Energy consumption in the United States amounts to the equivalent of the energy obtained by burning 7.0 gal of oil or 70. lb of coal per day per person. Using data in Table 20.4, carry out calculations to show that the energy evolved from these quantities of oil and coal is approximately equivalent. The density of fuel oil is approximately 0.8 g/mL. (1.00 gal = 3.785 L and 1.00 lb = 454 g)

Hydrogen can be produced using the reaction of steam (H$_2$O) with various hydrocarbons. Compare the mass of H$_2$ expected from the reaction of steam with 100.g each of methane, petroleum, and coal. (Assume complete reaction in each case. Use CH$_2$ and C as the representative formulas for petroleum and coal, respectively.)

Silver ions have long been known to have biocidal properties. The increasing use of silver for this purpose has led to greater silver concentrations in waste water, and there has been several concern regarding it. However, recent studies revealed that the silver was largely put back into the environment as ${Ag}_2 {~S}$. The solubility of this sulfide is $1.4 \times 10^{-4} {~g} / {L}$.

(a) Calculate the $K_{\text {sp }}^{\prime}$ for ${Ag}_2 {~S}$.

(b) How does the solubility of ${Ag}_2 {~S}$ change as the pH decreases?

A 2010 article in Science magazine described "Sewage Treatment with Anammox." The authors noted that "Fixed nitrogen such as ammonium and nitrate [ions] should be removed [from sewage] to avoid toxic algal blooms in the environment." One approach to removing ammonium ions is to use ammonium-oxidizing (anammox) bacteria. Two (unbalanced) reactions that are involved are:

$$\begin{aligned} & {NH}_4{ }^{+}({aq})+{NO}_2{ }^{-}({aq}) \rightarrow {N}_2({~g})+{H}_2 {O}(\ell) \\ & {NH}_4{ }^{+}({aq})+{O}_2({~g}) \rightarrow {NO}_2{ }^{-}({aq})+{H}_2 {O}(\ell) \end{aligned}$$

Balance these two equations in acid solution.

Calculate the mass of Mg that could be obtained by the process described in previous study question from 1.0 L of seawater. To prepare 100. kg of Mg, what volume of seawater would be needed? (The density of seawater is 1.025 g/cm$^3$.)

Although there are a number of magnesium containing minerals, the commercial source of this metal is seawater. Treatment of seawater with Ca(OH)$_2$ gives insoluble Mg(OH)$_2$. This reacts with HCl to produce MgCl$_2$, which is dried, and the metal is obtained by electrolysis of the molten salt. Write balanced net ionic equations for the three reactions described here.

In any solution, there must be a balance between the positive and negative charges of the ions that are present. Use the data in Table 20.2 to determine how close to a balance of charge is achieved for the ions in seawater. (The table lists only the major ions in seawater, and the balance between positive and negative charge will only be approximate.)

The food-frequency questionnaire (FFQ) is an instrument often used in dietary epidemiology to assess consumption of specific foods. A person is asked to write down the number of servings per day typically eaten in the past year of over 100 individual food items. A food-composition table is then used to compute nutrient intakes (protein, fat, etc.) based on aggregating responses for individual foods. The FFQ is inexpensive to administer but is considered less accurate than the diet record (DR) (the gold standard of dietary epidemiology). For the DR, a participant writes down the amount of each specific food eaten over the past week in a food diary and a nutritionist using a special computer program computes nutrient intakes from the food diaries. This is a much more expensive method of dietary recording. To validate the FFO, 173 nurses participating in the Nurses' Health Study completed 4 weeks of diet recording about equally spaced over a 12 -month period and an $\mathrm{FFO}$ at the end of diet recording. Data are presented in data set VALID.DAT at www.cengagebrain.com for saturated fat, total fat, total alcohol consumption, and total caloric intake for both the DR and FFQ. For the DR, average nutrient intakes were computed over the 4 weeks of diet recording. The table below shows the format of this file.

Format for VALID.DAT

Relate the nutrient density for total fat for the DR versus the FFQ using the quintile approach in the previous problem. Is the concordance between total fat for DR and FFQ stronger, weaker, or the same when total fat is expressed in terms of nutrient density as opposed to raw nutrient?

