# How To Begin The Second Year Of Implementing Eureka Math Chemistry and Thermodynamics

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## Chemistry and Thermodynamics

Lost in the forest of science.

The study of science begins for everyone as a small path in the forest of ignorance, but with effort and experience, this path becomes our personal highway of knowledge and information, opening many possibilities. Albert Einstein, like everyone else, started in the woods and proved that it was worth the effort to get out, not just for him, but for all his knowledge that he made for humanity. Science is not for everyone and few Einsteins exist. Unfortunately, many get lost, confused, and frustrated, giving up before they can utter their first “Eureka,” as a gem of knowledge settles in. Those “Eureka” moments can excite us to continue on our own particular path.

So the first step is to be motivated and want to know more.

The next important step is to pay attention to definitions: something that is important in all fields: in sports you need to know the rules to play the game: it is the same for science. Knowing the definitions clears up confusions, and applying them (problem solving) solidifies them. Eventually, the scientific method and thinking become a way of life, and offer insight into many situations, even outside your specialty.

A structure is born. For example, life sciences and medicine are based on biochemistry and pharmacology, which is based on organic chemistry, and organic depends on physical chemistry. Physical chemistry is based on physics, and mathematics is the logic that unites them all.

Along the way there are many sidelines, too numerous to list here: new materials, nanotechnology are two important and well-known disciplines. Also several areas overlap in multidisciplinary fields, such as physical chemistry and organic chemistry (physical-organic chemistry); organic synthesis and chemical kinetics (organocatalysis), inorganic and organic chemistry (organometallic chemistry): the list goes on and on.

Clearly, no one can become an expert in all these areas. However, a good foundation in the fundamentals of physical science allows one to at least be in a position to appreciate the work of others in the many areas of scientific endeavour. You can end up as a lawyer, social worker or in finance. A good scientific background will help the lawyer argue his case for, say, patent infringement; it helps the social worker understand the side effects of medications a client may be taking and allows the financier to make smart decisions about whether to invest in one mining company or another.

On the other hand, you could become a scientist which leads to many interesting careers.

Scientists and engineers

Science can be divided into two broad categories: basic science (research) and application of these ideas (engineering: also called Research and Development (R&D)). Today there are about ten times more engineers than scientists. It takes more effort and more people to take the fundamental ideas developed by a few and turn them into technology we use to improve our quality of life.

Consider the automobile industry. The internal combustion engine, based on the Otto cycle, was developed by a few (who proved it worked), and then many engineers took that basic idea and over the last hundred years developed the cars we have today.

To be a good engineer, you need to start with the basics and learn the basics before you can apply them.

The macroscopic and the microscopic

A broad division of science is the macroscopic (sample large enough to measure and examine) and the microscopic (atoms, molecules, and collections of these, too small to observe individually).

There are two main pillars of macroscopic science: thermodynamics (study of heat, work and efficiency) and classical mechanics (Newtonian physics that describes the movement of macroscopic objects).

The microscopic is governed by quantum mechanics.

Since microscopic particles have a lot of symmetry, the field of group theory (a mathematical subject) should be mentioned. This helps to visualize molecules and reactions, and is of particular relevance in the most fundamental science, which is physics. You don’t have to be a mathematician to use group theory. Mathematics is a tool of scientists: logic guides us.

The field of statistical mechanics relates macroscopic objects to their microscopic particles.

The example of chemistry

Chemistry is the study of the making and breaking of bonds, meaning that chemicals react to form different chemical products. A chemical reaction takes place if the conditions are right: two important conditions are energy and entropy. Both are substances and entropy is tangible like energy. How did this come about?

Engineers started noticing things a couple of hundred years ago: like horses walking in circles and driving machinery to drill cannons. Horses walked at a constant pace, (constant energy), but a dull bit produced a lot of heat and not much work (boring the barrel was slow), but a sharp bit produced much less heat and was more boring. This is the first law of thermodynamics:

Energy (horsepower) = heat (friction) + work (gun).

Clearly, energy isn’t cheap (horses need to be bought, fed and cared for), so it would be better to reduce heat loss and increase work done. That is, the efficiency of energy use became an important consideration.

