![]() The standard molar entropy, S o, is the entropy of 1 mole of a substance in its standard state, at 1 atm of pressure. ![]() The entropy of a substance can be obtained by measuring the heat required to raise the temperature a given amount, using a reversible process. Standard Entropy is defined as the absolute entropy of a substance at 25 C. The standard molar entropy of a substance is the absolute entropy of 1 mole of the substance in the standard state. Finally, substances with strong hydrogen bonds have lower values of S°, which reflects a more ordered structure. At absolute zero (0 K), the entropy of a pure, perfect crystal is zero. For example, compare the S° values for CH 3OH(l) and CH 3CH 2OH(l). Similarly, the absolute entropy of a substance tends to increase with increasing molecular complexity because the number of available microstates increases with molecular complexity. Soft crystalline substances and those with larger atoms tend to have higher entropies because of increased molecular motion and disorder. In contrast, graphite, the softer, less rigid allotrope of carbon, has a higher S° due to more disorder in the crystal. Gases are much more spread out than liquids or solids, so compounds that are gases will have a much higher molar entropy. The biggest influence on the molar entropy is the state of the substance. Among crystalline materials, those with the lowest entropies tend to be rigid crystals composed of small atoms linked by strong, highly directional bonds, such as diamond. Entropy is a measure of disorder, so compounds with higher molar entropy can be thought of as being more disordered. The first thing to do, in preparing to take the thermodynamic limit, is to write V as vN, E as eN, and E as eN so that the only size-dependent variable is N. \( \newcommand\) also reveals that substances with similar molecular structures tend to have similar S° values. Let’s take the thermodynamic limit of expression 2.5.13 (the entropy of a finite system) to find the entropy per particle of an infinite monatomic ideal gas.
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