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.

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?

Describe why it is easier to use $\Delta G$ to determine the spontaneity of a process rather than $\Delta S_{\mathrm{u}}$.

A beaker of water at 40 degree C and a beaker of ice water at 0 degree C are placed side by side in an insulated container. After some time has passed, the temperature of the water in the beaker on the left is 30 degree C and the temperature of the ice water is still 0 degree C. Describe what is happening in each beaker

(a) on the molecular level and

(b) in terms of the second law of thermodynamics.

Look up the value of the standard entropy for the following molecules: $\mathrm{SiO}_2(\mathrm{~s}), \mathrm{NH}_3(\mathrm{~g}), \mathrm{C}_2 \mathrm{H}_6(\mathrm{~g})$. Rank the compounds in order of increasing entropy and then explain why this ranking makes sense.

Look up the value of the standard entropy for the following molecules: $\mathrm{CH}_4(\mathrm{~g}), \mathrm{C}_2 \mathrm{H}_5 \mathrm{OH}(\ell), \mathrm{H}_2 \mathrm{C}_2 \mathrm{O}_4(\mathrm{~s})$. Rank the compounds in order of increasing entropy and then explain why this ranking makes sense.

Find websites describing two different attempts to reach the coldest temperature on record. What features do these experiments have in common?

Through photosynthesis, plants build molecules of sugar containing several carbon atoms from carbon dioxide. In the process, entropy is decreased. The reaction of $\mathrm{CO}_2$ with formic acid to form oxalic acid provides a simple example of a reaction in which the number of carbon atoms in a compound increases:

$$\mathrm{CO}_2(\mathrm{aq})+\mathrm{HCOOH}(\mathrm{aq}) \rightarrow \mathrm{H}_2 \mathrm{C}_2 \mathrm{O}_4(\mathrm{aq})$$

(a) Calculate the standard entropy change for this reaction and discuss the sign of $\Delta S^{\circ}$.

(b) How do plants carry out reactions that increase the number of carbon atoms in a sugar, given the changes in entropy for reactions like this?

Calculate the standard entropy change for the reaction $\mathrm{CO}_2(\mathrm{~g})+2 \mathrm{H}_2 \mathrm{O}(\ell) \rightarrow \mathrm{CH}_4(\mathrm{~g})+2 \mathrm{O}_2(\mathrm{~g})$. What does the sign of $\Delta S^{\circ}$ say about the spontaneity of this reaction?

Calculate $\Delta S^{\circ}$ for the dissolution of magnesium chloride: $\mathrm{MgCl}_2(\mathrm{~s}) \rightarrow \mathrm{Mg}^{2+}(\mathrm{aq})+2 \mathrm{Cl}^{-}(\mathrm{aq})$. Use your understanding of the solvation of ions at the molecular level to explain the sign of $\Delta S^{\circ}$.

If you scan the values for $S^{\circ}$ in Appendix $\mathrm{E}$, you will see that several aqueous ions have values that are less than zero. The third law of thermodynamics states that for a pure substance the entropy goes to zero only at 0 K. Use your understanding of the solvation of ions in water to explain how a negative value of $S^{\circ}$ can arise for aqueous species.

Use tabulated thermodynamic data to calculate the standard entropy change of each of the reactions listed below.

(a) $\mathrm{Fe}(\mathrm{s})+2 \mathrm{HCl}(\mathrm{g}) \rightarrow \mathrm{FeCl}_2$ (s) $+\mathrm{H}_2(\mathrm{~g})$

(b) $3 \mathrm{NO}_2(\mathrm{~g})+\mathrm{H}_2 \mathrm{O}(\ell) \rightarrow 2 \mathrm{HNO}_3(\ell)+\mathrm{NO}(\mathrm{g})$

(c) $2 \mathrm{~K}(\mathrm{~s})+\mathrm{Cl}_2(\mathrm{~g}) \rightarrow 2 \mathrm{KCl}(\mathrm{s})$

(d) $\mathrm{Cl}_2(\mathrm{~g})+2 \mathrm{NO}(\mathrm{g}) \rightarrow 2 \mathrm{NOCl}(\mathrm{g})$

(e) $\mathrm{SiCl}_4(\mathrm{~g}) \rightarrow \mathrm{Si}(\mathrm{s})+2 \mathrm{Cl}_2(\mathrm{~g})$

Suppose that you fi nd out that a system has an absolute entropy of zero. What else can you conclude about that system?