The Two Methods of CalculationThere are two distinct ways in which chemistry students in the US are taught to carry out their calculations. One method, which is used quite extensively in the early stages of the introductory courses, is known by three names: the "factor label" method, the "unit conversion" method, or the method of dimensional analysis (DA).The other method, which will be called the method of equations (ME), is used later in the introductory courses to deal with more complex problems such as pH and equilibrium-constant calculations. This method is the traditional method used in physical chemistry, physics, and mathematics. It is also called the method of relations.ME has the following steps.• Identify the quantities involved.• Express the relation between quantities with an equation.• Substitute for quantities.• Solve for the unknowns.
The effectiveness of problem solving as a learning tool is often diminished because students typically use only an algorithmic approach to get to the answer. We discuss a way of encouraging students to reflect on the solution to their problem by requiring them—after they have arrived at their solution—to draw solution maps. A solution map displays a logical analysis of the way one might arrive from the given data to the solution of the problem. The solution map includes a statement of all laws and principles used at every stage, so that students' knowledge base is reinforced. Problems have no unique solution maps, nor can recipes be given and blindly used to create a solution map. Thus drawing solution maps is open-ended, and the chances of students subverting the goal by using memorized routine procedures is avoided.
Differential equations are derived for the molar excess and mean molar quantities of a multicomponent system and are solved by the method of characteristics. The solution enables us to determine directly any molar excess quantity and the corresponding mean molar quantity when the partial molar value of one component is available as a function of composition. It is shown that equations to test the consistency of the experimental results can be derived.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.