# Why are absolute entropies given the units J mol−1 K−1?

I've just started looking at the concept of entropy and can't understand why absolute (or standard molar entropies) are given the units $\pu{J mol^−1 K^−1}$. Could someone explain the rationale for these units?

• So G = H-TS still works as expected - remember those 'absolute' entropies are specified at a standard temperature, and come in to play in expressions for Gibbs free energies as a function of temperature. – Jon Custer Feb 7 '17 at 18:36
• the OP asked such a basic question that I'm 99.9% sure that the OP has no idea what Gibbs free energy is either. – MaxW Feb 7 '17 at 18:39
• There are a number of formulas for entropy. Perhaps, from a classical thermodynamics standpoint, you have $\mathrm dS = \mathrm dq_\text{rev}/T$ (the Second Law). Heat has units of J and temperature units of K, so entropy itself has units of $\pu{J K^-1}$. Molar entropies then have units of $\pu{J K^-1 mol^-1}$. From a statistical mechanics standpoint, entropy assumes a more fundamental role, but the units are still the same: $S = k_\mathrm{B} \ln W$. As Jon mentioned: absolute entropies are no different from entropy changes, as far as units are concerned. – orthocresol Feb 7 '17 at 18:39
• It is because $T\Delta S$ is a quantity of heat now usually measured in Joules. The 'per mole' part is not fundamental but because it makes sense to standardise measurements. When an isothermal reaction runs reversibly, $T\Delta S$ is the heat absorbed from, or released to, the surroundings, thus the work done may be either greater or less than the heat of reaction. This was first clearly seen by Gibbs and thus the idea of free energy as $G=H-TS$. – porphyrin Feb 7 '17 at 20:59
• – orthocresol Feb 14 '17 at 23:21

The best explanation I can give is that in order to measure entropy for a process we can exploit the fact that it's a state function. Entropy doesn't depend on the pathway that we take. So if you take for example ice melting at 273 K, this process is thermodynamically reversible. At 273 K ice and liquid water are in a state of equilibrium, but if we apply heat we can cause ice to melt. So this allows us to measure $\Delta S$ directly by looking at how much heat we apply to cause this process to proceed. So we look at the amount of heat in joules and compare that to the temperature where we applied the heat.

If you want to think conceptually, think what adding heat will do to the system. We associate adding heat with an increase in entropy. But the magnitude of the change is related to the amount of energy the system currently has (which is directly related to its temperature in kelvin).

Standard entropies of formation are given in molar quantities because they assume the process is taking place to create 1 mole of the substance. Entropy itself is traditionally described with the units of J/K.