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Thermodynamics Formulas Chemistry

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The description of Thermodynamics Formulas Chemistry

Here is an example. Trinitrotoluene (TNT) can explode (a rapid chemical reaction). From the chemical formula it has three nitrogen bonds. Most chemical explosives contain nitrogen by the way. 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) âH = -3,400 kJmol-1

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

C12H22O11(s) + 12 O2(g) à12 CO2(g) + 11 H2O(l) âH = -5,644 kJ mol-1

Sucrose produces a lot more energy per mole that TNT! So why is not sucrose an explosive too? Sucrose burns slowly relative to TNT, with a corresponding slow release of carbon dioxide. TNT burns so fast that a lot of energy is released in a short period of time. Furthermore, solid TNT occupies a small volume, but the final volume is equal to 11 moles of gas (about 250 liters at STP). The destruction is not caused so much by the heat released but 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 to the surroundings as the gas expands, and this can cause damage.

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

Thermodynamics tells us which chemical reactions will proceed and which will not. Chemical Kinetics tells us how fast those reactions take place, and how much energy is needed to initiate a reaction. TNT is not very sensitive to shock because it has a high activation energy. On the other hand, Nitroglycerine, (NG), another chemical explosive (with lots of 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 nitroglycerine problem by inventing dynamite: reducing the sensitivity to shock by soaking NG in sawdust, paper or some absorptive material. The patent was so successful that he left us the legacy of the Nobel Prize.

Equilibrium thermodynamics is a closed field today with no new fundamental 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 fails to explain why these relationships exist. This is given by another elegant theory called Statistical Mechanics.
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