0.20 Equilibrium and the second law of thermodynamics  (Page 11/11)

It is important to note that the partial pressures in $Q$ need not be the equilibrium partial pressures. However, if the pressures in $Q$ are the equilibrium partial pressures, then $Q$ has the same value as $K_p$ , the equilibrium constant, by definition. Moreover, if the pressuresare at equilibrium, we know that $\Delta (G)=0$ . If we look back at [link] , we can conclude that

This is an exceptionally important relationship, because it relates two very different observations.To understand this significance, consider first the case where $\Delta (G^{°})< 0$ . We have previously reasoned that, in this case, the reactionequilibrium will favor the products. From [link] we can note that, if $\Delta (G^{°})< 0$ , it must be that $K_p> 1$ . Furthermore, if $\Delta (G^{°})$ is a large negative number, $K_p$ is a very large number. By contrast, if $\Delta (G^{°})$ is a large positive number, $K_p$ will be a very small (though positive) number much less than 1. In this case, the reactants will be strongly favored atequilibrium.

Note that the thermodynamic description of equilibrium and the dynamic description of equilibrium arecomplementary. Both predict the same equilibrium. In general, the thermodynamic arguments give us an understanding of the conditionsunder which equilibrium occurs, and the dynamic arguments help us understand how the equilibrium conditions are achieved.

Review and discussion questions

1. Each possible sequence of the 52 cards in a deck is equally probable. However, when you shuffle a deck and then examine the sequence, the deck is never ordered. Explain why interms of microstates, macrostates, and entropy.
2. Assess the validity of the statement, "In all spontaneous processes, the system moves toward a state of lowestenergy." Correct any errors you identify.
3. In each case, determine whether spontaneity is expected at low temperature, high temperature, any temperature, orno temperature:

   (a) $\Delta (H^{°})> 0$ , $\Delta (S^{°})> 0$

   (b) $\Delta (H^{°})< 0$ , $\Delta (S^{°})> 0$

   (c) $\Delta (H^{°})> 0$ , $\Delta (S^{°})< 0$

   (d) $\Delta (H^{°})< 0$ , $\Delta (S^{°})< 0$

4. Using thermodynamic equilibrium arguments, explain why a substance with weaker intermolecular forces has agreater vapor pressure than one with stronger intermolecular forces.
5. Why does the entropy of a gas increase as the volume of the gas increases? Why does the entropy decrease as thepressure increases?
6. For each of the following reactions, calculate the values of $\Delta (S^{°})$ , $\Delta (H^{°})$ , and $\Delta (G^{°})$ at $T=298K$ and use these to predict whether equilibrium will favor products or reactants at $T=298K$ . Also calculate $K_p$ .

   (a) $2\text{C}\text{O}\left(g\right)+{\text{O}}_2\left(g\right)\to 2\text{C}{\text{O}}_2\left(g\right)$

   (b) ${\text{O}}_3\left(g\right)+\text{N}\text{O}\left(g\right)\to \text{N}{\text{O}}_2\left(g\right)+{\text{O}}_2\left(g\right)$

   (c) $2{\text{O}}_3\left(g\right)\to 3{\text{O}}_2\left(g\right)$

7. Predict the sign of the entropy for the reaction $$2{\text{H}}_2\left(g\right)+{\text{O}}_2\left(g\right)\to 2{\text{H}}_2\text{O}\left(g\right)$$ Give an explanation, based on entropy and the Second Law, of why this reaction occurs spontaneously.
8. For the reaction ${\text{H}}_2\left(g\right)\to 2\text{H}\left(g\right)$ , predict the sign of both $\Delta (H^{°})$ and $\Delta (S^{°})$ . Should this reaction be spontaneous at high temperature or at lowtemperature? Explain.
9. For each of the reactions in [link] , predict whether increases in temperature will shift the reaction equilibrium more towardsproducts or more towards reactants.
10. Using [link] and [link] , show that for a given set of initial partial pressures where $Q$ is larger than $K_p$ , the reaction will spontaneously create more reactants. Also showthat if $Q$ is smaller than $K_p$ , the reaction will spontaneously create more products.