Solved: How much time (in years) does an 80-year-old

Three apprentice tailors (\(X\), \(Y\), and \(Z\)) are assigned the task of measuring the seam of a pair of trousers. Each one makes three measurements. The results in inches are \(X\) (31.5, 31.6, 31.4); \(Y\) (32.8, 32.3, 32.7); \(Z\) (31.9, 32.2, 32.1). The true length is 32.0 in. Comment on the precision and the accuracy of each tailor’s measurements.

Carry out the following conversions: (a) 22.6 m to decimeters, (b) 25.4 mg to kilograms, (c) 556 mL to liters, (d) 10.6 \(\mathrm{kg}/\mathrm{m}^3\) to \(\mathrm{g}/\mathrm{cm}^3\).

Carry out the following conversions: (a) 242 lb to milligrams, (b) 68.3 \(\mathrm{cm}^{3}\) to cubic meters, (c) 7.2 \(\mathrm{m}^{3}\) to liters, (d) 28.3 µg to pounds.

The average speed of helium at \(25^{\circ} \mathrm{C}\) is \(1255 \mathrm{~m} / \mathrm{s}\). Convert this speed to miles per hour (mph).

How many seconds are there in a solar year (365.24 days)?

How many minutes does it take light from the sun to reach Earth? (The distance from the sun to Earth is 93 million mi; the speed of light = \(3.00\times10^8\mathrm{\ m}/\mathrm{s}\).)

A jogger runs a mile in 8.92 min. Calculate the speed in (a) in/s, (b) m/min, (c) km/h. (1 mi = 1609 m; 1 in = 2.54 cm.)

A 6.0-ft person weighs 168 lb. Express this person’s height in meters and weight in kilograms. (1 lb = 453.6 g; 1 m = 3.28 ft.)

The speed limit on parts of the German autobahn was once set at 286 kilometers per hour (km/h). Calculate the speed limit in miles per hour (mph).

For a fighter jet to take off from the deck of an aircraft carrier, it must reach a speed of 62 m/s. Calculate the speed in miles per hour (mph)

The “normal” lead content in human blood is about 0.40 part per million (that is 0.40 g of lead per million grams of blood). A value of 0.80 part per million (ppm) is considered to be dangerous. How many grams of lead are contained in \(6.0\times10^3\mathrm{\ g}\) of blood (the amount in an average adult) if the lead content is 0.62 ppm?

Carry out the following conversions: (a) 1.42 light- years to miles (a light-year is an astronomical measure of distance—the distance traveled by light in a year, or 365 days; the speed of light is \(3.00 \times 10^{8}\) m/s). (b) 32.4 yd to centimeters, (c) \(3.0 \times 10^{10}\) cm/s to ft/s.

Carry out the following conversions: (a) 70 kg, the average weight of a male adult, to pounds. (b) 14 billion years (roughly the age of the universe) to seconds. (Assume there are 365 days in a year.) (c) 7 ft 6 in, the height of the basketball player Yao Ming, to meters. (d) \(88.6\mathrm{\ m}^3\) to liters.

Aluminum is a lightweight metal (density = 2.70 \(\mathrm{g}/\mathrm{cm}^3\)) used in aircraft construction, high-voltage transmission lines, beverage cans, and foils. What is its density in \(\mathrm{kg}/\mathrm{m}^3\)?

The density of ammonia gas under certain conditions is 0.625 g/L. Calculate its density in \(\mathrm{g} / \mathrm{cm}^{3}\)

Give one qualitative and one quantitative statement about each of the following: (a) water, (b) carbon, (c) iron, (d) hydrogen gas, (e) sucrose (cane sugar), (f) table salt (sodium chloride), (g) mercury, (h) gold, (i) air.

Which of the following statements describe physical properties and which describe chemical properties? (a) Iron has a tendency to rust, (b) Rainwater in industrialized regions tends to be acidic, (c) Hemoglobin molecules have a red color, (d) When a glass of water is left out in the sun, the water gradually disappears, (e) Carbon dioxide in air is converted to more complex molecules by plants during photosynthesis.

In 2008, about 95.0 billion lb of sulfuric acid were produced in the United States. Convert this quantity to tons.

