13 Entropy and Free Energy

13 Entropy and Free Energy - 13. Entropy and Free Energy...

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© David Hanson, Stony Brook University, 2008 Reproduction or distribution by any means is prohibited by law. 1 13. Entropy and Free Energy 13.1. Spontaneous Reactions Some chemical reactions are spontaneous, others are not. Spontaneous means resulting from a natural inclination, arising from a momentary impulse, or occurring without any apparent external cause. For example, if you mix baking soda (sodium hydrogen carbonate) and vinegar (acetic acid) together, carbon dioxide gas will be produced spontaneously. (Try this at home!) Similarly, a mixture of hydrogen and oxygen gases will explode spontaneously if it is ignited by a tiny spark. (Don’t try this at home!) In contrast, even a bolt of lightening will not cause a mixture of nitrogen and oxygen gases (air) to explode like a mixture of hydrogen and oxygen does! Sometimes a spontaneous reaction is called product-favored, and a reaction that is not spontaneous is called reactant-favored. The key to understanding why some reactions are spontaneous and others are not is the concept of entropy . 13.2. What is entropy? The basic idea is that changes or chemical reactions are spontaneous if they produce a more probable situation. The most probable situation is the one that has the largest number of states accessible to it. For example, consider the books on your bookshelf as a system. At the beginning of the semester, you may line up all your books alphabetically with the bindings facing outward and the titles on the binding facing left. There is only one possible arrangement or state like this for your books. As the semester progresses, you use your books and replace them on the shelf without exercising any special care. A large number of different arrangements or states now are accessible, and your books will end up in one of those. They no longer will be in alphabetical order, and bindings will be facing in different directions. Preserving the initial state throughout the semester is just not very probable. Entropy is a measure of the number of states accessible to a system. So the entropy of your books increased during the semester, and it would have required work on your part to prevent this increase from happening. The number of states accessible to a system of atoms and molecules is determined by the way energy is distributed or dispersed over the atoms and molecules. A greater dispersal of energy produces a larger number of accessible states and a more probable situation. Spontaneous chemical reactions or spontaneous changes in general increase the dispersal of energy, resulting in a larger number of accessible states and a more probable situation. For example, consider how 2 quanta (units) of energy can be dispersed over 10 atoms. If both quanta are used to excite a single atom, there are only 10 states available, which correspond to the 10 different atoms. However, if the energy is dispersed and only
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13 Entropy and Free Energy - 13. Entropy and Free Energy...

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