In the 19th century, thermodynamics evolved further motivated by the need to increase the efficiency of the steam engine that drove the industrial revolution. The first steam engines were about 3% efficient, so improvements were needed. Adding a second cylinder, for example, made things a lot better, but could they do more? Could the dream of 100% efficiency, i.e. perpetual motion, come true?

This led Sadi Carnot in the 1830s to define a cycle for the steam engine from which entropy was discovered and the Second Law of Thermodynamics was formulated: it was shown that perpetual motion was impossible The Otto cycle was developed for an internal combustion engine about forty years later.

Although alchemy is an ancient subject, it was only after the First and Second Laws of Thermodynamics were developed that chemistry really took off. Many participated in its development. In addition to Sadi Carnot, some notable names are James Maxwell, Rudolf Clausius, James Joule, Willard Gibbs and Ludwig Boltzmann.

The ideas they developed apply well to chemistry. When the bonds are broken, energy must be added to the system; and when bonds are formed, energy is released into the environment. Some chemical reactions produce more randomness (higher entropy) and sometimes more order (lower entropy) as atoms rearrange to form products. Both energy (heat and work) and entropy (randomness) play an important role in the spontaneity of a chemical reaction.

Here is an example. Trinitrotoluene (TNT) can explode (a rapid chemical reaction). The chemical formula has three nitrogen bonds. By the way, most chemical explosives contain nitrogen. The combustion of one mole of TNT releases 3,400 kJ mol-1 of energy,

C7H5N3O6(s) + 21/4 O2(g) à7 CO2(g) + 5/2 H2O(g) + 3/2 N2 (g) âˆ†H = -3,400 kJmol-1

Compare this, however, with the energy of burning sugar as sucrose (a slow chemical reaction),

C12H22O11(s) + 12 O2(g) to 12 CO2(g) + 11 H2O(l) âˆ†H = -5.644 kJ mol-1

Sucrose produces much more energy per mole than TNT! So why isn’t sucrose also an explosive? Sucrose burns slowly relative to TNT, with a correspondingly slow release of carbon dioxide. TNT burns so fast that a lot of energy is released in a short period of time. Also, solid TNT takes up a small volume, but the final volume is equal to 11 moles of gas (about 250 liters at STP). The destruction is caused not so much by the heat released but by the rapid expansion of the gases produced. Using the First Law, the energy released by one mole, (3,400 kJ) goes into some heat, but a lot of work is done on the surroundings as the gas expands, and this can cause damage.

This is where entropy comes in. Notice that the right side of the TNT burn has only 21/4 = 5.25 moles of gas, while the RHS has 11 moles of gas. This means that there is more clutter on the RHS than on the LHS. Clearly, the rapid expansion of the explosive combustion of TNT can lead to destruction (it would throw Humpty Dumpty off his wall) and cause greater disorder, and thus entropy increases. Both energy and entropy are favorable for this reaction to proceed. This is not always the case, especially in biological processes, where entropy, not energy, is the main driving force.

Thermodynamics tells us which chemical reactions will occur and which will not. Chemical kinetics tells us how fast these reactions take place and how much energy is needed to start a reaction. TNT is not very sensitive to shock because it has a high activation energy. On the other hand, nitroglycerin (NG), another chemical explosive (with many nitrogen bonds), explodes with a small shock and cannot be transported in liquid form at room temperature. It has a low activation energy. Alfred Nobel solved the nitroglycerin problem by inventing dynamite: reducing shock sensitivity by soaking NG in sawdust, paper, or some absorbent material. The patent was so successful that it left us with the legacy of the Nobel Prize.

Equilibrium thermodynamics is a closed field today with no fundamental new research being done. It is a beautiful, complete and compact theory that gives the relationship between the macroscopic quantities we can measure: energy, heat capacities, compressibility factors and many more, with wide application.

Thermodynamics is essential knowledge for all chemists. However, thermodynamics does not explain why these relationships exist. This is given by another elegant theory called Statistical Mechanics.

Physical Chemistry covers all of this.

There’s a lot more to say, but that’s a summary. In fact, many say that thermodynamics is not a good name because it describes equilibrium properties, not dynamics. A better name would be thermostatic, but no one calls it that.

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