Given are several gasoline vehicles and their fuel consumption averages.

$$\begin{array}{ll} \text { Buick } & 27 \mathrm{mpg} \\ \text { BMW } & 28 \mathrm{mpg} \\ \text { Honda Civic } & 35 \mathrm{mpg} \\ \text { Geo } & 46 \mathrm{mpg} \\ \text { Neon } & 38 \mathrm{mpg} \\ \text { Land Rover } & 16 \mathrm{mpg} \end{array}$$

Could a histogram be used in this case? Why or why not?

Suppose that the following behavioural equations best describe the economy:

$$\begin{aligned} C &=c_0+c_1 Y_D \\ Y_D &=Y-T \\ I &=b_0+b_1 Y \end{aligned}$$

Government spending and taxes are constant. Assume if customers elected to increase their consumption expenditure, which would result in a rise in c0. What impact would this have had on private saving, investment, and output? Explain. What would have happened to the amount consumed?

Suppose that the consumption matrix for the linear production model is

$$\left[\begin{array}{ll} 1 & 1 \\ \frac{1}{2} & \frac{1}{2} \end{array}\right] \text {. }$$

(a) Find the production vector for the dernand vector

$$\left[\begin{array}{l}1 \\ 3\end{array}\right]$$

. (b) Find the production vector for the demand vector

$$\left[\begin{array}{l}2 \\ 0\end{array}\right]$$

.

Energy use: A sample of $10$ households was monitored for one year. The household income (in $\$1000s$) and the amount of energy consumed (in $1010$ joules) were determined. The results follow.

$$\begin{array}{cccc} \hline \textbf{Income} & \textbf{Energy} \hspace{25pt} & \textbf{Income} & \textbf{Energy}\\ \hline 31 & 16.0 \hspace{25pt} & 96 & 98.3\\ 40 & 40.2 \hspace{25pt} & 70 & 93.8\\ 28 &29.8 \hspace{25pt} & 100 & 77.1\\ 48 & 45.6 \hspace{25pt} & 145 & 114.8\\ 195 & 184.6 \hspace{25pt} & 78 & 67.0\\ \hline \end{array}$$

$\textbf{a.}\hspace{10pt}$ Compute the least-squares line for predicting energy consumption $(y)$ from income $(x)$.

$\textbf{b.}\hspace{10pt}$ Compute a $95\%$ confidence interval for the slope.

$\textbf{c.}\hspace{10pt}$ Test $H_0: \beta_1 = 0$ versus $H_1: \beta_1 > 0$. Can you conclude that income is useful in predicting energy consumption? Use the $\alpha = 0.01$ level of significance.

Olestra is a fat substitute approved by the FDA for use in snack foods. Because there have been anecdotal reports of gastrointestinal problems associated with olestra consumption, a randomized, double-blind, placebo-controlled experiment was carried out to compare olestra potato chips to regular potato chips with respect to GI symptoms (“Gastrointestinal Symptoms Following Consumption of Olestra or Regular Triglyceride Potato Chips,” J. of the Amer. Med. Assoc., 1998: 150–152). Among 529 individuals in the TG control group, 17.6% experienced an adverse GI event, whereas among the 563 individuals in the olestra treatment group, 15.8% experienced such an event. a. Carry out a test of hypotheses at the 5% significance level to decide whether the incidence rate of GI problems for those who consume olestra chips according to the experimental regimen differs from the incidence rate for the TG control treatment. b. If the true percentages for the two treatments were 15% and 20%, respectively, what sample sizes (m=n) would be necessary to detect such a difference with probability .90?

River Queen Corporation began operations early in the current year, building luxury boats. During the year, the company started and completed 40 boats at a cost of $\$ 80,000$ per unit. Of these, 30 were sold for $\$ 130,000$ each and 10 remain in finished goods inventory. In addition, the company had five partially completed units in its factory at year-end. Total costs for the year (summarized alphabetically) were as follows:

Compute the following for the current year:

d. Gross profit on sales.