Approximate Relations in pH Calculations for Aqueous Solutions of Extremely Weak Acids: A Topic for Problem-Based Learning

Abstract

This paper describes the implementation of problem-based learning in chemical education with regard to the impact that protolytic reactions have on equilibria. The problem-based task presented here is focused on extremely weak acids and calcuation of the pH value of their aqueous solutions. The task is based on comparisons of K a ranges over which calculations using the universal cubic equation, quadratic equation with a nonlinear term, and the simplest equation for pH calculation (pH = −log[H + ]) are each valid. Our students observed that an extremely weak acid can be defined as an acid with a pK a greater than 8.13, with a relative error of 0.005 pH units, or 7.89, with a relative error of 0.01 pH units. Under these conditions, the quadratic equation without linear term serves as a universal formula. Students then solved a criterial equation using a quadratic equation without a linear term and the simplest formula to estimate the critical concentration, which is dependent on the pK a value. Below this concentration, the simplest formula cannot be used. During practical applications, students observed that the critical concentration for hydrogen peroxide is very high (0.193 mol L −1 ) and that the pH of its aqueous solution should be calculated according to a quadratic equation without a linear term in most of the practical examples. When traditional educational methods were used, students were unable to solve this problem properly, so we searched for a new way to solve this task. Taking into account the principles of problem-based learning, we designed a didactic cycle (as represented by a flowchart) for solving the above-mentioned problem. In this cycle, learning was aimed at the students, and the teacher only served as a facilitator. In this situation, the students' own work, research, and discovery were highlighted, together with the development of their chemical, mathematical, and IT skills.

Introducing Iterative Methods to Undergraduate Chemistry Students—A Spreadsheet-Based Approach

“…The exact calculation of the pH of an aqueous solution of a weak monoprotic acid has to consider the two simultaneous and interlinked chemical equilibria, namely, the acid dissociation and the autoprotolysis of water. The rigorous mathematical treatment, taking charge balance and mass balance into account (see Supporting Information), results in the general polynomial equation: where K a is the acid dissociation constant, K w is the ion-product of water and a is the acid concentration. , …”

“…where K a is the acid dissociation constant, K w is the ion-product of water and a is the acid concentration. 12,13 Although the cubic eq 4 can be solved analytically, the process is rather cumbersome. Therefore, depending on the concentration and strength of the weak acid, different approximate formulas are often used, the mathematical expressions of which are presented in the Quick Guide to Exercises of the Supporting Information and in Figure 1.…”

Turning around Cycles: An Approach Based on Selected Problems/Cases to Stimulate Collaborative Learning about Krebs and His Four Metabolic Cycles

“… 10 − 13 Herein we will use the term PBL in its “weak” meaning, that is, learning based in the resolution of problems and cases, as it has been frequently used in articles published in journals of science education, including the Journal of Chemical Education . 14 − 21 The active learning strategy presented in this manuscript was established by proposing a numerous and varied set of guided tasks, differing from the traditional PBL approach, in which a “problem” is presented for students to solve. The design, implementation, and evaluation of this teaching resource has been monitored through the use of an educational research methodology named Design-Based Research (DBR).…”

Recenzovaný sborník příspěvků Interdisciplinární mezinárodní vědecké konference doktorandů a odborných asistentů QUAERE 2022

“…V prípade slabých kyselín je odvodenie kritérií použitia aproximatívnych vzťahov zložitejšie ako u silných kyselín, nakoľko kritická koncentrácia závisí okrem chyby aj od sily príslušnej slabej kyseliny, vyjadrenej disociačnou konštantou. Navyše sa treba rozhodovať medzi štyrmi vzťahmi (rovnice 1-4), ktorými je rovnovážna koncentrácia vodíkových iónov určená (Bellová, 2018b).…”