(a) In Gaussian units, show that the square of a potential difference $\left(\phi_{2}-\phi_{1}\right)^{2}$ has the same dimensions as force. (In SI units, $\epsilon_{0}\left(\phi_{2}-\phi_{1}\right)^{2}$ has the same units as force.) This tells us that the electrostatic forces between bodies will largely be determined, as to order of magnitude, by the potential differences involved. Dimensions will enter only in ratios, and there may be some constants like $4 \pi$. What is the order of magnitude of force you expect with 1 statvolt potential difference between something and something else? (b) Practically achievable potential differences are rather severely limited, for reasons having to do with the structure of matter. The highest man-made difference of electric potential is about $10^{7}$ volts, achieved by a Van de Graaff electrostatic generator operating under high pressure. (Billion-volt accelerators do not involve potential differences that large.) How many pounds force are you likely to find associated with a “square megavolt”? These considerationsmay suggestwhy electrostatic motors have not found much application.

Write the common name for calcium carbonate.

A forest contains about 500 trees. You randomly pick 67 trees and find that 27 of them are oaks. b. Predict how many oak trees there are in the forest.

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

Write the common name for O$_3$.

How many grams of solid iron (III) chloride ($\mathrm{FeCl_{3}}$) are produced when 2.00 moles of solid iron (Fe) are combined with chlorine gas $\left(\mathrm{Cl}_{2}\right)$?

1. Analyze the Problem Known: __________ Unknown: __________ You are given the moles of the reactant, Fe, and must determine the mass of the product, $\mathrm{FeCl_{3}}$, therefore, you will do a mole to mass conversion.
2. Solve for the Unknown Write the balanced chemical equation. Identify the known and unknown substances.

$$\mathrm{Fe}(\mathrm{s})+\square \mathrm{Cl}_{2}(\mathrm{g})=\square \mathrm{FeCl}_{3}(\mathrm{s})$$

List the mole ratios for this equation. Multiply the number of moles of Fe by the mole ratio.

$$\square \text{mol Fe} \times \frac{\square \mathrm{mol} \ \mathrm{FeCl_{3}}}{\square\mathrm{mol \ Fe}} = \square \mathrm{mol \ FeCl_{2}}$$

Multiply the moles of $\mathrm{FeCl}_{3}$ by the molar mass of $\mathrm{FeCl}_{3}$.

$$\operatorname{mol} \mathrm{FeCl}_{3} \times \frac{\mathrm{g} \mathrm{FeCl}_{3}}{1 \mathrm{mol} \mathrm{FeCl}_{3}}=\square \mathrm{gFeCl}_{3}$$

3. Evaluate the Answer The given number of moles has $\square$ digits, so the mass of $\mathrm{FeCl}_{3}$ must have $\square$ digits.

For each of the following sentences, choose the correct word or words in parentheses. Base your answers on the rules of standard, formal usage.

Do you remember borrowing a dollar (off, off of, from) me?

Pine trees grow throughout a large tract of forest. Suppose a highway is built through the forest, effectively dividing it in half. Is it likely that the two groups of pine trees will evolve separately? Explain your prediction.

An annual report issued by General Motors Corporation included the following information:

$$\begin{array}{|cc} \text{Inventories are valued using various cost methods. The percentage of year-end}\\ \text{inventories valued using each of these methods is:}\\ \text {LIFO} & \cdots\cdots\cdots\cdots\cdots\cdots\cdots\cdots & 50\%& \\ \text { FIFO and Average Cost} & \cdots\cdots\cdots\cdots\cdots\cdots\cdots\cdots & 50 \% & \\ \text {If the LIFO method of valuation had not been used, total inventories would have } \\ \text {been \$1.4 billion more than reported.} \\ \end{array}$$

c. On the basis of the information from the company's annual report, do its inventory replacement costs appear to be rising or falling? Explain.

A lumber company owns a forest that is of rectangular shape, $1\ \mathrm{mi} \times 2\ \mathrm{mi} .$ The company wants to cut a uniform strip of trees along the outer edges of the forest. At most, how wide can the strip be if the company wants at least $1 \frac{5}{16}\ \mathrm{mi}^{2}$ of forest to remain?

Vintage Motors, Inc., was formed on January 1, 2018. The following transactions occurred during 2018: On January 1, 2018, Vintage issued its common stock for $430,000. Early in January, Vintage made the following cash payments: a.$160,000 for equipment
b. $234,000 for inventory (six cars at$39,000 each)
c. $18,000 for 2018 rent on a store building

In February, Vintage purchased four cars for inventory on account. The cost of this inventory was$192,000 ($48,000 per car). Before year-end, the company paid off$153,600 of this debt. The company uses the first-in, first-out (FIFO) method to account for its inventory.

During 2018, Vintage sold seven autos for a total of $504,000. Before year-end, it had collected 90% of this amount. The business employs two people. The combined annual payroll is$60,000, of which Vintage owes $11,000 at year-end. At the end of the year, the company paid income taxes of$22,000.

Late in 2018, Vintage declared and paid cash dividends of $13,000. For equipment, Vintage uses the straight-line depreciation method, over five years, with zero residual value.

Requirements 3. Prepare Vintage’s statement of cash flows for the year ended December 31, 2018. Format cash flows from operating activities using the indirect method.

What does it mean for three events to be mutually exclusive?

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 $\mathrm{HF}$.

If $P (A) = 0.3$, $P (B) = 0.4$, and $P (A\ \text{or}\ B) = 0.7$, are $A$ and $B$ mutually exclusive?