Natural gas (methane) is being used in experimental vehicles as a clean-burning fuel.

(a) Write the equation for the combustion of $\mathrm{CH}_4(\mathrm{~g})$, assuming that all reactants and products are in the gas phase.

(b) Use data from Appendix $\mathrm{E}$ to calculate $\Delta S^{\circ}$ for this reaction.

(c) Calculate $\Delta G^{\circ}$ and show that the reaction is spontaneous at $25^{\circ} \mathrm{C}$.

The kinetic energy of molecules is often used to induce chemical reactions. The bond energy in an $\mathrm{O_2}$ molecule is $8.22\times10^{-19}$ J. Can an $\mathrm{O_2}$ molecule traveling at 780 m/s provide enough energy to break the $\mathrm{O=O}$ bond? What is the minimum velocity of an $\mathrm{O_2}$ molecule that would give a kinetic energy capable of breaking the bond if it is converted with 100% efficiency?

Some climbing ropes are designed to noticeably stretch under a load to lessen the forces in a fall. A $10 \mathrm{~m}$ length of climbing rope is supporting a climber; this causes the rope to stretch by $60 \mathrm{~cm}$. If the climber is supported by a $20 \mathrm{~m}$ length of the same rope, by how much does the rope stretch?
A. $30 \mathrm{~cm}$
B. $60 \mathrm{~cm}$
C. $90 \mathrm{~cm}$
D. $120 \mathrm{~cm}$

Some climbing ropes are designed to noticeably stretch under a load to lessen the forces in a fall. A weight is attached to $10 \mathrm{~m}$ length of climbing rope, which then stretches by $20 \mathrm{~cm}$. Now, this single rope is replaced by a doubled rope-two pieces of rope next to each other. How much does the doubled rope stretch?
A. $5.0 \mathrm{~cm}$
B. $10 \mathrm{~cm}$
C. $20 \mathrm{~cm}$
D. $40 \mathrm{~cm}$

The combustion of acetylene is used in welder's torches because it produces a very hot flame.

$$\begin{aligned} \mathrm{C}_2 \mathrm{H}_2(\mathrm{~g})+\frac{5}{2} \mathrm{O}_2(\mathrm{~g}) \rightarrow 2 \mathrm{CO}_2(\mathrm{~g})+\mathrm{H}_2 \mathrm{O}(\mathrm{g}) \\ \Delta H^{\circ}=-1255.5 \mathrm{~kJ} \end{aligned}$$

(a) Use data in Appendix $\mathrm{E}$ to calculate $\Delta S^{\circ}$ for this reaction.

(b) Calculate $\Delta G^{\circ}$ and show that the reaction is spontaneous at $25^{\circ} \mathrm{C}$.

(c) Is there any temperature range in which this reaction is not spontaneous?

(d) Do you think you could use Equation to calculate such a temperature range reliably? Explain your answer.

For the reaction $\mathrm{NO}(\mathrm{g})+\mathrm{NO}_2(\mathrm{~g}) \rightarrow \mathrm{N}_2 \mathrm{O}_3(\mathrm{~g})$, use tabulated thermodynamic data to calculate $\Delta H^{\circ}$ and $\Delta S^{\circ}$. Then use those values to answer the following questions.

(a) Is this reaction spontaneous at 25 degree C ? Explain your answer.

(b) If the reaction is not spontaneous at 25 degree C , will it become spontaneous at higher temperatures or lower temperatures?

(c) To show that your prediction is accurate, choose a temperature that corresponds to your prediction in part (b) and calculate $\Delta G$. (Assume that both enthalpy and entropy are independent of temperature.)

Distinguish between a reversible and an irreversible process.

Why is the free energy change of a system equal to the maximum work rather than just the work?

The reaction

$$\mathrm{CO}_2(\mathrm{~g})+\mathrm{H}_2(\mathrm{~g}) \rightarrow \mathrm{CO}(\mathrm{g})+\mathrm{H}_2 \mathrm{O}(\mathrm{g})$$

is not spontaneous at room temperature but becomes spontaneous at a much higher temperature. What can you conclude from this about the signs of $\Delta H^{\circ}$ and $\Delta S^{\circ}$, assuming that the enthalpy and entropy changes are not greatly affected by the temperature change? Explain your reasoning.

Discuss the effect of temperature change on the spontaneity of the following reactions at $1 \mathrm{~atm}$. (a) $\mathrm{Al}_2 \mathrm{O}_3(\mathrm{~s})+2 \mathrm{Fe}(\mathrm{s}) \rightarrow 2 \mathrm{Al}(\mathrm{s})+\mathrm{Fe}_2 \mathrm{O}_3(\mathrm{~s}) \Delta H^{\circ}=+851.5 \mathrm{~kJ} ; \quad \Delta S^{\circ}=+38.5 \mathrm{~J} / \mathrm{K}$

(b)

$$\begin{aligned} \mathrm{N}_2 \mathrm{H}_4(\ell) \rightarrow & \mathrm{N}_2(\mathrm{~g})+2 \mathrm{H}_2(\mathrm{~g}) \\ & \Delta H^{\circ}=-50.6 \mathrm{~kJ} ; \quad \Delta S^{\circ}=0.3315 \mathrm{~kJ} / \mathrm{K}\end{aligned}$$

(c) $\mathrm{SO}_3(\mathrm{~g}) \rightarrow \mathrm{SO}_2(\mathrm{~g})+\frac{1}{2} \mathrm{O}_2(\mathrm{~g}) \Delta H^{\circ}=98.9 \mathrm{~kJ} ; \quad \Delta S^{\circ}=+0.0939 \mathrm{~kJ} / \mathrm{K}$

Use the web to learn how many pounds of plastics are recycled in your area each year. How has this value changed during the past decade?

Calculate $\Delta G^{\circ}$ at 45 degree C for reactions for which

(a) $\Delta H^{\circ}=293 \mathrm{~kJ} ; \Delta S^{\circ}=-695 \mathrm{~J} / \mathrm{K}$

(b) $\Delta H^{\circ}=-1137 \mathrm{~kJ} ; \Delta S^{\circ}=0.496 \mathrm{~kJ} / \mathrm{K}$

(c) $\Delta H^{\circ}=-86.6 \mathrm{~kJ} ; \Delta S^{\circ}=-382 \mathrm{~J} / \mathrm{K}$

There is another free energy state function, the Helmholtz free energy (F), defined as F = E - TS. Comparing this to the definition of G, we see that internal energy has replaced enthalpy in the definition. Under what conditions would this free energy tell us whether or not a process is spontaneous?

Under what conditions does $\Delta G$ allow us to predict whether a process is spontaneous?