**ERIC Number:**EJ1195799

**Record Type:**Journal

**Publication Date:**2018-Sep

**Pages:**6

**Abstractor:**As Provided

**ISBN:**N/A

**ISSN:**ISSN-0021-9584

**EISSN:**N/A

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

Bellová, Renata; Melichercíková, Danica; Tomcík, Peter

Journal of Chemical Education, v95 n9 p1548-1553 Sep 2018

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[subscript 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[superscript +]]) are each valid. Our students observed that an extremely weak acid can be defined as an acid with a pK[subscript 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[subscript 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[superscript -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.

Descriptors: Chemistry, Problem Based Learning, Equations (Mathematics), Mathematical Formulas, Problem Solving, Science Education

Division of Chemical Education, Inc. and ACS Publications Division of the American Chemical Society. 1155 Sixteenth Street NW, Washington, DC 20036. Tel: 800-227-5558; Tel: 202-872-4600; e-mail: eic@jce.acs.org; Web site: http://pubs.acs.org/jchemeduc

**Publication Type:**Journal Articles; Reports - Descriptive

**Education Level:**N/A

**Audience:**N/A

**Language:**English

**Sponsor:**N/A

**Authoring Institution:**N/A

**Grant or Contract Numbers:**N/A