Question

Predict the sign of $\mathbf{∆}{\mathbf{S}}_{\mathbf{surr}}$ for the following processes.

1. ${\mathbf{H}}_{\mathbf{2}}\mathbf{O}\mathbf{}\left(I\right)\mathbf{\to }{\mathbf{H}}_{\mathbf{2}}\mathbf{O}\mathbf{}\left(g\right)$
2. ${\mathbf{I}}_{\mathbf{2}}\mathbf{}\left(g\right)\mathbf{}\mathbf{\to }{\mathbf{I}}_{\mathbf{2}}\mathbf{}\left(s\right)$

Short answer

Answer

1. The sign of$\mathbf{∆}{\mathbf{S}}_{\mathbf{surr}}$for the${\mathrm{H}}_2\mathrm{O}\left(\mathrm{I}\right)\to {\mathrm{H}}_2\mathrm{O}\left(\mathrm{g}\right)$ process is negative.
2. The sign of$\mathbf{∆}{\mathbf{S}}_{\mathbf{surr}}$for the${\mathrm{I}}_2\left(\mathrm{g}\right)\to {\mathrm{I}}_2\left(\mathrm{s}\right)$process is positive.

Step-by-step solution

Step 1: Introduction to the Concept

Entropyis a characteristic of a system that quantifies the unpredictability or degree of chaos. It's a state function,after all. With an increase in the universe's entropy, spontaneous change occurs.

$\mathbf{∆}{\mathbf{S}}_{\mathbf{univ}}\mathbf{=}\mathbf{∆}{\mathbf{S}}_{\mathbf{sys}}\mathbf{+}\mathbf{∆}{\mathbf{S}}_{\mathbf{surr}}------\left(1\right)$

The entropy change of the system and its surroundings equal to the entropy change of the cosmos.

The following is the relationship betweenentropy change and enthalpy changefor the surrounding:

$\mathbf{∆}{\mathbf{S}}_{\mathbf{surr}}\mathbf{=}{}_{\mathbf{‐}}\mathbf{∆}\mathbf{H}\mathbf{/}\mathbf{T}-----\left(2\right)$

$\begin{array}{rcl}∆{\mathrm{S}}_{\mathrm{surr}}& =& \mathrm{Entropy}\mathrm{change}\mathrm{of}\mathrm{the}\mathrm{environment}\\ ∆\mathrm{H}& =& \mathrm{Enthalpy}\mathrm{change}\\ \mathrm{T}& =& \mathrm{Temperature}\end{array}$

Step 2: Solution Explanation

a)

From the given reaction,

${\mathrm{H}}_2\mathrm{O}\left(\mathrm{I}\right)\to {\mathrm{H}}_2\mathrm{O}\left(\mathrm{g}\right)$

This is the vaporization of water in which the system absorbs heat from the environmentto make the phase shift from liquid to gaseous. This is an endothermic reactionwith a positive $∆\mathrm{H}$level. As a result, $\mathbf{∆}{\mathbf{S}}_{\mathbf{surr}}$would be negative, according to equation (2).

Step 3: Solution Explanation

b)

From the given reaction,

${\mathrm{I}}_2\left(\mathrm{g}\right)\to {\mathrm{I}}_2\left(\mathrm{s}\right)$

The de-sublimation or deposition of iodine gas into a solidis represented by this given reaction. The system releases heatto the environment in this process, which is an exothermic reaction with a negative $∆\mathrm{H}$. As a result, $\mathbf{∆}{\mathbf{S}}_{\mathbf{surr}}$should be positive, according to equation (2).