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.

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

Explain why the ratio is considerably smaller than $90 \mathrm{~J} / \mathrm{K} \cdot \mathrm{mol}$ for liquid $\mathrm{HF}$.

What measures can a court take in order to guarantee the right to a fair trial in the face of media scrutiny?

a. The court can limit journalists' access to particularly sensitive trials.

b. The court can exercise prior restraint against the publication of information that might influence the jury.

c. The court can force journalists to hold back sensitive information until after the trial has ended.

d. The court can threaten journalists with fines and imprisonment for revealing sensitive information.

e. The Supreme Court has never upheld a restriction on the press in the interest of a fair trial.

An aeration basin is used to oxygenate wastewater at 283 K. The basin is filled to a depth of 4.55 m with $283 \mathrm{m}^{3}$ wastewater of 0.050 mmole/L initial dissolved oxygen $\left(\mathrm{O}_{2}\right)$ cocentration. The filled basin is then aerated with six six spargers, with each sparger delivering compressed air to bottom of the basin at a volumetric flow rate of $7.08 \times 10^{-3} \mathrm{m}^{3} / \mathrm{s}$. The dissolved solids content will be low enough that Henry's law will be obeyed, with a Henry's law constant of $H=3.27 \times 10^{4} \mathrm{atm}$ $\left(p_{A}=H \cdot x_{A}^{\circ}\right)$ at 283 K. For purposes of this calculation, it may be assumed that the rate of $\mathrm{O}_{2}$ transferred to the liquid is small relative to molar flow rate of $\mathrm{O}_{2}$ in the aeration gas. a. Determine the dissolved oxygen concentration after a 5.0 min aeration time. b. Determine the time required to bring the dissolved oxygen concentration up to a concentration of 0.20 mmole/L (1 mmole/L = 1 gmole/m$^{3}$).

Water and ethanol, $\mathrm{CH}_3 \mathrm{CH}_2 \mathrm{OH}(\mathrm{l})$, are miscible, that is, they can be mixed in all proportions. However, when these liquids are mixed, the total volume of the resulting solution is not equal to the sum of the pure liquid volumes, and we say that the volumes are not additive. For example, when $50.0 \mathrm{~mL}$ of water and $50.0 \mathrm{~mL}$ of $\mathrm{CH}_3 \mathrm{CH}_2 \mathrm{OH}(1)$, are mixed at $20^{\circ} \mathrm{C}$, the total volume of the solution is $96.5 \mathrm{~mL}$, not $100.0 \mathrm{~mL}$. (The volumes are not additive because the interactions and packing of water molecules are slightly different from the interactions and packing of $\mathrm{CH}_3 \mathrm{CH}_2 \mathrm{OH}$ molecules.) Calculate the molarity of $\mathrm{CH}_3 \mathrm{CH}_2 \mathrm{OH}$ in a solution prepared by mixing $50.0 \mathrm{~mL}$ of water and $50.0 \mathrm{~mL}$ of $\mathrm{CH}_3 \mathrm{CH}_2 \mathrm{OH}(\mathrm{l})$ at $20^{\circ} \mathrm{C}$. At this temperature, the densities of water and ethanol are $0.99821$ $\mathrm{g} / \mathrm{mL}$ and $0.7893 \mathrm{~g} / \mathrm{mL}$, respectively.

Which forest biome has the richest soil type?

"Amy Lloyd is interested in leasing a new Honda and has contacted three automobile dealers for pricing information. Each dealer offered Amy a closed-end 36-month lease with no down payment due at the time of signing. Each lease includes a monthly charge and a mileage allowance. Additional miles receive a surcharge on a per-mile basis. The monthly lease cost, the mileage allowance, and the cost for additional miles follow:

$$\begin{aligned} &\text { Cost per }\\ &\begin{array}{lccc} {\text { Dealer }} & \text { Monthly Cost } & \text { Mileage Allowance } & \text { Additional Mile } \\ \text { Hepburn Honda } & \$ 299 & 36,000 & \$ 0.15 \\ \text { Midtown Motors } & \$ 310 & 45,000 & \$ 0.20 \\ \text { Hopkins Automotive } & \$ 325 & 54,000 & \$ 0.15 \end{array} \end{aligned}$$

Amy decided to choose the lease option that will minimize her total 36 -month cost. The difficulty is that Amy is not sure how many miles she will drive over the next three years. For purposes of this decision, she believes it is reasonable to assume that she will drive 12,000 miles per year, 15,000 miles per year, or 18,000 miles per year. With this assumption Amy estimated her total costs for the three lease options. For example, she figures that the Hepburn Honda lease will cost her $36(\$ 299)+\$ 0.15(36,000-36,000)=\$ 10,764$ if she drives 12,000 miles per year, 36( $\$ 299)+\$ 0.15(45,000-36,000)=\$ 12,114$ if she drives 15,000 miles per year, or $36(\$ 299)+\$ 0.15(54,000-36,000)=\$ 13,464$ if she drives 18,000 miles per year.