In determining the density of a rectangular metal bar. a student made the following measurements: length, 8.53 cm; width, 2.4 cm; height, 1.0 cm; mass, 52.7064 g. Calculate the density of the metal to the correct number of significant figures.

Calculate the mass of each of the following: (a) a sphere of gold with a radius of 10.0 cm [the volume of a sphere with a radius r is \(V=(4 / 3) \pi r^{3}\); the density of gold = \(19.3\mathrm{\ g}/\mathrm{cm}^3\)], (b) a cube of platinum of edge length 0.040 mm (the density of platinum = \(21.4\mathrm{\ g}/\mathrm{cm}^3\)), (c) 50.0 mL of ethanol (the density of ethanol = 0.798 g/mL).

A cylindrical glass bottle 21.5 cm in length is filled with cooking oil of density 0.953 g/mL. If the mass of the oil needed to fill the bottle is 1360 g, calculate the inner diameter of the bottle.

The following procedure was used to determine the volume of a flask. The flask was weighed dry and then filled with water. If the masses of the empty flask and filled flask were 56.12 g and 87.39 g, respectively, and the density of water is 0.9976 \(\mathrm{g}/\mathrm{cm}^3\), calculate the volume of the flask in \(\mathrm{cm}^{3}\).

The speed of sound in air at room temperature is about 343 m/s. Calculate this speed in miles per hour. (1 mi = 1609 m.)

A piece of silver (Ag) metal weighing 194.3 g is placed in a graduated cylinder containing 242.0 mL of water. The volume of water now reads 260.5 mL. From these data calculate the density of silver.

The experiment described in Problem 1.61 is a crude but convenient way to determine the density of some solids. Describe a similar experiment that would enable you to measure the density of ice. Specifically, what would be the requirements for the liquid used in your experiment?

A lead sphere of diameter 48.6 cm has a mass of \(6.852 \times 10^{5}\) g. Calculate the density of lead.

Lithium is the least dense metal known (density: \(0.53 \mathrm{g} / \mathrm{cm}_{3}\)). What is the volume occupied by \(1.20 \times 10^{3} \mathrm{g}\) of lithium?

The medicinal thermometer commonly used in homes can be read \(\pm 0.1^{\circ} \mathrm{F}\), whereas those in the doctor's office may be accurate to \(\pm 0.1^{\circ} \mathrm{C}\). In degrees Celsius, express the percent error expected from each of these thermometers in measuring a person's body temperature of \(38.9^{\circ} \mathrm{C}\).

Vanillin (used to flavor vanilla ice cream and other foods) is the substance whose aroma the human nose detects in the smallest amount. The threshold limit is \(2.0\times10^{-11}\ g\) per liter of air. If the current price of 50 g of vanillin is $112. determine the cost to supply- enough vanillin so that the aroma could be detected in a large aircraft hangar with a volume of \(5.0 \times 10^{7} \mathrm{ft}^{3}\).

At what temperature does the numerical reading on a Celsius thermometer equal that on a Fahrenheit thermometer?

Suppose that a new temperature scale has been devised on which the melting point of ethanol (-117.3°C) and the boiling point of ethanol (78.3°C) are taken as 0°S and 100°S, respectively, where S is the symbol for the new temperature scale. Derive an equation relating a, reading on this scale to a reading on the Celsius scale. What would this thermometer read at 25°C?

A resting adult requires about 240 mL of pure oxygen/ min and breathes about 12 times every minute. If inhaled air contains 20 percent oxygen by volume and exhaled air 16 percent, what is the volume of air per breath? (Assume that the volume of inhaled air is equal to that of exhaled air.)

(a) Referring to Problem 1.69, calculate the total volume (in liters) of air an adult breathes in a day. (b) In a city with heavy traffic, the air contains \(2.1\times10^{-6}\mathrm{\ L}\) of carbon monoxide (a poisonous gas) per liter. Calculate the average daily intake of carbon monoxide in liters by a person.

Three different 25.0-g samples of solid pellets are added to 20.0 mL of water in three different measuring cylinders. The results are shown here. Given the densities of the three metals used, identify each sample of solid pellets: \(\text{ A }\ (2.9\mathrm{\ g}/\mathrm{cm})\), \(\text{ B }\ \left(8.3\mathrm{\ g}/\mathrm{cm}^3\right)\), and \(\mathrm{C}\ \left(3.3\mathrm{\ g}/\mathrm{cm}^3\right)\).

