How About Booger Problems in Reaction Stoichiometry

[David Cameron]

TL;DR

The more difficult type of problem, the "Booger problem," is best at exercising logical thinking by the student in solving the problem.

I have taught introductory general chemistry to engineering majors for over 30 years. Upon one occasion, a student told me "I sort of like the homework ... except the booger problems that I can't do." But it is exactly those problems, the more difficult type of problems, that give the student the best problem solving exercise to prepare for quizzes and tests. I have developed a special tool for working out booger problems in reaction stoichiometry. I call this tool the "arrow diagram method." The method is described at www.jimetherdrift2013.net/arrowdiagram.html. The method is very helpful in solving "booger problems" like the following:

NH3 (g) + 5 O2(g) = 4 NO (g) + H2O (l)

When 42 grams of ammonia are reacted with 60 grams of oxygen in a closed container, the final mixture of gases in the container is 42.0 % NO(g) by mass. What is the percent yield of the reaction? ( = 69.1 %)

The arrow diagram solution to this problem, and a couple of similar problems, are posted at www.jimetherdrift2013.net/arrowdiagram.html.

 

[mjc123]

So how does this differ from the conventional ICE table method?

 

[David Cameron]

The arrow diagram is very much like the conventional ICE Table. Sometimes, however, the ICE Table uses "mole ratio" to express moles formed or moles used, and the arrow diagram never uses anything like the "mole ratio." The arrow diagram is a little more "dramatic" with the reaction as a PROCESS, using arrows to represent molar changes for reactants and products. Students are most surprised when a reaction has to proceed in the reverse direction to establish equilibrium, so the arrows go down on the right side of the reaction, and up on the left side.

 

[DrDu]

I think in physics we have good reasons to introduce concepts like "mass m", "pressure P", "volume V" and "amount of substance n" and to distinguish them clearly from their units. Hence my question: why do you start out with an equation for P but then instead of n, use "moles of xy"?

 

[David Cameron]

I hope this will answer your question. With no temperature or container volume given in the initial problem, there is no way to do calculations with the Ideal Gas Law. Logic, not PV = nRT, is the key to solving this kind of problem. One of the key ideas in solving this problem is that chemical reactions never change TOTAL grams. So with three gases and one liquid in the container at equilibrium, the total grams of gas must be 102 minus the grams of liquid water formed, and 42% of these grams of gas must be grams of NO (g) formed by the reaction. With unit conversion factors in place

(4X mole NO formed)(30 g NO/1 mole NO) = 0.42 (102 grams - (6Xmole H2O formed (18 g H2O/1 mole H2O)))

Solving this equation gives X(actual) = 0.2591. Moles of NO (g) or of H2O (l) actually formed can then be calculated using the value of X(actual) and the percent yield can be calculated as the ratio of actual moles
NO (g) formed over theoretical yield in moles of NO (g) (1.0364/1.500) or actual moles of H2O (l) formed over theoretical yield of H2O (l) in moles (1.5546/2.250) = 69.1%

A complete solution using the "arrow diagram" is posted at www.jimetherdrift2013.net/arrowdiagram.html

 

[DrDu]

So what you call $x$ seems to be what is usually called the "extent of reaction" $\xi=(n_i-n_i^0)/\nu_i$?

 

[David Cameron]

Yes, X(actual), calculated from a measurement given in the problem, IS the extent of reaction. The value of
X(actual) is useful for many things ... such as to calculate actual amount of heat evolved by an exothermic reaction. Students learn reasonably well to set up a logical equation for the calculation of X(actual) from a measured value (like gas pressure or volume of gas), then use the value of X(actual) to answer the question asked in the problem.