Problems with method of teaching rate law

The topic of * chemical reaction rates* and the important rate laws which govern them is a headache topic every year in chemistry classes across the country. The knowledge required to understand reaction kinetics itself is already quite complex, but this is only amplified in complexity by the way the topic is taught. The main fault is that too much focus is put on the memorization of reaction rate equations and graph shapes and too little focus on how we arrive at these equations and how we can interpret these graphs. This article will further discuss the problems with this method of teaching and provide some potential solutions that could go a long way towards making rate laws far more understandable for students.

## The problem with memorizing

Memorization plays a key part in students’ academic careers in almost every subject. In math you must learn and memorize formulas such as Pythagoras’ theorem, in biology you must remember the 4 bases that make up every strand of DNA. These memorizations are essential as there is no real alternative to teaching these concepts other than going over different examples until students are competent at dealing with related problems.

However, every now and then a topic comes up that is inherently difficult to teach, and a quick solution is simply asking students to memorize the equations and steps to answer exam questions without a conceptual understanding. One such topic appears in advance chemistry courses and time and again causes problems for students is chemical kinetics. The kinetics of chemical reactions dictate if they will occur under certain conditions, how fast they will occur and how much product they will produce per unit of reactant. Thus, kinetics are extremely important for small and industrial scale reactions. Despite this, a core principle of kinetics, the rate laws, is taught inadequately in many schools. The concepts involved are very difficult to grasp for new students and due to the teaching methods employed all the student can do is hope that they can remember the equations and what shape 0^{th},1^{st} and 2^{nd} order reaction graphs look like. This is counter effective and we will explain why.

## Calculus integration

The equations given to students in the chemistry exam booklets are what are known as the integrated rate equations. These equations will not be new to the students when they are sitting the exam, they will be solidly memorized in their minds. However, they will most likely not understand how they go from these:

**Rate = k Rate = k[A] Rate = k[A]2**

To these:

**[A] = -kt + [A]**₀

**ln[A] = -kt + ln[A]**₀

**1/[A] = kt + 1/[A]**₀

The mathematics behind these equations is relatively simple calculus, which could be performed by students at a 9th to 12th grade level. Reaction rates measure the rate of change of concentration of reactant or product over time. A key concept within calculus involves establishing rates of change. Thus, it is quite clear to any reader that the gap between the two types of equation above must be filled by some calculus, in this case some simple integration. Students in high school chemistry are not taught this integration, but instead are merely taught that the equations correspond to 0^{th}, 1^{st} and 2^{nd} order reactions respectively, and that each will correspond to a characteristic graph shape when the variable on the left-hand side is plotted against time. This appears to be a missed opportunity for teachers to amalgamate two core subjects, math and chemistry. Countless times every year in every math classroom the question “when will I ever use this in my life?” is asked. The answer to this with respect to calculus is in the chemistry classroom, and in later life potentially in the laboratory. By connecting these two ideas of calculus and chemistry, not only will the concept of reaction rates and rate laws become more tangible to students, but the uses of core mathematical principles will become more relatable and thus more interesting to students.

## The approach

The main advantage of changing the way rate laws are taught is a greater understanding of the subject and thus better exam scores. However, a ** time saving** is also there to be made. By spending even just an additional 20 minutes going over the math behind the equations, a teacher may save countless hours of student misunderstanding and wasted study time trying to memorize concepts instead of learning them. Simple steps can be taken to implement this new method of teaching into a tight curriculum.

Mathematics and chemistry

When the time comes to teach the rate laws, the teacher should go through the basic concepts that govern reaction rates, and then show the class the 3 differential rate laws, explaining which equation corresponds to which order of reaction. The teacher should then take these equations and convey to the class the relationship between concentration and time, by substituting in the d[A]/dt function instead of simply “rate”. From here, the teacher should walk the class through the steps of integration relevant to each order of reaction, before arriving at the integrated forms. This way, the student does not first see the integrated equation without knowledge of how it is obtained, instead they are shown the connection between the two forms. The teacher could show all 3 order equations at once, or they could show one and ask the students to work through the other 2, to really get the ideas cemented in their minds. When these integrated equations are understood, the graphs that are a favorite of the exam board to test this understanding will also become much more readable. The teacher will be able to use examples to show how these graphs are formed and what the data actually represents rather than just a memorable shape. The mathematics does not take an eternity to cover, and less than a full lesson could be devoted to it. However, it will prove invaluable to the students full understanding of the differential and integrated rate laws.

## Conclusion

calculus

A great deal is to be gained from simple adjustments to the teaching curriculum within a small but important part of advance chemistry courses in the high school. This will help students’ understanding of the core concepts of reaction rates, and help them to apply the concepts and approach to answering exam questions. Time can be saved by reducing the amount required to study this part of the course, and teachers’ time will be saved as less questions should arise from students gaining proper understanding of this section. Finally, by showing students how their math class relates to their chemistry class, their minds will be further opened to consider what other links can be made to make their learning experience more efficient and interesting.