A student is given a crucible and asked to prove whether it is made of pure platinum. She first weighs the crucible in air and then weighs it suspended in water (density = 0.9986 g/mL). The readings are 860.2 g and 820.2 g, respectively. Based on these measurements and given that the density of platinum is \(21.45\mathrm{\ g}/\mathrm{cm}^3\), what should her conclusion be? (Hint: An object suspended in a fluid is buoyed up by the mass of the fluid displaced by the object. Neglect the buoyance of air.)

The surface area and average depth of the Pacific Ocean are \(1.8\times10^8\mathrm{\ km}^2\) and \(3.9\times10^3\mathrm{\ m}\), respectively. Calculate the volume of water in the ocean in liters.

The unit "troy ounce" is often used for precious metals such as gold (Au) and platinum (Pt). (1 troy ounce = 31.103 g.) (a) A gold coin weighs 2.41 troy ounces. Calculate its mass in grams. (b) Is a troy ounce heavier or lighter than an ounce? (1 lb = 16 oz; 1 lb = 453.6 g.)

Osmium (Os) is the densest element known (density = 22.57 \(\mathrm{g}/\mathrm{cm}^3\)). Calculate the mass in pounds and in kilograms of an Os sphere 15 cm in diameter (about the size of a grapefruit). See Problem 1.57 for volume of a sphere.

Percent error is often expressed as the absolute value of the difference between the true value and the experimental value, divided by the true value: \(\text { percent error }=\frac{\mid \text { true value }-\text { experimental value } \mid}{\mid \text { true value } \mid} \times 100 \%\) The vertical lines indicate absolute value. Calculate the percent error for the following measurements: (a) The density of alcohol (ethanol) is found to be 0.802 g/mL. (True value: 0.798 g/mL.) (b) The mass of gold in an earring is analyzed to be 0.837 g. (True value: 0.864 g.)

The natural abundances of elements in the human body, expressed as percent by mass, are: oxygen (O), 65 percent; carbon (C), 18 percent; hydrogen (H), 10 percent; nitrogen (N), 3 percent; calcium (Ca), 1.6 percent; phosphorus (P), 1.2 percent; all other elements, 1.2 percent. Calculate the mass in grams of each element in the body of a 62-kg person.

The men's world record for running a mile outdoors (as of 1999) is 3 min 43.13 s. At this rate, how long would it take to run a 1500-m race? (1 mi = 1609 m.)

Venus, the second closest planet to the sun, has a surface temperature of \(7.3\times10^2\mathrm{\ K}\). Convert this temperature to \({ }^{\circ} \mathrm{C}\) and \({ }^{\circ} \mathrm{F}\).

Chalcopyrite, the principal ore of copper (Cu). contains 34.63 percent Cu by mass. How many grams of Cu can be obtained from \(5.11\times10^3\mathrm{\ kg}\) of the ore?

It has been estimated that \(8.0\times10^4\) tons of gold (Au) have been mined. Assume gold costs $948 per ounce. What is the total worth of this quantity of gold?

Measurements show that 1.0 g of iron (Fe) contains \(1.1 \times 10^{22}\) Fe atoms. How many Fe atoms are in 4.9 g of Fe, which is the total amount of iron in the body of an average adult?

A 1.0-mL volume of seawater contains about \(4.0\times10^{-12}\mathrm{\ g}\) of gold. The total volume of ocean water is \(1.5\times10^{21}\mathrm{\ L}\). Calculate the total amount of gold (in grams) that is present in seawater, and the worth of the gold in dollars (see Problem 1.82). With so much gold out there, why hasn't someone become rich by mining gold from the ocean?

The thin outer layer of Earth, called the crust, contains only 0.50 percent of Earth's total mass and yet is the source of almost all the elements (the atmosphere provides elements such as oxygen, nitrogen, and a few other gases). Silicon (Si) is the second most abundant element in Earth's crust (27.2 percent by mass). Calculate the mass of silicon in kilograms in Earth's crust. (The mass of Earth is \(5.9 \times 10^{21}\) tons. 1 ton = 2000 lb; 1 lb = 453.6 g.)

