Mathematically Modeling Dilution (original) (raw)
Related papers
Understanding Mental Models of Dilution in Thai Students
2009
The purpose of this study was to investigate Thai students' understanding of dilution and related concepts. The literature suggests that a complete understanding of chemistry concepts such as dilution entails understanding of and the ability to integrate mental models across three levels of representation: the macroscopic, sub-microscopic and symbolic. In this work students' understanding was probed using the interview about events (IAE) approach employing open-ended questions, and also by analysis of student descriptions, and drawings. The research findings suggest that all students were able to answer openended questions related to dilution and related concepts. Less able students presented representations at the symbolic level and subsequently described events at the submicroscopic and macroscopic levels. However, these latter representations typically were unrelated to the representations presented at the symbolic level. In contrast, more able students were able to present consistent representations of dilution at each level of representation.
Microorganisms are often counted in the laboratory using such methods as the viable plate count where a dilution of a sample is plated onto (or into) an agar medium. After incubation, plates with 30-300 colonies per standard-sized plate are counted. This number of colonies (30-300) was chosen because the number counted is high enough to have statistical accuracy, yet low enough to avoid nutrient competition among the developing colonies. Each of the colonies is presumed to have arisen from only one cell, although this may not be true if pairs, chains, or groups of cells are not completely broken apart before plating. It is possible, but unlikely, for an original (undiluted) sample of microorganisms which is to be counted to have 30-300 cells/ml so that a pour plate using a 1 ml volume from the sample will give good results. More likely, a sample will have greater numbers of cells/ml; sometimes, as in the case of unpolluted water samples, the sample will have less. In either case, the sample must be manipulated so that it contains a number of cells in the correct range for plating. If the cell number is high, the sample is diluted; if too low, the sample is concentrated. Dilutions are performed by careful, aseptic pipetting of a known volume of sample into a known volume of a sterile buffer, water, or saline . This is mixed well and can be used for plating and/or further dilutions. If the number of cells/ml is unknown, then a range of dilutions are usually prepared and plated.
Difficulties of novice students in solving the final concentration value of a mixture of solutions
Chemistry Teacher International
In this paper, we investigated and classified the answers of college freshmen when asked about “the final concentration value of a mixture of solutions ”. Prior to the explanation of the topic in class, a diagnostic questionnaire on “solutions” was presented to 532 first year students in the chemistry course at the University of Buenos Aires. The questionnaire consisted of three questions assessing the same concept: the calculation of the final concentration of a solution obtained mixing a concentrated and a dilute solution of the same solute. The format of the three questions was multiple choice answer with justification, but they differed in their chemical language style: chemical formulas, verbal-procedural, and visual languages were used. It was noted a trend to apply mathematical calculations, when chemical problems are addressed, even when such calculations are not necessary. Thus, obtaining a numerical result would be considered appropriate by the students, with no analysis o...
Mathematical Treatment to Understanding the Concentration Terms
https://www.ijrrjournal.com/IJRR\_Vol.6\_Issue.1\_Jan2019/Abstract\_IJRR0026.html, 2019
Concentration of solutions issues are among the foremost necessary and at that time one amongst the foremost difficult topics in general chemistry. The aim of this study is to work out the concentration of the solutions in the mole concept and stoichiometry that students typically performing the calculations associated with concentration such as molarity, normality etc. The study concerned school and under graduate students have learned the ideas of mole and concentration of solutions before the study. Mastery of the mole concept thought is foundational to understanding concentration of solutions. Specifically, students faced difficulties understanding the utilization. In this paper the scarcity of simple mathematical treatment to understanding the preparation of a concentration solutions viz. Molar, Normal etc. thought seemed to lead students to suppose the utilization of the simple mathematical formulae and steps to resolve the queries.
2011
Share feedback about the accessibility of this item. This is the publisher's version of the work. This publication appears in Gettysburg College's institutional repository by permission of the copyright owner for personal use, not for redistribution. Cupola permanent link:
The Chemical Educator
In this study we report that students as well as teachers inappropriately transfer what they have learned in their study of gaseous equilibrium systems to aqueous equilibrium solutions. Adding water to aqueous equilibria is viewed as: (a) similar to the case involving the addition of solids in heterogeneous equilibria; (b) the addition of one reactant. Those explanations do not consider the increased volume of the solution. Also, the molar concentration concept is not appropriately transferred to the context of aqueous chemical equilibria. Both students and teachers often think that changes in the amount of aqueous equilibrium solutions mean an addition of one of the reactants only. It is concluded that those misconceptions may be derived from the application of simple associative rules that consist of mechanical, algorithmic and limited statements. In addition, a poor representation of the problem, which often reduces the factors to be considered, may be behind the reported misconc...
Dilution and Concentration of Pharmaceutical Solutions and Other Physical Mixtures
Pharmaceutical Calculations, 2019
This chapter is essentially divided in two parts, that is, dilutions in drug compounding and dilutions in drug analysis, which are more useful to individuals engaged in research projects and laboratory work. The concept of dilution is first explained using a mass balance equation that was generated based on the fact that the mass of a substance is preserved during dilution processes implicated in compounded drug preparations. This same equation is then used to calculate the concentration of drugs in pharmaceutical products prepared by diluting a known amount of drug with other excipients or to calculate concentration of drugs in patient’s dose. The concept of the dilution factor is introduced to cope with problems that deal with the construction of calibration curves for quantitative drug analysis in dosage forms and biological fluids. In the second part of the chapter, it is made clear that dilution is usually made by reducing the mass of the drug present in the original stock solu...
Modification of the Basic Dilution Equation for the Programming of Serial Dilutions
2021
Stock solutions made with accurately weighable quantities of biologically active compounds often do not result in physically measurable delivery volumes, delivered to cell cultures, assay buffers etc., consequently requiring delineation of the serial dilution steps of the stock solution in a case by case manner. The basic dilution equation (C1V1 = C2V2) alone is not amenable for the programming and computerization of the serial dilutions. The best solution to this dilemma is to develop an equation with the delivery volume as one of the variables. We present here a modified dilution equation (MDA) that has the delivered volume as one of the variables. We demonstrate with examples how the equation can be used in delineating serial dilution steps either manually or through programming. The equation is D = C1p/C2V2, where D is the fold dilution required of a stock solution of C1 concentration which is diluted and delivered (pipetted) at a volume p to cell culture media, assay mixture et...
Chem. Educ. Res. Pract., 2012
This paper reports on students' understanding of sugar concentration in aqueous solutions presented in two different modes: a visual submicroscopic mode for particles and a verbal mode referring to macroscopic amounts of sugar. One hundred and forty-five tertiary college students studying some form of first-year chemistry participated in the study. For problems of a similar nature, students were much more successful in solving solution concentration problems that were presented verbally than were presented using a submicroscopic representation of particles. The implications of this for chemistry education are outlined in the paper. One contributing factor to the poor success rate with submicroscopic representations (SMR) was possibly the fact that the SMR were presented in multiple-choice format whereas the verbal representations required a short-answer response. While the multiple-choice format may prove deceptive, on account of the way students interpret alternatives containing visual images, students agreed it also proved instructive in highlighting the importance of accounting for volume change in concentration calculations.