Chapter 1

What are the principal reasons that one theory might be adopted over a conflicting one?

A common belief among scientists is that there exists an underlying order to nature. Einstein described this belief in the words "God is subtle, but He is not malicious." What do you think Einstein meant by this remark?

Describe several ways in which a scientific law differs from a legislative law.

Describe the necessary characteristics of an experiment that is suitable to test a theory.

Describe the necessary characteristics of a scientific theory.

State whether the following properties of matter are physical or chemical. (a) An iron nail is attracted to a magnet. (b) A piece of paper spontaneously ignites when its temperature reaches \(451^{\circ} \mathrm{F}\). (c) A bronze statue develops a green coating (patina) over time. (d) A block of wood floats on water.

State whether the following properties are physical or chemical. (a) A piece of sliced apple turns brown. (b) A slab of marble feels cool to the touch. (c) A sapphire is blue. (d) A clay pot fired in a kiln becomes hard and covered by a glaze.

Indicate whether each sample of matter listed is a substance or a mixture; if it is a mixture, indicate whether it is homogeneous or heterogeneous. (a) clean fresh air (b) a silver-plated spoon (c) garlic salt (d) ice

Indicate whether each sample of matter listed is a substance or a mixture; if it is a mixture, indicate whether it is homogeneous or heterogeneous. (a) a wooden beam (b) red ink (c) distilled water (d) freshly squeezed orange juice

Suggest physical changes by which the following mixtures can be separated. (a) iron filings and wood chips (b) ground glass and sucrose (cane sugar) (c) water and olive oil (d) gold flakes and water

What type of change-physical or chemical-is necessary to separate the following? [Hint: Refer to a listing of the elements.] (a) sugar from a sand/ sugar mixture (b) iron from iron oxide (rust) (c) pure water from seawater (d) water from a slurry of sand in water

Express each number in exponential notation. (a) \(8950 .;\)(b) \(10,700 . ;(\text { c) } 0.0240 ; \text { (d) } 0.0047 ; \text { (e) } 938.3 ; \text { (f) } 275,482\).

Express each number in common decimal form. (a) \(3.21 \times 10^{-2}\) (b) \(5.08 \times 10^{-4}\) (c) \(121.9 \times 10^{-5}\) (d) \(16.2 \times 10^{-2}\)

Express each value in exponential form. Where appropriate, include units in your answer. (a) speed of sound (sea level): 34,000 centimeters per second (b) equatorial radius of Earth: 6378 kilometers (c) the distance between the two hydrogen atoms in the hydrogen molecule: 74 trillionths of a meter (d) \(\frac{\left(2.2 \times 10^{3}\right)+\left(4.7 \times 10^{2}\right)}{5.8 \times 10^{-3}}=\)

Express each value in exponential form. Where appropriate, include units in your answer. (a) solar radiation received by Earth: 173 thousand trillion watts (b) average human cell diameter: 1 ten-millionth of a meter (c) the distance between the centers of the atoms in silver metal: 142 trillionths of a meter (d) \(\frac{\left(5.07 \times 10^{4}\right) \times\left(1.8 \times 10^{-3}\right)^{2}}{0.065+\left(3.3 \times 10^{-2}\right)}=\)

Indicate whether each of the following is an exact number or a measured quantity subject to uncertainty. (a) the number of sheets of paper in a ream of paper (b) the volume of milk in a liter bottle (c) the distance between Earth and the sun (d) the distance between the centers of the two oxygen atoms in the oxygen molecule

Indicate whether each of the following is an exact number or a measured quantity subject to uncertainty. (a) the number of pages in this text (b) the number of days in the month of January (c) the area of a city lot (d) the distance between the centers of the atoms in a gold medal

Express each of the following to fur significant figures. (a) 3984.6 (b) 422.04 (c) 0.0033 (d) 902.10 (e) 0.02173 (f) 7000 (g) 7.02 (h) 67,000,000

How many significant figures are shown in each of the following? If this is indeterminate, explain why. (a) 450 ; (b) 98.6 ; (c) $0.0033 ; (d) 902.10 ; (e) 0.02173 ; (f) 7000 ; (g) 7.02 ; (h) 67,000,000

Perform the following calculations; express each answer in exponential form and with the appropriate number of significant figures. (a) \(0.406 \times 0.0023=\) (b) \(0.1357 \times 16.80 \times 0.096=\) (c) \(0.458+0.12-0.037=\) (d) \(32.18+0.055-1.652=\)

Perform the following calculations; express each number and the answer in exponential form and with the appropriate number of significant figures. (a) \(\frac{320 \times 24.9}{0.080}=\) (b) \(\frac{432.7 \times 6.5 \times 0.002300}{62 \times 0.103}=\) (c) \(\frac{32.44+4.9-0.304}{82.94}=\) (d) \(\frac{8.002+0.3040}{13.4-0.066+1.02}=\)

