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The Chemical Educator

ISSN: 1430-4171 (electronic version)

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Abstract Volume 8 Issue 5 (2003) pp 295-297

Weak Electrolytes: When Should We Solve the Quadratic Equation?

Yuanjian Deng

Department of Chemistry, Texas Southern University, Houston, Texas 77004, deng_yj@tsu.edu
Received June 2, 2003. Accepted August 12, 2003.

Published online: 27 August 2003

Abstract. The so-called “5% rule” is introduced in freshman chemistry when calculations of equilibrium concentrations for a weak electrolyte are involved. In particular, this rule is widely used for the calculation of concentrations of hydrogen ions for a weak acid and hydroxide ions for a weak base. The application of this rule involves two steps: (1) calculating the hydrogen ion concentration using the simplified formula, and (2) computing the ratio of the calculated hydrogen ion concentration to the nominal concentration of the weak acid. If the ratio is greater than 5%, the quadratic formula should be used to obtain the correct concentration of hydrogen ion. In this article, a simpler criterion based on the ratio of the initial concentration of the weak acid to the acid dissociation constant has been developed to help students decide when to solve the quadratic equation. The reason why this ratio is chosen is that it is related to the percent ionization. We have found that when this ratio, initial concentration/equilibrium constant, is equal to or greater than 400, the simplified equation will be satisfactory; otherwise, the original quadratic equation should be solved using the quadratic formula.

Key Words:  In the Classroom; general chemistry; math

(*) Corresponding author. (E-mail: deng_yj@tsu.edu)

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Issue date: October 1, 2003

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