Question

Question: (a) Why is the entropy change of the system negative for the reaction in Problem 25, when the ions become dispersed through a large volume of solution? (Hint: Think about the role of the solvent, water.)

(b) Use Appendix D to calculate for the corresponding dissolution of${\mathbf{\text{CaF}}}_{\mathbf{2}}\mathbf{\left(}\mathit{s}\mathbf{\right)}$ . Explain why this value is even more negative than that given in Problem 25 .

Short answer

(a)The minimization of entropy for water will compensate for the increase in entropy from the ions, therefore making the overall change in entropy negative.

(b)The entropy is$∆S\mathit{°}=-149.57{\mathrm{JK}}^{-1}$

Step-by-step solution

Given data

The standard entropy of the given reaction is:
$$\begin{gathered} ∆\mathrm{S}°({\mathrm{CaF}}_2,\mathrm{s})=68.87{\mathrm{JK}}^{-1} \\ ∆\mathrm{S}°({{\mathrm{Ca}}^2}^{+},\mathrm{aq})=-53.1\mathrm{J}{\mathrm{K}}^{-1} \end{gathered}$$

$∆\mathrm{S}°(\mathrm{F},\mathrm{aq})=-13.8{\mathrm{JK}}^{-1}$

Concept of spontaneity

In thermodynamics, a spontaneous process is one that takes place without the addition of matter or electrical energy to the system. In a fully isolated system, a spontaneous process is characterised by an increase in entropy.

(a) Spontanitity of the reaction

The reaction:

${\text{CaCl}}_2\left(s\right)\to {\text{Ca}}^{2+}\left(aq\right)+2{\text{Cl}}^{-}\left(aq\right)$

The reaction is spontaneous even though its entropy change is negative:

$∆\mathrm{S}°=-44.7{\mathrm{JK}}^{-1}$

It needs to determine why the entropy change is negative when the ions become dispersed through a large volume of solution.

Explanation on entropy

When a dissociation takes place, the produced ions have higher randomness which increases the general entropy. This would mean that the change in entropy would be positive. However, we'd like to require notice of the water which is that the solvent during this case. Water will experience a decrease in entropy because the water within the hydrated state is more structured and so as than pure water. The hydrated state represents the water molecules bonding with the and ions.

(b) The calculation of entropy change for CaF2(s)→Ca2+(aq)+2F-(aq)

Conclusion

The reason why the entropy of dissociation of CaF₂ is more negative than that of CaCl₂ is because of the electronegativity of F. Because of this electronegativity, it will form stronger bonds with the water molecules - hydrogen bonds. These bonds result in a strong fixated structure, which ultimately decreases the entropy even more.