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In the ideal gas, $3R/2$ is the thermodynamic entropy of one Mol. The factor $\frac{3}{2}$ comes from $ST=N\bar{E}=N\frac{3k}{2}T=\frac{3R}{2}T$. The energy of 1 Mol of ideal gas is either given by $3pV/2$ or $3RT/2$ or $ST$. (In the ideal gas) the entropy does not depend on temperature. That is why one writes the $T$ separate in $TS$. For non-ideal gases ...

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Here are two common ways of measuring the entropy change in a reaction: Measure the equilibrium constant $K$ at multiple temperatures. This gives you the Gibbs energy (via $\Delta_r G^\circ = - R T \ln{K}$) and, via the van't Hoff relationship, the enthalpy. You can calculate the entropy from those two. Use microcalorimetry in a titrating mode. You get the ...

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As an interesting bit of history, Boltzmann was the first one to describe entropy as a "measure of disorder" of a system. It's worth noting that he didn't know this was an oversimplification. In reality, entropy is best described as a measure of the number of ways that energy can be distributed in energy levels between or within particles. From this, it's ...

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