Chapter 1

A brand new silver U.S. dollar weighs 0.934 oz. Express this mass in grams and kilograms. \((1 \mathrm{oz}=28.35 \mathrm{g} .)\)

A U.S. dime weighs \(2.5 \mathrm{g} .\) What is the U.S. dollar value of exactly \(1 \mathrm{kg}\) of dimes?

What volume of gold would be equal in mass to a piece of copper with a volume of \(125 \mathrm{cm}^{3} ?\)

What is the volume of \(1.00 \mathrm{kg}\) of mercury?

A student wonders whether a piece of jewelry is made of pure silver. She determines that its mass is \(3.17 \mathrm{g} .\) Then she drops it into a 10 -mL graduated cylinder partially filled with water and determines that its volume is \(0.3 \mathrm{mL}\). Could the jewelry be made of pure silver?

The average density of Earth is \(5.5 \mathrm{g} / \mathrm{cm}^{3} .\) The mass of Venus is \(81.5 \%\) of Earth's mass, and the volume of Venus is \(88 \%\) of Earth's volume. What is the density of Venus?

The sun is a sphere with an estimated mass of \(2 \times 10^{30} \mathrm{kg} .\) If the radius of the sun is \(7.0 \times 10^{5} \mathrm{km}\) what is the average density of the sun in units of grams per cubic centimeter? The volume of a sphere is \(\frac{4}{3} \pi r^{3}\)

Which of the following numbers have just three significant figures? (a) \(7.02 ;\) (b) \(6.452 ;\) (c) \(302 ;\) (d) \(6.02 \times 10^{23}\) (c) \(12.77 ;\) (f) 3.43

Which of the following numbers have four significant figures? (a) \(0.0592 ;\) (b) \(0.08206 ;\) (c) \(8.314 ;\) (d) 273.15 (e) \(5.091 \times 10^{3} ;\) (f) 9.490

Perform each of the following calculations and express the answer with the correct number of significant figures: a. \(3.15 \times 2255 / 7.7=\) b. \(\left(6.7399 \times 10^{-18}\right) \times\left(1.0135 \times 10^{3}\right) /(52.67+0.144)=\) c. \((4.7+58.69) /\left(6.022 \times 10^{23} \times 6.864\right)=\) d. \((76.2-60.0) /\left[43.53 \times\left(9.988 \times 10^{4}\right)\right]=\)

Perform each of the following calculations, and express the answer with the correct number of significant figures: a. \([(12 \times 60.0)+55.3] /\left(5.000 \times 10^{3}\right)=\) b. \(3.1416 \times(2.031)^{2} \times 3.75 \times 8.00=\) c. The number of cubic centimeters in 389 cubic inches d. The average (mean) of \(8.7,8.5,8.5,8.9,\) and 8.8

Liquid helium boils at \(4.2 \mathrm{K}\). What is the boiling point of helium in degrees Celsius?

Liquid hydrogen boils at \(-253^{\circ} \mathrm{C} .\) What is the boiling point of \(\mathrm{H}_{2}\) on the Kelvin scale?

Ethyl chloride acts as a mild topical anesthetic because it chills the skin when sprayed on it. It dulls the pain of injury and is sometimes used to make removing splinters easier. The boiling point of ethyl chloride is \(12.3^{\circ} \mathrm{C} .\) What is its boiling point on the Fahrenheit and Kelvin scales?

The temperature of the dry ice (solid carbon dioxide) in ice cream vending carts is \(-78^{\circ} \mathrm{C} .\) What is this temperature on the Fahrenheit and Kelvin scales?

The highest temperature ever recorded in the United States is $134^{\circ} \mathrm{F}\( at Greenland Ranch, Death Valley, California, on July \)13,1913 .$ What is this temperature on the Celsius and Kelvin scales?

Which confidence interval is the largest for a given value of \(n: 50 \%, 90 \%,\) or \(95 \% ?\)

The concentration of ammonia in an aquarium tank is determined each day for a week. Which of these measures of the variability in the results of these analyses is greater: (a) mean \(\pm\) standard deviation, or (b) \(95 \%\) confidence interval? Explain your selection.

If the results of Grubbs' test indicate that a suspect data point is not an outlier at the \(95 \%\) confidence level, could it be one at the \(99 \%\) confidence level?

Glucose concentrations in the blood above \(110 \mathrm{mg} / \mathrm{dL}\) can be an early indication of several medical conditions, including diabetes. Suppose analyses of a series of blood samples from a patient at risk of diabetes produce the following results: \(106,99,109,108,\) and \(105 \mathrm{mg} / \mathrm{dL}\) a. What are the mean and the standard deviation of the data? b. Patients with blood glucose levels above \(120 \mathrm{mg} / \mathrm{dL}\) are considered diabetic. Is this value within the \(95 \%\)confidence interval of these data?

Use Grubbs' test to decide whether the value 3.41 should be considered an outlier in the following data set from the analyses of portions of the same sample conducted by six groups of students: 3.15,3.03,3.09,3.11,3.12 and 3.41

Use Grubbs' test to decide whether any one of the values in the following set of replicate measurements should be considered an outlier: \(61,75,64,65,64,\) and 66.

A farmer applies 1.50 metric tons of a fertilizer that contains \(10 \%\) nitrogen to his fields each year (1 metric ton \(=1000 \mathrm{kg}\) ). Fifteen percent of the fertilizer washes into a stream that runs through the farm. If the stream flows at an average rate of 1.4 cubic meters per minute, what is the additional concentration of nitrogen (expressed in milligrams of nitrogen per liter) in the stream water due to the farmer's yearly application of fertilizer?

Table salt contains \(1.54 \mathrm{g}\) of chlorine (as chloride ions) for every \(1.00 \mathrm{g}\) of sodium ions. Which of the following mixtures would react to produce NaCl with no sodium or chlorine left over? a. \(11.0 \mathrm{g}\) of sodium and \(17.0 \mathrm{g}\) of chlorine b. 6.5 g of sodium and \(10.0 \mathrm{g}\) of chlorine c. \(6.5 \mathrm{g}\) of sodium and \(12.0 \mathrm{g}\) of chlorine d. \(6.5 \mathrm{g}\) of sodium and \(8.0 \mathrm{g}\) of chlorine

Gasoline and water are immiscible. Regular-grade (87 octane) gasoline has a lower density \((0.73 \mathrm{g} / \mathrm{mL})\) than water \((1.00 \mathrm{g} / \mathrm{mL}) .\) A \(100-\mathrm{mL}\) graduated cylinder with an inside diameter of \(3.2 \mathrm{cm}\) contains \(34.0 \mathrm{g}\) of gasoline and \(34.0 \mathrm{g}\) of water. What is the combined height of the two liquid layers in the cylinder? The volume of a cylinder is \(\pi r^{2} b,\) where \(r\) is the radius and \(b\) is the height.

In 1999 a drug overdose incident occurred when a prescription that called for a patient to receive 0.5 grain of the powerful sedative phenobarbital each day was misread, and the patient was given 0.5 gram of the drug. Actually, four intravenous injections of 130 mg each were administered each day for 3 days. How many times as much phenobarbital was administered with respect to the prescribed amount? \((1 \text { grain }=64.79891 \mathrm{mg}\).)