The radius of a copper (Cu) atom is roughly \(1.3 \times10^{-10}\) m. How many times can you divide evenly a piece of 10-cm copper wire until it is reduced to two separate copper atoms? (Assume there are appropriate tools for this procedure and that copper atoms are lined up in a straight line, in contact with each other. Round off your answer to an integer.)

One gallon of gasoline in an automobile's engine produces on the average 9.5 kg of carbon dioxide, which is a greenhouse gas, that is, it promotes the warming of Earth's atmosphere. Calculate the annual production of carbon dioxide in kilograms if there are 40 million cars in the United States and each car covers a distance of 5000 mi at a consumption rate of 20 miles per gallon.

A sheet of aluminum (Al) foil has a total area of 1.000 \(\mathrm{ft}^{2}\) and a mass of 3.636 g. What is the thickness of the foil in millimeters? (Density of Al = 2.699 \(\mathrm{g} / \mathrm{cm}^{3}\).)

Explain what is meant by the scientific method.

A piece of platinum metal with a density of \(21.5\mathrm{\ g}/\mathrm{cm}^3\) has a volume of \(4.49\mathrm{\ cm}^3\). What is its mass?

Which of the following statements is true? (a) A hypothesis always leads to the formulation of a law. (b) The scientific method is a rigid sequence of steps in solving problems. (c) A law summarizes a series of experimental observations; a theory provides an explanation for the observations.

What is the difference between qualitative data and quantitative data?

The density of the sulfuric acid in a certain car battery is 1.41 g/mL. Calculate the mass of 242 mL of the liquid.

Classify the following as qualitative or quantitative statements, giving your reasons. (a) The sun is approximately 93 million mi from Earth. (b) Leonardo da Vinci was a better painter than Michelangelo. (c) Ice is less dense than water. (d) Butter tastes better than margarine. (e) A stitch in time saves nine.

Which of the following diagrams represent elements and which represent compounds? Each color sphere (or truncated sphere) represents an atom

Convert (a) \(327.5^{\circ} \mathrm{C}\) (the melting point of lead) to degrees Fahrenheit; (b) \(172.9^{\circ} \mathrm{F}\) (the boiling point of ethanol) to degrees Celsius; and (c) 77 K, the boiling point of liquid nitrogen, to degrees Celsius.

An ice cube is placed in a closed container. On heating, the ice cube first melts and the water then boils to form steam. Which of the following statements is true? (a) The physical appearance of the water is different at every stage of change. (b) The mass of water is greatest for the ice cube and least for the steam.

Classify each of the following statements as a hypothesis, a law, or a theory. (a) Beethoven’s contribution to music would have been much greater if he had married. (b) An autumn lead gravitates toward the ground because there is an attractive force between the leaf and Earth. (c) All matter is composed of very small particles called atoms.

Determine the number of significant figures in each of the following measurements: (a) 24 mL, (b) 3001 g, (c) \(0.0320\mathrm{\ m}^3\), (d) \(6.4 \times 10^{4}\) molecules, (e) 560 kg.

The diagram is (a) shows a compound made up of atoms of two elements (represented by the green and red spheres) in the liquid state. Which of the diagrams in (b)-(d) represents a physical change and which diagrams represent a chemical change?

Given an example for each of the following terms: (a) matter, (b) substance, (c) mixture.

Carry out the following arithmetic operations and round off the answers to the appropriate number of significant figures: (a) \(26.5862 \mathrm{~L}+0.17 \mathrm{~L}\), (b) \(9.1 \mathrm{~g}-4.682 \mathrm{~g}\), (c) \(7.1 \times 10^{4} \mathrm{dm} \times 2.2654 \times 10^{2} \mathrm{dm}\), (d) \(6.54 \mathrm{~g} \div 86.5542 \mathrm{~mL}\), (e) \(\left(7.55 \times 10^{4} \mathrm{~m}\right)-\left(8.62 \times 10^{3} \mathrm{~m}\right)\).

The density of copper is \(8.94\mathrm{\ g}/\mathrm{cm}^3\) at \(20^{\circ} \mathrm{C}\) and \(8.91\mathrm{\ g}/\mathrm{cm}^3\) at \(60^{\circ}\). This density decrease is the result of which of the following? (a) The metal expands. (b) The metal contracts. (c) The mass of the metal increases. (d) The mass of the metal decreases.

