Draw the products of the following reactions. If the products can exist as stereoisomers, show which stereoisomers are formed. a.

$$cis-2-pentene + HCl,$$

b.

$$trans-2-pentene + HCl,$$

c.

$$1-ethylcyclohexene + H_2O + H_2SO_4,$$

d.

$$2,3-dimethyl-3-hexene + H_2, Pd/C,$$

e.

$$1,2-dimethylcyclohexene + HCl,$$

f.

$$1,2-dideuteriocyclohexene + H_2, Pd/C,$$

g.

$$3,3-dimethyl-1-pentene + Br_2/CH_2Cl_2,$$

h.

$$(E)-3,4-dimethyl-3-heptene + H_2, Pd/C,$$

i.

$$(Z)-3,4-dimethyl-3-heptene + H_2, Pd/C,$$

j.

$$1-chloro-2-ethylcyclohexene + H_2, Pd/C$$

Which of the following molecules is a dipole?

(a) $\mathrm{HBr}$
(b) $\mathrm{CH}_4$
(c) $\mathrm{H}_2$
(d) $\mathrm{CO}_2$

On the said page of Physics: Calculus by Eugene Hecht (Pacific Grove, CA: Brooks/Cole, 1996), in the course of deriving the formula $T=2 \pi \sqrt{L / g}$ for the period of a pendulum of length L, the author obtains the equation $a_T=-g \sin \theta$ for the tangential acceleration of the bob of the pendulum. He then says, "for small angles, the value of $\theta$ in radians is very nearly the value of $\sin \theta$; they differ by less than 2% out to about 20 degrees."

Use a graphing device to determine the values of x for which sin x and x differ by less than 2%. Then verify Hecht's statement by converting from radians to degrees.

HERE COME THE CLOWNS! is the name of a traveling circus. The ledger accounts as of the business at June 30, 2011, are listed here in alphabetical order:

$$\begin{array}{|cc} \text { Accounts Payable } & \$ 26,100 & \text{Notes Payable} & \$180,000 \\ \text { Accounts Receivable } & 7,450 & \text{Notes Receivable} & 9,500 \\ \text { Animals } & 189,060 & \text{ Props and Equipment} &89,580\\ \text {Cages } & 24,630 & \text {Retained Earnings} & 27,230\\ \text { Capital Stock } & 310,000 & \text{Salaries Payable} & 9,750 \\ \text {Cash } & ? & \text{Tents} &63,000 \\ \text { Costumes } & 31,500 & \text{Trucks and Wagons} & 105,840 \\ \end{array}$$

Instructions
a. Prepare a balance sheet by using these items and computing the amount of Cash at June 30, 2011. Organize your balance sheet similar to the one illustrated in Exhibit 2-10. (After "Accounts Receivable," you may list the remaining assets in any order.) Include a proper balance sheet heading.

Draw the mechanism for formation of the two addition products.

Bay City has a 20% chance of having a flood in any given decade. The table shows the results of a simulation using random numbers to find the experimental probability that there will be a flood in Bay City in at least 1 of the next 5 decades. In the table, the number 1 represents a decade with a flood. The numbers 2 through 5 represent a decade without a flood.

$$\begin{matrix}\text{Trial} & \text{Numbers generated}\\\text{1} & \text{2, 2, 5, 5, 5}\\\text{2} & \text{3, 2, 3, 5, 4}\\\text{3} & \text{5, 5, 5, 4, 3}\\\text{4} & \text{5, 1, 3, 3, 5}\\\text{5} & \text{4, 5, 5, 3, 2}\\\text{6} & \text{4, 2, 2, 5, 4}\\\text{7} & \text{1, 3, 2, 4, 4}\\\text{8} & \text{3, 5, 5, 2, 1}\\\text{9} & \text{4, 3, 3, 2, 5}\\\text{10} & \text{5, 4, 1, 2, 1}\\\end{matrix}$$

According to the simulation, what is the experimental probability of a flood in Bay City in at least 1 of the next 5 decades.

How many molecules of aspirin,

$$\mathrm { C } _ { 9 } \mathrm { H } _ { 8 } \mathrm { O } _ { 4 }$$

, are there in a 100.0 mg tablet of aspirin?

Suggest why $\mathrm{Be}^{2+}$ has a higher affinity for $\mathrm{H}_2 \mathrm{O}$ molecules than $\mathrm{Mg}^{2+}$.

Determine the mass, in grams, of $4.18 \times 10^{24}$ molecules of $\mathrm{C}_2 \mathrm{H}_4(\mathrm{OH})_2$.

Does the vapor pressure of a liquid substance change as the liquid is heated? Explain.

If $R$ denotes the reaction of the body to some stimulus of strength $x$, the sensitivity $S$ is defined to be the rate of change of the reaction with respect to $x$. A particular example is that when the brightness $x$ of a light source is increased, the eye reacts by decreasing the area $R$ of the pupil. The experimental formula

$$R=\frac{40+24 x^{0.4}}{1+4 x^{0.4}}$$

describes the dependence of $R$ on $x$ when $R$ is measured in square millimeters and $x$ is measured in appropriate units of brightness.

Find the sensitivity.

Illustrate above part by graphing both $R$ and $S$ as functions of $x$. Comment on the values of $R$ and $S$ at low levels of brightness. Is this what you would expect?

Read each question. Eliminate any unreasonable answers. Then use the information in the question to solve. The table shows the surface areas, in square kilometers, of the oceans.

$$\begin{matrix} \text{Ocean} & Area (km^2)\\ \text{Pacific} & \text{156,000,000}\\ \text{Atlantic} & \text{77,000,000}\\ \text{Indian} & \text{69,000,000}\\ \text{Southern} & \text{20,000,000}\\ \text{Arctic} & \text{14,000,000}\\ \end{matrix}$$

Which of the following represents the area of the Arctic Ocean in scientific notation? A. $0.14 \times 10^{8}$ B. $1.4 \times 10^{7}$ C. $1.4 \times 10^{8}$ D. $14 \times 10^{6}$

a. Draw the major product(s) of the reaction of 1-methylcyclohexene with the following reagents, disregarding stereoisomers: 1.

$$NBS/Δ/peroxide,$$

$$Br_2/CH_2Cl_2,$$

$$HBr,$$

$$HBr/peroxide,$$

b. For each reaction, show which stereoisomers are obtained.

Explain the problem with the following statement and correct it. "When a chemical equation is balanced, the number of molecules of each type on both sides of the equation is equal."