DDT (molar mass = 354.49 g/mol) was a widely used insecticide that was banned from use in the United States in 1973. This ban was brought about due to the persistence of DDT in many different ecosystems, leading to high accumulations of the substance in many birds of prey. The insecticide was shown to cause a thinning of egg shells, pushing many birds toward extinction. If a 20-L drum of DDT was spilled into a pond, resulting in a DDT concentration of $8.75 \times 10 ^ { - 5 }\ \mathrm { M } ,$ how long would it take for the levels of DDT to reach a concentration of $1.41 \times 10 ^ { - 7 }\ \mathrm { M }$ (a level that is generally assumed safe in mammals)? Assume the decomposition of DDT is a first-order process with a half-life of 56.0 days.

Solve each inequality and graph the solutions. |3x|+2<8

The following output presents the results of a hypothesis test for a population mean.

$$\begin{array}{l} \hline \text{Test of mu = 53.5 vs not = 53.5}\\ \text{The assumed standard deviation = 2.3634}\\ \\ \begin{array}{rrrrlrr} \text{N} & \text{Mean} & \text{SE Mean} & 98\% & \text{CI} & \text{Z} & \text{P}\\ 145 & 53.246 & 0.1962 & (52.861, & 53.631) & -1.29 & 0.196\\ \end{array}\\ \hline \end{array}$$

$\textbf{a.}\hspace{10pt}$ What are the null and alternate hypotheses?

$\textbf{b.}\hspace{10pt}$ What is the value of the test statistic?

$\textbf{c.}\hspace{10pt}$ What is the $P$-value?

$\textbf{d.}\hspace{10pt}$ Do you reject $H_0$ at the $\alpha = 0.05$ level?

A first-order reaction is 75.0% complete in 320 s. What are the first and second half-lives for this reaction?

Obtain an estimate for each computation by rounding the numbers so that the resulting arithmetic can easily be performed by hand or in your head. Then use a calculator to perform the computation. How reasonable is your estimate when compared to the actual answer?

$$8.93 + 1.04 + 19.26$$

The rate law for the decomposition of phosphine $\left( \mathrm { PH } _ { 3 } \right)$ is

$$\text {Rate} = - \frac { d \left[ \mathrm { PH } _ { 3 } \right] } { d t } = k \left[ \mathrm { PH } _ { 3 } \right]$$

It takes $120 .$ s for the concentration of 1.00 $M\ \mathrm { PH } _ { 3 }$ to decrease to 0.250 M. How much time is required for 2.00 $M\ \mathrm { PH } _ { 3 }$ to decrease to a concentration of 0.350 $\mathrm { M } ?$

From 1500 lottery tickets that are sold, 3 tickets are to be selected for first, second, and third prizes. How many possible outcomes are there?

Theophylline is a pharmaceutical drug that is sometimes used to help with lung function. You observe a case where the initial lab results indicate that the concentration of theophylline in a patient’s body decreased from $2.0 \times 10^{-3}\ M$ to $1.0 \times 10^{-3}\ M$ in 24 hours. In another 12 hours the drug concentration was found to be $5.0 \times 10^{-4}\ M.$ What is the value of the rate constant for the metabolism of this drug in the body?

A certain first-order reaction is 45.0% complete in 65 s. What are the values of the rate constant and the half-life for this process?

At a particular temperature, a 3.0-L flask contains 2.4 moles of

$$Cl_2,$$

1.0 mole of NOCI, and

$$4.5 \times 10 ^ { - 3 }$$

mole of NO. Calculate K at this temperature for the following reaction.

$$2 \mathrm { NOCl } ( g ) \rightleftharpoons 2 \mathrm { NO } ( g ) + \mathrm { Cl } _ { 2 } ( g )$$

Write a mechanism for the formation of $tert$-butylbenzene from benzene and $tert$-butyl alcohol in the presence of phosphoric acid.

State whether

$$f ( x ) = 2 x ^ { 2 } - 9$$

is a linear function. Explain.

One mechanism for the destruction of ozone in the upper atmosphere is

$$\begin{array} {l} \mathrm{O}_{3}(g)+\mathrm{NO}(g) \longrightarrow \mathrm{NO}_{2}(g)+\mathrm{O}_{2}(g) & Slow \\ \mathrm{NO}_{2}(g)+\mathrm{O}(g) \longrightarrow \mathrm{NO}(g)+\mathrm{O}_{2}(g) & Fast \\ \hline \text{Overall reaction} \quad \mathrm{O}_{3}(g)+\mathrm{O}(g) \longrightarrow 2 \mathrm{O}_{2}(g) & {} \\ \end{array}$$

Which species is a catalyst?

Use the Binomial Theorem to expand each expression. Determine the largest integer n for which your calculator will compute

$$\dfrac{n}{100}$$