Are all exothermic reactions spontaneous?


> 
> $\ce{GaAs (s)}$ is used in solar cells deployed on satellites found in the orbit of Earth. The best way to make these materials is through a technique called "molecular beam epitaxy", in which the following spontaneous chemical reaction takes place:
> $$\ce{Ga(g) + As(g) -> GaAs(s)}$$
> Pick the statement which best describes this process:
> 
> 
> (A) The process is endothermic.  
> 
> (B) The process is exothermic.  
> 
> (C) The process leads to a decrease in the entropy of the universe.  
> 
> (D) The process leads to an increase in the entropy of the system.  
> 
> (E) The process leads to a decrease in the temperature of the system.
> 
> 
> 


The key says the correct answer is B. I am wondering if this is because all exothermic reactions are spontaneous?




No, it is not the case that all exothermic reactions are spontaneous. More generally, it doesn't even make sense to make a broad statement that a reaction is or is not spontaneous without also specifying the concentrations of reactants and products, since for a certain relative concentration of reactants and products, the reaction might be spontaneous in the forward direction, while for another set of relative concentrations it might be spontaneous in the reverse direction. [See illustration below.]


One could, however, make the general statement that chemicals will react spontaneously if, in so doing, the entropy of the universe increases. This, however, is not one of the options you are given.


Why, then, is "B" the correct choice? Answer: It's because this Ga and As are forming a chemical bond, and bond formation is exothermic. In addition, there is a phase change here from a gas to a solid, and that is also exothermic. Furthermore, since Ga and As are both monatomic gases in this reaction, no chemical bonds need to be broken to allow the Ga and As to combine. Thus, since we have chemical bonds being formed but not broken, and a phase change from gas to solid, the reaction is exothermic.


Here's a graphical illustration of the general concept articulated in the first paragraph:


[![enter image description here](https://i.stack.imgur.com/AxnHo.png)](https://i.stack.imgur.com/AxnHo.png)


 6

**The entropy of the system decreases**


All the reactants are mono-atomic gases, and the product is a solid. This is a strong indication that the entropy of the system decreases.


**The reaction is spontaneous**


That statement from the text of the question means that the Gibbs energy of reaction is negative. It is not clear if this refers to standard conditions, or to the current conditions. The question could be more specific in that regard.


**Enthalpy of reaction**


If the reaction entropy is negative and the reaction Gibbs energy is negative, the reaction enthalpy has to be negative as well because it is the sum of the Gibbs energy and the entropy times the (positive) temperature.


$$\Delta\_r G = \Delta\_r H - T \Delta\_r S$$


$$\Delta\_r H = \Delta\_r G + T \Delta\_r S$$



> 
> Are all exothermic reactions spontaneous?
> 
> 
> 


No, but all reactions that are spontaneous at standard state (interpreted to mean that at standard state, equilibrium lies in the forward direction, i.e. K > 1 and $\Delta\_r G^\circ < 0$) are either exothermic ($\Delta\_r H^\circ < 0$) or show a positive standard entropy of reaction ($\Delta\_r S^\circ > 0$), or both. This ensures that the Gibbs energy of reaction is negative and that the entropy of the universe increases (those two are linked in the absence of non-PV work).



> 
> [theorist] The direction of spontaneity is merely a function of where the reaction mixture is relative to the equilibrium constant. 
> 
> 
> 


The argument I made above does not preclude finding a reaction with positive $\Delta\_r H^\circ$ and negative $\Delta\_r S^\circ$ that goes forward. In this case, K will be smaller 1, but reaction conditions can be chosen so that Q is smaller than 1 as well, and furthermore smaller than K, which is always possible by increasing reactant concentrations or by removing product. 



> 
> [Textbook question]Pick the answer that best describes this process.
> 
> 
> 


Answers A) and E) are linked. An endothermic process (A) will decrease the temperature of the system (E). So those two answers are out if there is only one correct answer. Answer C) goes against the second law of thermodynamics, so most teachers would mark it wrong. Above, I made an argument that the reaction has a negative standard entropy of reaction (less freedom for the atoms when they go from mono-atomic gas to a solid compounds); answer D) posits the opposite, so it is out. 


 5

I would add that, given that the entropy change associated with the formation of the solid is almost certainly negative, the only way the reaction can proceed spontaneously at constant T and p is if it is exothermic, invoking the condition that $\Delta G = \Delta H - T \Delta S<0$ or $$\frac{\Delta H}{T} <\Delta S$$ for a spontaneous process. 


That the process *is* exothermic can be justified using the arguments presented by theorist.


 0

A exothermic reaction has the energy to proceed spontaneously. It may or may not depending on the kinetics. The reaction could be sterically hindered for example, and need a catalyst to happen at all. 


 -2