Give an answer for the follwoing exercise.

(a) Trouton's rule states that the ratio of the molar heat of vaporization of a liquid $\left(\Delta H_{\text {vap }}\right)$ to its boiling point in kelvins is approximately $90 \mathrm{~J} / \mathrm{K} \cdot \mathrm{mol}$. Use the following data to show that this is the case and explain why Trouton's rule holds true.

$$\begin{array}{lcc} & \boldsymbol{T}_{\mathbf{b p}}\left({ }^{\circ} \mathbf{C}\right) & \boldsymbol{\Delta} \boldsymbol{H}_{\text {vap }}(\mathbf{k} \mathbf{J} / \mathbf{m o l}) \\ \hline \text { Benzene } & 80.1 & 31.0 \\ \text { Hexane } & 68.7 & 30.8 \\ \text { Mercury } & 357 & 59.0 \\ \text { Toluene } & 110.6 & 35.2 \end{array}$$

(b) Use the values in the table to calculate the same ratio for ethanol and water. Explain why Trouton's rule does not apply to these two substances as well as it does to other liquids.

$$\begin{array}{ccc} \text { Substance } & \text { Boiling point }\left({ }^{\circ} \mathrm{C}\right) & \Delta H_{\text {vap }}(\mathrm{kJ} / \mathrm{mol}) \\ \text { Argon }(\mathrm{Ar}) & -186 & 6.3 \\ \text { Benzene }\left(\mathrm{C}_6 \mathrm{H}_6\right) & 80.1 & 31.0 \\ \text { Ethanol }\left(\mathrm{C}_2 \mathrm{H}_5 \mathrm{OH}\right) & 78.3 & 39.3 \\ \text { Diethyl ether }\left(\mathrm{C}_2 \mathrm{H}_5 \mathrm{OC}_2 \mathrm{H}_5\right) & 34.6 & 26.0 \\ \text { Mercury }\left(\mathrm{Hg}^2\right) & 357 & 59.0 \\ \text { Methane }\left(\mathrm{CH}_4\right) & -164 & 9.2 \\ \text { Water }\left(\mathrm{H}_2 \mathrm{O}\right) & 100 & 40.79 \end{array}$$

Calculate the equilibrium pressure of $\mathrm{CO}_2$ due to the decomposition of barium carbonate $\left(\mathrm{BaCO}_3\right)$ at $25^{\circ} \mathrm{C}$.

Ammonium nitrate dissolves spontaneously and endothermically in water. What can you deduce about the sign of $\Delta S$ for the solution process?

Consider the following facts: Water freezes spontaneously at $-5^{\circ} \mathrm{C}$ and $1 \mathrm{~atm}$, and ice has a lower entropy than liquid water. Explain how a spontaneous process can lead to a decrease in entropy.

A student placed $1 \mathrm{~g}$ of each of three compounds $\mathrm{A}$, $\mathrm{B}$, and $\mathrm{C}$ in a container and found that after $1$ week no change had occurred. Offer some possible explanations for the fact that no reactions took place. Assume that $\mathrm{A}$, $\mathrm{B}$, and $\mathrm{C}$ are totally miscible liquids.

Calculate $\Delta G$ for the reaction

$$\mathrm{H}_2 \mathrm{O}(l) \rightleftarrows \mathrm{H}^{+}(a q)+\mathrm{OH}^{-}(a q)$$

at $25^{\circ} \mathrm{C}$ for the following initial concentrations.

(a) $\left[\mathrm{H}^{+}\right]=1.0 \times 10^{-7} \mathrm{M},\left[\mathrm{OH}^{-}\right]=1.0 \times 10^{-7} \mathrm{M}$

(b) $\left[\mathrm{H}^{+}\right]=1.0 \times 10^{-3} M$, $\left[\mathrm{OH}^{-}\right]=1.0 \times 10^{-4} M$

(c) $\left[\mathrm{H}^{+}\right]=1.0 \times 10^{-12} M$, $\left[\mathrm{OH}^{-}\right]=2.0 \times 10^{-8} M$

(d) $\left[\mathrm{H}^{+}\right]=3.5 \mathrm{M},\left[\mathrm{OH}^{-}\right]=4.8 \times 10^{-4} \mathrm{M}$

(a) How much work does a major-league pitcher do on the baseball when he throws a 90.0 mi/h (40.2 m/s) fastball? The mass of a baseball is 153 g. (b) How many fastballs would a pitcher have to throw to "burn off" a 1520 kcal meal? Assume that 80.0% of the chemical energy in the food is converted to thermal energy and only 20.0% becomes the kinetic energy of the fastballs.

Predict the signs of $\Delta H, \Delta S$, and $\Delta G$ of the system for the following processes at $1 \mathrm{~atm}$ :

(a) ammonia melts at $-60^{\circ} \mathrm{C}$

(b) ammonia melts at $-77.7^{\circ} \mathrm{C}$

(c) ammonia melts at $-100^{\circ} \mathrm{C}$ (The normal melting point of ammonia is $-77.7^{\circ} \mathrm{C}$.)

In the metabolism of glucose, the first step is the conversion of glucose to glucose 6-phosphate: glucose $+\mathrm{H}_3 \mathrm{PO}_4 \longrightarrow$ glucose 6-phosphate $+\mathrm{H}_2 \mathrm{O}$ $\Delta G^{\circ}=13.4 \mathrm{~kJ} / \mathrm{mol}$ Because $\Delta G^{\circ}$ is positive, this reaction does not favor the formation of products. Show how this reaction can be made to proceed by coupling it with the hydrolysis of ATP. Write an equation for the coupled reaction, and estimate the equilibrium constant for the coupled process.

Referring to the metabolic process involving glucose in the given figure shown earlier, calculate the maximum number of moles of ATP that can be synthesized from ADP from the breakdown of 1 mole of glucose.

What is the relationship between entropy and the number of possible arrangements of molecules in a system?

What is the role of ATP in biological reactions?

What is a coupled reaction? What is its importance in biological reactions?

Calculate $\Delta G^{\circ}$ for the process

$$\text { C(diamond) } \rightleftarrows \text { C(graphite) }$$

Is the formation of graphite from diamond favored at $25^{\circ} \mathrm{C}$ ? If so, why is it that diamonds do not become graphite on standing?