# Entropy increase of both system and surroundings [closed]

In "why chemical reactions happen" the author (James Keeler) says that "a process which leads to an increase in the entropy of the system can be ... exothermic." Could someone please give me an example of a process which is exothermic and increases the entropy of the system? It seems strange to me how a system can release energy in the form of heat while also increasing its own entropy.

• Could you edit the question to specify which author said the quoted bit, and in which book or article? Could you also edit the question to tell us why you are asking this? – Karsten Theis Jul 29 at 13:49

## 1 Answer

We don't need to go to nuclear fusion to find an example. Lots of chemical reactions meet your criteria of being both exothermic (releasing heat to the surroundings) and increasing the entropy of the system.

A reaction is spontaneous if the free energy change of the reaction is negative ($$\Delta_rG <0)$$.The free energy change of a reaction at constant temperature is equal to the sum of the enthalpy change ($$\Delta_rH$$) and the temperature multiplied by the negative entropy change ($$-T\Delta_rS$$):

$$\Delta_rG = \Delta_rH - T\Delta_rS$$

One way for $$\Delta_rG$$ to be negative is for $$\Delta_rH$$ to be negative and $$\Delta_rS$$ to be positive. In a reaction conducted at constant pressure, the enthalpy change $$\Delta_rH$$ is equal to the heat exchanged between the system (reactants) and the surroundings. When $$\Delta_rH <0$$, the reaction is exothermic.

To find examples that meen your criteria, you only need a source of standard entropy and ethalpy data so that you can calculate $$\Delta_rH$$ and $$\Delta_rS$$ for a reaction. There are many such examples of reactions that are exothermic and have a positive entropy change of the system. Below is a simple example:

$$\ce{C(s) + O2(g) -> CO2(g)}$$

Use the NIST Chemistry Webbook, here are the standard enthalpies of formation and standard entropies of formation for carbon, oxygen, and carbon dioxide:

$$\begin{array}{|l|c|c|} \hline & \Delta_fH^\circ\ \mathrm{(kJ/mol)} & \Delta S^\circ\ \mathrm{J\cdot K/mol} \\ \hline \ce{C(g)} & 0 & 5.8 \\ \ce{O2(g)} & 0 & 205.15 \\ \ce{CO2(g)} & -383.52 & 213.79 \\ \hline \Delta_r & -383.52 & 2.84 \\ \hline \end{array}$$

At all temperatures, this reaction is exothermic and has a positive entropy change for the system.