Perform the following calculations and retain the appropriate number of significant figures in each result. (a) \(\left(38.4 \times 10^{-3}\right) \times\left(6.36 \times 10^{5}\right)=\) (b) \(\frac{\left(1.45 \times 10^{2}\right) \times\left(8.76 \times 10^{-4}\right)}{\left(9.2 \times 10^{-3}\right)^{2}}=\) (c) \(24.6+18.35-2.98=\) (d) \(\left(1.646 \times 10^{3}\right)-\left(2.18 \times 10^{2}\right)+\left[\left(1.36 \times 10^{4}\right)\right.\) [Hint: The significant figure rule for the extraction of a root is the same as for multiplication.] \(\left.\times\left(5.17 \times 10^{-2}\right)\right]=\) (e) \(\frac{-7.29 \times 10^{-4}+\sqrt{\left(7.29 \times 10^{-4}\right)^{2}+4(1.00)\left(2.7 \times 10^{-5}\right)}}{2 \times(1.00)}\)

Express the result of each of the following calculations in exponential form and with the appropriate number of significant figures. (a) \(\left(4.65 \times 10^{4}\right) \times\left(2.95 \times 10^{-2}\right) \times\left(6.663 \times 10^{-3}\right) \times 8.2=\) (b) \(\frac{1912 \times\left(0.0077 \times 10^{4}\right) \times\left(3.12 \times 10^{-3}\right)}{\left(4.18 \times 10^{-4}\right)^{3}}=\) {c} \(\left(3.46 \times 10^{3}\right) \times 0.087 \times 15.26 \times 1.0023=\) (d) \(\frac{\left(4.505 \times 10^{-2}\right)^{2} \times 1.080 \times 1545.9}{0.03203 \times 10^{3}}=\) (e) \(\frac{\left(-3.61 \times 10^{-4}\right)+\sqrt{\left(3.61 \times 10^{-4}\right)^{2}+4(1.00)\left(1.9 \times 10^{-5}\right)}}{2 \times(1.00)}\) [Hint: The significant figure rule for the extraction of a root is the same as for multiplication.]

An American press release describing the 1986 nonstop, round-the-world trip by the ultra-lightweight aircraft Voyager included the following data: flight distance: \(25,012 \mathrm{mi}\) flight time: 9 days, 3 minutes, 44 seconds fuel capacity: nearly 9000 lb fuel remaining at end of flight: \(14 \mathrm{gal}\) To the maximum number of significant figures permitted, calculate (a) the average speed of the aircraft in kilometers per hour (b) the fuel consumption in kilometers per kilogram of fuel (assume a density of \(0.70 \mathrm{g} / \mathrm{mL}\) for the fuel)

Perform the following conversions. (a) \(0.127 \mathrm{L}=\)_________\(\mathrm{mL}\) (b) \(15.8 \mathrm{mL}=\)_________\(\mathrm{L}\) (c) \(2896 \mathrm{mm}=\)__________\(\mathrm{L}\) (d) \(2.65 \mathrm{m}^{3}=\)__________\(\mathrm{cm}^{3}\)

Perform the following conversions. (a) \(1.55 \mathrm{kg}=\)________\(\mathrm{g}\) (b) \(642 \mathrm{g}=\)________\(\mathrm{kg}\) (c) \(2896 \mathrm{mm}=\)________\(\mathrm{cm}\) (d) \(0.086 \mathrm{cm}=\)________\(\mathrm{mm}\)

Perform the following conversions from non-SI to SI units. (Use information from the inside back cover, as needed.) (a) 68.4 in. \(=\)________cm (b) \(94 \mathrm{ft}=\)________m (c) \(1.42 \mathrm{lb}=\)________g (d) \(248 \mathrm{lb}=\)________kg (e) \(1.85 \mathrm{gal}=\)________dm\(^3\) (f) \(3.72 \mathrm{qt}=\)________mL

Determine the number of the following: (a) square meters \(\left(\mathrm{m}^{2}\right)\) in 1 square kilometer \(\left(\mathrm{km}^{2}\right)\) (b) cubic centimeters \(\left(\mathrm{cm}^{3}\right)\) in 1 cubic meter \(\left(\mathrm{m}^{3}\right)\) (c) square meters \(\left(\mathrm{m}^{2}\right)\) in 1 square mile \(\left(\mathrm{mi}^{2}\right)\) \((1 \mathrm{mi}=5280 \mathrm{ft})\)

Which is the greater mass, \(3245 \mu \mathrm{g}\) or \(0.00515 \mathrm{mg} ?\) Explain.

Which is the greater mass, \(3257 \mathrm{mg}\) or \(0.000475 \mathrm{kg} ?\) Explain.

The non-SI unit, the hand (used by equestrians), is 4 inches. What is the height, in meters, of a horse that stands 15 hands high?

A non-SI unit of mass used in pharmaceutical work is the grain (gr) \((15 \mathrm{gr}=1.0 \mathrm{g}) .\) An aspirin tablet contains 5.0 gr of aspirin. A 155 lb arthritic individual takes two aspirin tablets per day. (a) What is the quantity of aspirin in two tablets, expressed in milligrams? (b) What is the dosage rate of aspirin, expressed in milligrams of aspirin per kilogram of body mass? (c) At the given rate of consumption of aspirin tablets, how many days would it take to consume 1.0 kg of aspirin?

