Q20.47 P - Chemistry: Molecular Nature Of Matter And Change

Question

(a) Is an endothermic reaction more likely to be spontaneous at higher temperatures or lower temperatures? Explain.

(b) The change depicted below occurs at constant pressure. Explain your answers to each of the following: 

(1) What is the sign of  $\mathbf{\Delta H}$? 

(2) What is the sign of  $\mathbf{\Delta S}$? 

(3) What is the sign of  ${\mathbf{\Delta S}}_{\mathbf{surr}}$? 

(4) How does the sign of $\mathbf{\Delta G}$ vary with temperature?

Step-by-Step Solution

Answer

(a)  At higher temperatures, an endothermic reaction is more likely to be spontaneous.

(b)  The signs for $\mathrm{\Delta H}, \mathrm{\Delta S}, {\mathrm{\Delta S}}_{\mathrm{surr}}$ are positive, negative, positive respectively and  $\mathrm{\Delta G}$ will be negative at high temperatures.

Step 1: Concept Introduction.

A spontaneous reaction is one in which the energy is released suddenly and the reaction occurs quickly. Entropy is a measure of a system's unpredictability or disorder in general. Entropy is a thermodynamic property that describes how a system behaves in terms of temperature, pressure, entropy, and heat capacity. Gibbs free energy, also known as Gibbs function, Gibbs energy, or free enthalpy, is a term used to measure the greatest amount of work done in a thermodynamic system when temperature and pressure remain constant.

Step 2: Endothermic reaction being spontaneous.

(a)

Note that an endothermic reaction is a reaction that absorbs heat. Therefore, the heat is in the reactant side.

 $\mathrm{heat}+\mathrm{reactant}\rightleftharpoons \mathrm{product}$

According to Le Chatelier's principle, when one chemical species is in excess, it will ruin the equilibrium and will proceed to the reaction where it will be consumed to restore the equilibrium. For an endothermic reaction to proceed spontaneously, the heat should be in excess. 

 

Therefore, an endothermic reaction is more likely spontaneous at higher temperatures.

 

Step 3: Sign of ΔH ,   ΔS ,   ΔS surr ,   ΔG .

(b)

(1) In a particular spontaneous reaction, the entropy of the system decreases. That means that the value for the system decreases. This means that $\text{ΔH}$ is a positive number.

(2) In a particular spontaneous reaction, the entropy of the system diminishes. That means that the value of the system decreases. This means that  ${\text{ΔS}}_{\text{sys}}$ is a negative number.

(3) It is known that  ${\text{ΔS}}_{\text{univ}}$ is equal to ${\text{ΔS}}_{\text{sys}}$ plus  ${\text{ΔS}}_{\text{surr}}$ and the whole thing here is the spontaneous process. So, ${\text{ΔS}}_{\text{univ}}$should be a positive number. And from the previous thing, it is known, that as is a negative number.

So, in order to make this sum a positive number, must be a positive number and also a greater magnitude, then .

(4) In a particular spontaneous reaction, the entropy of the system decreases. That means that the value of the system decreases. At high temperatures, $\text{ΔG}$ will be negative. 

 

Therefore, the signs are obtained.