# Change in entropy of a chemical reaction in vacuum

$$\require{cancel}$$ I'm currently taking Thermodynamics and I've come across a book which claims there are chemical reactions with a negative change in entropy which are spontaneous. Nonetheless, it argues this does not violate the second principle of thermodynamics because said reactions are exothermic and therefore the total increase in entropy of the thermodynamic universe is still positive, as the heat transferred to the system's surroundings heats them up and therefore increases their entropy. Mathematically, this could be written as:

$$\Delta S_U = \Delta S_R + \Delta S_S > 0$$

Where:

• $$\Delta S_U>0$$: Change in entropy of the thermodynamic Universe
• $$\Delta S_R<0$$: Change in etropy of the chemical reaction
• $$\Delta S_S>0$$: Change in entropy of the system's surroundings

However, say we take these chemicals to outer space and mix them there, in total vacuum. In this scenario, there is nothing they could exchange heat with, let alone do work. Therefore, the change in entropy of the chemical reaction (which is negative by hypothesis) would now constitute the total increase in entropy of the thermodynamic Universe, which would now be negative too, thus violating the second principle. Again, mathematically:

$$\Delta S_U = \Delta S_R + \cancel{\Delta S_S} < 0$$

What am I getting wrong? I've drawn a conclusion that goes against the second principle so I know I'm wrong somewhere but I don't exactly know where. Perhaps the chemical reaction would not take place in said vacuum conditions?

• Liquid water will freeze in space. All you need is that H is more negative than TS (G = H-TS). Commented Nov 1, 2023 at 18:47
• Are you, or your books, by any chance ,confuse entropy with enthalpy? Commented Nov 1, 2023 at 18:53
• You haven't accounted for emitted radiative heat, which carries entropy. Commented Nov 1, 2023 at 19:01
• Are you referring to the Standard Entropy of Reaction when you are referring to "entropy change of reaction?" Commented Nov 2, 2023 at 10:44

## 1 Answer

For the given scenario I believe that as there is no medium for heat and sound conduction then the reaction would emit energy in the form of electromagnetic wave which also contribute in increase in entropy abiding the theory of Emission Spectrum and also not violation the 2nd law of Thermodynamics. Also assuming the the reaction occurs in a closed container the change in pressure will compensate for the increase in entropy (or) keeping pressure and temperature constant expansion in the volume by using the gas equation from Kinetic Theory of Gases.

Hope this helps. Do correct me if I'm wrong!