In an engineering reference book, you find that the density of iron is \(0.284 \mathrm{lb} / \mathrm{in.}^{3} .\) What is the density in \(\mathrm{g} / \mathrm{cm}^{3} ?\)

In a user's manual accompanying an American-made automobile, a typical gauge pressure for optimal performance of automobile tires is \(32 \mathrm{lb} / \mathrm{in} .^{2} .\) What is this pressure in grams per square centimeter and kilograms per square meter?

The volume of a red blood cell is about \(90.0 \times 10^{-12} \mathrm{cm}^{3} .\) Assuming that red blood cells are spherical, what is the diameter of a red blood cell in millimeters?

We want to mark off a thermometer in both Celsius and Fahrenheit temperatures. On the Celsius scale, the lowest temperature mark is at \(-10^{\circ} \mathrm{C},\) and the highest temperature mark is at \(50^{\circ} \mathrm{C} .\) What are the equivalent Fahrenheit temperatures?

The highest and lowest temperatures on record for San Bernardino, California, are \(118^{\circ} \mathrm{F}\) and \(17^{\circ} \mathrm{F}\), respectively. What are these temperatures on the Celsius scale?

The absolute zero of temperature is \(-273.15^{\circ} \mathrm{C}\) Should it be possible to achieve a temperature of \(-465^{\circ} \mathrm{F} ?\) Explain.

A family/consumer science class is given an assignment in candy-making that requires a sugar mixture to be brought to a "soft-ball" stage \(\left(234-240^{\circ} \mathrm{F}\right)\). A student borrows a thermometer having a range from \(-10^{\circ} \mathrm{C}\) to \(110^{\circ} \mathrm{C}\) from the chemistry laboratory to do this assignment. Will this thermometer serve the purpose? Explain.

You decide to establish a new temperature scale on which the melting point of mercury \(\left(-38.9^{\circ} \mathrm{C}\right)\) is \(0^{\circ} \mathrm{M},\) and the boiling point of mercury \(\left(356.9^{\circ} \mathrm{C}\right)\) is \(100^{\circ} \mathrm{M} .\) What would be (a) the boiling point of water in \(^{\circ} \mathrm{M} ;\) and \((\mathrm{b})\) the temperature of absolute zero in \(^{\circ}\text{M}\)?

You decide to establish a new temperature scale on which the melting point of ammonia \(\left(-77.75^{\circ} \mathrm{C}\right)\) is \(0^{\circ}\) A and the boiling point of ammonia \(\left(-33.35^{\circ} \mathrm{C}\right)\) is \(100^{\circ}\) A. What would be (a) the boiling point of water in \(^{\circ}$$\text{A}\); and (b) the temperature of absolute zero in \(^{\circ}$$\text{A}\)?

A 2.18 L sample of butyric acid, a substance present in rancid butter, has a mass of 2088 g. What is the density of butyric acid in grams per milliliter?

A 15.2 L sample of chloroform at \(20^{\circ} \mathrm{C}\) has a mass of 22.54 kg. What is the density of chloroform at \(20^{\circ} \mathrm{C}\), in grams per milliliter?

To determine the volume of an irregularly shaped glass vessel, the vessel is weighed empty \((121.3 \mathrm{g})\) and when filled with carbon tetrachloride (283.2 g). What is the volume capacity of the vessel, in milliliters, given that the density of carbon tetrachloride is \(1.59 \mathrm{g} / \mathrm{mL} ?\)

A solution consisting of \(8.50 \%\) acetone and \(91.5 \%\) water by mass has a density of \(0.9867 \mathrm{g} / \mathrm{mL} .\) What mass of acetone, in kilograms, is present in 7.50 L of the solution?

A solution contains \(10.05 \%\) sucrose (cane sugar) by mass. What mass of the solution, in grams, is needed for an application that requires \(1.00 \mathrm{kg}\) sucrose?

A fertilizer contains \(21 \%\) nitrogen by mass. What mass of this fertilizer, in kilograms, is required for an application requiring \(225 \mathrm{g}\) of nitrogen?

A vinegar sample is found to have a density of \(1.006 \mathrm{g} / \mathrm{mL}\) and to contain \(5.4 \%\) acetic acid by mass. How many grams of acetic acid are present in \(1.00 \mathrm{L}\) of this vinegar?

Calculate the mass of a block of iron \(\left(d=7.86 \mathrm{g} / \mathrm{cm}^{3}\right)\) with dimensions of \(52.8 \mathrm{cm} \times 6.74 \mathrm{cm} \times 3.73 \mathrm{cm}\).

Calculate the mass of a cylinder of stainless steel \(\left(d=7.75 \mathrm{g} / \mathrm{cm}^{3}\right)\) with a height of \(18.35 \mathrm{cm}\) and a radius of \(1.88 \mathrm{cm}\).