Chapter 7, Problem 7.18UKC

What are the signs of  ΔH, ΔS, and ΔG for the spontaneous conversion of a crystalline solid into a gas? Explain.

Interpretation Introduction

Interpretation:

The signs of $\Delta H$, $\Delta S$ and $\Delta G$ for the spontaneous conversion reaction of crystalline gas has to be determined.

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 7.18UKC

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

Explanation of Solution

During the conversion of solid to gas, the heat energy is absorbed. Thus it is an endothermic reaction. Therefore, the sign of change in enthalpy $\Delta H$ is positive.

Crystalline solid is converted to gas. Gaseous particles have more freedom comparing to solid particle and thus disorder is high in gas.  Therefore, the sign of change in entropy $\Delta S$ is positive.

Conversion of solid to gas is a spontaneous reaction.  Therefore, the sign of change in free energy $\Delta G$ is negative.

Conclusion

The signs of $\Delta H$, $\Delta S$ and $\Delta G$ for the spontaneous conversion reaction of crystalline gas was determined.