If Amy has no idea which of the three mileage assumptions is most appropriate, what is the recommended decision (leasing option) using the optimistic, conservative, and minimax regret approaches?"

we described how the speed of light varies with wavelength (or frequency) for transparent solids. But the speed of light in matter is also a function of temperature and pressure. This dependence is most marked for gases and is instrumental in producing such things as mirages and atmospheric refraction, the latter phenomenon being the displacement of an astronomical object (like the Sun or another star) from its true position because of the passage of its light through the atmosphere. Because Earth's atmosphere is a gaseous mixture and easily compressed, its density is highest near Earth's surface and gradually declines with altitude. Thus, the speed of light in the atmosphere is lowest near the surface and gradually gets higher, approaching $c$ as one goes farther and farther into space. Using this fact and the law of refraction, sketch the path a light ray from the Sun would follow upon entering Earth's atmosphere, and predict the apparent position of the Sun relative to its true position. What does this tell you about the actual location of the Sun's disk relative to your local horizon when you see it apparently setting brilliantly in the west in the evening?

Use prior restraint and libel to explain the limits placed on the free press.

Determine whether the events are mutually exclusive or not mutually exclusive. Then find the probability. Round to the nearest tenth of a percent if necessary.

Rolling a pair of dice and a sum of 8 or 12 is rolled

The concentration of hydrogen ions in a substance is denoted by $\left[\mathrm{H}^{+}\right]$, measured in moles per liter. The pH of a substance is defined by the logarithmic function $\mathrm{pH}=-\log \left[\mathrm{H}^{+}\right]$. This function is used to measure the acidity of a substance. The pH of water is 7. A substance with a pH less than 7 is an acid, whereas one that has a pH of more than 7 is a base. a. Find the pH of the following substances. Round answers to one digit. b. Determine whether the substance is an acid or a base. i. $\operatorname{Eggs}:\left[\mathrm{H}^{+}\right]=1.6 \times 10^{-8} \mathrm{mol} / \mathrm{L}$ ii. Beer: $\left[\mathrm{H}^{+}\right]=3.16 \times 10^{-3} \mathrm{mol} / \mathrm{L}$ iii. Tomato Juice: $\left[\mathrm{H}^{+}\right]=7.94 \times 10^{-5} \mathrm{mol} / \mathrm{L}$

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.

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

Why do you think the courts are reluctant to allow prior restraint?

A drilling mud is a slurry pumped into oil wells being drilled. The mud has several functions: It floats rock cuttings to the top of the well where they can easily be removed; lubricates and cools the drill bit; and keeps loose solids and water from leaking into the borehole. A drilling mud is prepared by blending (SG = 4.37) with seawater (SG = 1.03). The seawater has a dissolved salt content of approximately 3.5 wt%. You have been asked to determine the specific gravity of the mud and the wt% barite. You collect a sample of the mud from a blending tank on an oil platform and make the following observations: (i) The mud appears homogeneous, even after standing for 2 days; (ii) the tare mass of the calibrated vessel into which you pour the sample of mud is 118 g; (iii) the volume of the collected sample is 100 mL, and the mass of the collection vessel and sample is 323 g; and (iv) the mass of the vessel and residue remaining after completely evaporating water from the sample is 254 g. a) Estimate the specific gravity of the mud and the wt% barite. b) What is the practical importance of Observation (i)?

The number of vehicles sold in the United States (in millions) for each year is shown in the table below, along with the proportion of those vehicles that were made by General Motors.

$$\begin{array}{lcc} \text { Year } & \text { Cars Sold (millions) } & \text { Percent GM } \\ \hline 1950 & 6.0 & 50.2 \\ 1955 & 7.8 & 50.4 \\ 1960 & 7.3 & 44.0 \\ 1965 & 10.3 & 49.9 \\ 1970 & 10.1 & 39.5 \\ 1975 & 10.8 & 43.1 \\ 1980 & 11.5 & 44.0 \end{array}$$

$$\begin{array}{ccc} \text { Year } & \text { Cars Sold (millions) } & \text { Percent GM } \\ \hline 1985 & 15.4 & 40.1 \\ 1990 & 13.5 & 36.0 \\ 1995 & 15.5 & 31.7 \\ 2000 & 17.4 & 28.6 \\ 2005 & 16.9 & 26.9 \\ 2010 & 11.6 & 19.1 \\ 2015 & 17.5 & 17.6 \end{array}$$

To find the answers to the following questions, use a statistical software programme. Is the number of cars sold directly or indirectly related to GM’s percentage of the market? Draw a scatter diagram to show your conclusion.