Many years ago, as a faculty member in a physical science department at a private university, I attended a seminar presented by another faculty member. The presenter suggested that the fundamental ideas of quantum theory should be presented to students earlier in their academic programs to "brainwash" (his actual word!) them into believing the ideas more readily. The objective of this effort would be to enable the brainwashed students to be more capable of doing the complex calculations required in a later course in quantum mechanics.
Woah!! Hold on a minute! Is that what teaching is supposed to be about? To brainwash (!) students into being clones of us teachers? For me, teaching is far different. For me, teaching could never be called "brainwashing". In my opinion, teachers should first help students learn all they can about the observable facts applicable to a given topic. Then students should learn the set of ideas scientists use to explain the observable facts. But if a student has well-considered doubts about the actual truth of some of the ideas, those doubts should be left intact. It is these doubts that might lead an educated student, especially a "great spirit" educated student, to obtain "proof" that some currently accepted idea is not actually true. This kind of doubt and disproof is how science grows. Without growth, there is no healthy, real science. Without growth, there is only a sort of quasi-religious, believed scientific dogma.
I have taught general chemistry. Upon one occassion, a student (a great spirit thinker, by the way!) commented to me that "I sort of like the homework ... except the booger problems I can't do." But it is exactly these problems, the booger problems, that most challenge and encourage students to use their own logical thinking. As an example of this sort of problem, with calculations being based on a measured true fact rather than on the erroneously assumed total consumption of the limiting reagent, consider the following problem:
Formulas for ideal gases are then used to convert the relationship for pressures into a relationship for moles of gas:
The gas constant, the temperature, and the volume all cancel out, leaving only moles of gas:
final mole N2= 1.30 ( final mole NH3+final mole NO )
This last equation is especially well suited to the use of the arrow diagram. In its general form, the preliminary arrow diagram for the given reaction would be set up as follows:
With all values in moles, the amount of each substance initially present is placed at the initial end of each arrow (Note: It is not always true that the initial amount of a given reaction product is zero moles.) Changes (in moles used for reactants and moles formed for products) are placed in the middle of each arrow. And moles present in the final reaction mixture (i.e., at chemical equilibrium) is placed at the terminal end of each arrow. The problem gives the grams of gas put in at the start of the reaction, with only the water vapor being not put in. The grams are converted to moles by conventional unit conversions, and the next set up for of the arrow diagram looks like the following:
The fundamental need to answer any question about a reaction is to calculate the value of "x" as a number in the arrow diagram, then use that value to answer the particular question asked. The relationship for final moles is given by the logical equation developed previously, so using terms from the arrow diagram:
( 0.8929 + 5x ) final moles N2 = 1.30 [ (1.294 - 4x) mole NH3 + (1.167 - 6x) mole NO ]
Solving this equation,x = 0.1281 with no unit, as the value of "x" applies to the reaction as a whole.
The value of "x", once known, should be used in the most direct way possible to answer the question asked in a particular problem. There is no real need to complete the arrow diagram with all numbers in place, but if done, the completed arrow diagram would look like the following:
Conventional unit conversions, using values from the numerically complete arrow diagram, would now be able to answer any given question about the reaction and the changes the reaction causes.
There are various ways to calculate the percent yield of the reaction to answer the question, but the simplest way would probably be to use the value of "x" calculated from the given fact about final partial pressures (this value being "xact" since it corresponds to the actual extent of the reaction) and the value represented as "x100" (this value representing what "x" would be to cause total consumption of the limiting reagent). The value of "x100" can usually be calculated by simply dividing the initial moles of each reactant by its stoichiometric coefficient in the reaction:
Then calculating the percent yield of the reaction:
This is the type of problem that best challenges the student to use his/her own logical thinking in solving the problem. The use of the arrow diagram helps many students in solving such problems with their owm logic.