Chapter 15.5, Problem 51SSC

Interpretation Introduction

Interpretation: Whether the given reaction is spontaneous or not needs to be determined.

Concept Introduction: A reaction is spontaneous if its Gibbs free energy change is negative. Gibbs free energy change is given by:

  $\begin{array}{l}\Delta G=\Delta H-T\Delta S\\ \text{where}\\ \Delta G\text{is}\text{change}\text{in}\text{Gibbs}\text{free}\text{energy}\\ \Delta H\text{is}\text{change}\text{in}\text{enthalpy}\\ \Delta S\text{is}\text{change}\text{in}\text{entropy}\\ T\text{is}\text{Temperature}\text{of}\text{reaction}\end{array}$

Answer to Problem 51SSC

The given reaction is spontaneous.

Explanation of Solution

Given Information:

  $\begin{array}{c}\Delta H=-20.\text{5}\text{kJ}\\ \Delta S=-35\text{J/K}\\ =-\text{0}\text{.035}\text{kJ/K}\\ T=2\text{98}\text{K}\end{array}$

Calculation:

Putting the values into the formula:

  $\begin{array}{c}\Delta G=\Delta H-T\Delta S\\ =-20.5-\left(298\right)\left(-0.035\right)\\ =-20.5+10.43\\ =-10.07kJ\end{array}$

As Gibbs free energy change is negative, therefore reaction is spontaneous.

Conclusion

The data given has negative Gibbs free energy change, therefore, reaction is spontaneous.