Chapter 16, Problem 16.20CP

Ideal gases A (red spheres) and B (blue spheres) occupy two separate bulbs. The contents of both bulbs constitute the initial state of an isolated system. Consider the process that occurs when the stopcock is opened.

(a)    Sketch the final (equilibrium) state of the system.

(b)    What are the signs (+, –, or 0) of ΔH, ΔS, and ΔG for this process? Explain.

(c)    How does this process illustrate the second law of thermodynamics?

(d)    Is the reverse process spontaneous or nonspontaneous? Explain.

Interpretation Introduction

Interpretation:

The final equilibrium state of the system when the stopcock is opened has to be sketched.

Concept Introduction:

A spontaneous process takes place without the influence of any external source whereas a nonspontaneous process needs an external source to take place.

A spontaneous reaction is always moving in such a way that the reaction mixture achieves equilibrium.

Answer to Problem 16.20CP

Explanation of Solution

When the stopcock is opened, a spontaneous reaction is taken place where the gas A and gas B mix with each other until the gases achieve equilibrium.

The final equilibrium state of the system when the stopcock is opened is given below,

Interpretation Introduction

Interpretation:

The signs of $\Delta H$, $\Delta S$ and $\Delta G$ for the process is to be explained.

Concept Introduction:

• Enthalpy$\left(H\right)$: It is the total amount of heat in a particular system.

If the value obtained for $\text{ΔH}$ in a reaction is positive then it is an endothermic reaction whereas the value obtained for $\text{ΔH}$ is negative it is an exothermic reaction.

• Entropy$\left(S\right)$: it is used to describe the disorder. It is the amount of arrangements possible in a system at a particular state.

If the disorder increases in a system, then $\Delta S>0$

If the disorder decreases in a system, then $\Delta S<0$

• Free energy change$\left(\Delta G\right)$: change in the free energy takes place while reactants convert to product.

Spontaneous reactions releases the free energy and has $\Delta G<0$ (exergonic)

Nonspontaneous reactions absorbs the free energy and has $\Delta G>0$ (endergonic)

Answer to Problem 16.20CP

$\Delta H$ is zero, $\Delta S$ is positive and $\Delta G$ is negative

Explanation of Solution

When the stopcock is opened, a spontaneous reaction is taken place where the gas A and gas B mix with each other until the gases achieve equilibrium.

During the mixing of two ideal gases A and B, the heat energy is neither gained nor lost. The heat remains the same Therefore, change in enthalpy $\Delta H$ is zero.

During the mixing of two ideal gases A and B, the gases gets more freedom comparing and thus disorder in gas increases Therefore, the entropy increases and is positive.

The mixing of two ideal gases A and B when the stopcock is opened is a spontaneous reaction. Therefore, the sign of change in free energy $\Delta G$ is negative.

Interpretation Introduction

Interpretation:

Second law of thermodynamics illustrated by the process has to be described.

Concept Introduction:

• Second law of Thermodynamics is stated as follows,

“ In any spontaneous process Entropy of the Universe always increases.”

• Entropy of the universe is referred as total entropy which is the sum of entropy of the system and entropy of surroundings.

$\Delta S_{total}=\Delta {\text{S}}_{sys}+\Delta S_{surr}$

Explanation of Solution

Given that the system is isolated one and hence heat is neither absorbed from the surroundings nor evolved into the surroundings. Thus there is no change in enthalpy that $\Delta H=0\text{ and also }\Delta {\text{S}}_{surr}=0.$ Hence $\Delta S_{total}=\Delta {\text{S}}_{sys}>0$ so the process is spontaneous.

Interpretation Introduction

Interpretation:

The reverse process is whether spontaneous or not has to be described.

Concept Introduction:

• Second law of Thermodynamics is stated as follows,

“ In any spontaneous process Entropy of the Universe always increases.”

• Entropy of the universe is referred as total entropy which is the sum of entropy of the system and entropy of surroundings.

$\Delta S_{total}=\Delta {\text{S}}_{sys}+\Delta S_{surr}$

Explanation of Solution

Given that the system is isolated and in the reverse process, the gas mixture of A and B has to be separate and compressed to the respective bulbs. It requires an external force and the free energy is absorbed.

Here the $\Delta G$ value is positive. Therefore, the reverse process is nonspontaneous