivation and regression-analysis modules enable the interdisciplinary integration of theoretical chemistry and computational tools. The process of deriving chromatographic retention-time equations through this methodological approach proved more convincing than the current textbook practice of directly presenting conclusions. The developed innovative “theoretical-model visualizable-model-parameter adjustable-interactive-knowledge generating” model provides a new avenue for addressing teaching challenges associated with chromatography theory， and its open-source framework and modular design philosophy can offer valuable references for the digital teaching reform in analytical chemistry.

Key words: instrumental analysis course, plate theory, GeoGebra platform, interactive learning, chromatographic elution profile simulation, digital teaching

CLC Number:

O658

ZHANG Yuhan, HE Junyao, LIN Shujing, AI Bingjian, SHI Zhihong, ZHANG Hongyi. Development and practice of an interactive chromatography learning tool for beginners based on GeoGebra： a case study of plate theory[J]. Chinese Journal of Chromatography, 2025, 43(9): 1078-1085.

Figures/Tables 9

Table 1 Procedures of operation for simulated chromatographic elution profile of single-component sample by GeoGebra

Line No.	Input	Comment
1	$C 0$ =1	initial concentration
2	$t m = 3$	dead time
3	$β = 2$	phase ratio
4	$n = 100$	number of plates
5	$K = 3$	distribution coefficient
6	$v (t) = t n (K / β + 1) t m$	Equation （9）^*
7	$f (t) = 1 1 + K C 0 1 2 π n (v (t) n) n ⋅ e n - v (t)$	Equation （4）^*

Table 1 Procedures of operation for simulated chromatographic elution profile of single-component sample by GeoGebra

Line No.	Input	Comment
1	$C 0$ =1	initial concentration
2	$t m = 3$	dead time
3	$β = 2$	phase ratio
4	$n = 100$	number of plates
5	$K = 3$	distribution coefficient
6	$v (t) = t n (K / β + 1) t m$	Equation （9）^*
7	$f (t) = 1 1 + K C 0 1 2 π n (v (t) n) n ⋅ e n - v (t)$	Equation （4）^*

Fig. 1 Simulated chromatographic elution profile of single-component sample by GeoGebra

Table 2 Procedures of operation for simulated chromatographic elution profiles of dual-component sample （K=3 and 1.8） by GeoGebra

Line No.	Input	Comment
1	$C 0$ = 1	initial concentration of component A
2	$t m = 3$	dead time
3	$β = 2$	phase ratio
4	$n = 100$	number of plates
5	$v (t, K) = t n t m (1 + K / β)$	Equation （9）^*
6	$f (t, K) = 1 1 + K C 0 1 2 π n (v (t, K) n) n ⋅ e n - v (t, K)$	Equation （4）^*
7	$f (t, 3)$	simulating profile of $K = 3$
8	$f (t, 1.8)$	simulating profile of $K = 1.8$

Table 2 Procedures of operation for simulated chromatographic elution profiles of dual-component sample （K=3 and 1.8） by GeoGebra

Line No.	Input	Comment
1	$C 0$ = 1	initial concentration of component A
2	$t m = 3$	dead time
3	$β = 2$	phase ratio
4	$n = 100$	number of plates
5	$v (t, K) = t n t m (1 + K / β)$	Equation （9）^*
6	$f (t, K) = 1 1 + K C 0 1 2 π n (v (t, K) n) n ⋅ e n - v (t, K)$	Equation （4）^*
7	$f (t, 3)$	simulating profile of $K = 3$
8	$f (t, 1.8)$	simulating profile of $K = 1.8$

Fig. 2 Simulated chromatographic elution profiles of dual-component sample by GeoGebra

Table 3 Procedures of operation for simulated chromatographic elution profiles of five-component sample （K=1，3，5，7，9） by GeoGebra

Line No.	Input	Comment
1	$C 0$ = 1	initial concentration of the sample
2	$t m = 3$	dead time
3	$β = 2$	phase ratio
4	$n = 100$	number of plates
5	$v (t, K) = t n t m (1 + K / β)$	Equation （9）^*
6	$f (t, K) = 1 1 + K C 0 1 2 π n (v (t, K) n) n ⋅ e n - v (t, K)$	Equation （4）^*
7	$f (t, 1)$	simulating profile of $K = 1$
8	$f (t, 3)$	simulating profile of $K = 3$
9	$f (t, 5)$	simulating profile of $K = 5$
10	$f (t, 7)$	simulating profile of $K = 7$
11	$f (t, 9)$	simulating profile of $K = 9$

Table 3 Procedures of operation for simulated chromatographic elution profiles of five-component sample （K=1，3，5，7，9） by GeoGebra

Line No.	Input	Comment
1	$C 0$ = 1	initial concentration of the sample
2	$t m = 3$	dead time
3	$β = 2$	phase ratio
4	$n = 100$	number of plates
5	$v (t, K) = t n t m (1 + K / β)$	Equation （9）^*
6	$f (t, K) = 1 1 + K C 0 1 2 π n (v (t, K) n) n ⋅ e n - v (t, K)$	Equation （4）^*
7	$f (t, 1)$	simulating profile of $K = 1$
8	$f (t, 3)$	simulating profile of $K = 3$
9	$f (t, 5)$	simulating profile of $K = 5$
10	$f (t, 7)$	simulating profile of $K = 7$
11	$f (t, 9)$	simulating profile of $K = 9$

Fig. 3 Simulated chromatographic elution profile of five-component sample by GeoGebra

Table 4 Operational procedures for linear regression analysis between retention time and distribution coefficient with GeoGebra

Line No.	Input	Comment
1	A=（1，4.5）	$K = 1, t = 4.5$
2	B=（3，5，3）	$K = 3, t = 7.5$
3	C=（5，10.5）	$K = 5, t = 10.5$
4	D=（7，13.5）	$K = 7, t = 13.5$
5	E=（9，16.5）	$K = 9, t = 16.5$
6	fitline （｛A，B，C，D，E｝）	conducting linear fitting
7	corresponding coefficient （｛A，B，C，D，E｝）	showing correlation coefficient

Table 4 Operational procedures for linear regression analysis between retention time and distribution coefficient with GeoGebra

Line No.	Input	Comment
1	A=（1，4.5）	$K = 1, t = 4.5$
2	B=（3，5，3）	$K = 3, t = 7.5$
3	C=（5，10.5）	$K = 5, t = 10.5$
4	D=（7，13.5）	$K = 7, t = 13.5$
5	E=（9，16.5）	$K = 9, t = 16.5$
6	fitline （｛A，B，C，D，E｝）	conducting linear fitting
7	corresponding coefficient （｛A，B，C，D，E｝）	showing correlation coefficient

Fig. 4 （a） Interface of GeoGebra calculation cloud platform and （b） its working interface

Fig. 5 Main input contents and simulated chromatographic elution profiles of dual-component sample by GeoGebra

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