Give an example of a homogeneous mixture and an example of a heterogeneous mixture.

A roll of aluminum foil has a mass of 1.07 kg. What is its mass in pounds?

Using the examples, explain the difference between a physical property and a chemical property.

The volume of a room is \(1.08\times10^8\mathrm{\ dm}^3\), What is the volume in \(\mathrm{m}^{3}\)?

How does an intensive property differ from an extensive property? Which of the following properties are intensive and which are extensive? (a) length, (b) volume, (c) temperature, (d) mass.

The density of the lightest metal, lithium (Li ), is \(5.34\times10^2\mathrm{\ kg}/\mathrm{m}^3\). Convert the density to \(\mathrm{g} / \mathrm{cm}^{3}\).

Give an example of an element and a compound. How do elements and compounds differ?

Problem 9PE Give an example of an element and a compound. How do elements and compounds differ?

What is the number of known elements?

Do the following statements describe chemical or physical properties? (a) Oxygen gas supports combustion. (b) Fertilizers help to increase agricultural production, (c) Water boils below 100°C on top of a mountain, (d) Lead is denser than aluminum, (e) Uranium is a radioactive element.

Does each of the following describe a physical change or a chemical change? (a) The helium gas inside a balloon tends to leak out after a few hours. (b) A flashlight beam slowly gets dimmer and finally goes out. (c) Frozen orange juice is reconstituted by adding water to it. (d) The growth of plants depends on the sun’s energy in a process called photosynthesis. (e) A spoonful of table salt dissolves in a bowl of soup.

Problem 13P Give the names of the elements represented by the chemical symbols Li, F, P, Cu, As, Zn, CI, Pt, Mg. U. Al. Si, Ne. (See Table 1.1 and the inside front cover.)

Give the chemical symbols for the following elements: (a) cesium, (b) germanium, (c) gallium, (d) strontium, (e) uranium, (f) selenium, (g) neon, (h) cadmium. (See Table 1.1 and the inside front cover.)

Classify each of the following substances as an element or a compound: (a) hydrogen, (b) water, (c) gold, (d) sugar.

Classify each of the following as an element, a compound, a homogeneous mixture, or a heterogeneous mixture: (a) water from a well, (b) argon gas, (c) sucrose, (d) a bottle of red wine, (e) chicken noodle soup, (f) blood flowing in a capillary, (g) ozone.

Name the SI base units that are important in chemistry. Give the SI units for expressing the following: (a) length, (b) volume, (c) mass, (d) time, (e) energy, (f) temperature.

Write the numbers represented by the following prefixes: (a) mega-, (b) kilo-, (c) deci-, (d) centi-, (e) milli-, (f) micro-, (g) nano-, (h) pico-.

What units do chemists normally use for density of liquids and solids? For gas density? Explain the differences.

Describe the three temperature scales used in the laboratory and in everyday life: the Fahrenheit scale, the Celsius scale, and the Kelvin scale.

The density of methanol, a colorless organic liquid used as solvent, is 0.7918 g/mL. Calculate the mass of 89.9 mL of the liquid.

Bromine is a reddish-brown liquid. Calculate its density (in g/mL) if 586 g of the substance occupies 188 mL.

Convert the following temperatures to degrees Celsius or Fahrenheit: (a) \(95^{\circ} \mathrm{F}\), the temperature on a hot summer day; (b) \(12^{\circ} \mathrm{F}\), the temperature on a cold winter day; (c) a \(102^{\circ} \mathrm{F}\) fever; (d) a furnace operating at \(1852^{\circ} \mathrm{F}\); (e) \(-273.15^{\circ} \mathrm{C}\) (theoretically the lowest attainable temperature.

(a) Normally the human body can endure a temperature of \(105^{\circ} \mathrm{F}\) for only short periods of time without permanent damage to the brain and other vital organs. What is this temperature in degrees Celsius? (b) Ethylene glycol is a liquid organic compound that is used as an antifreeze in car radiators. It freezes at \(-11.5^{\circ} \mathrm{C}\). Calculate its freezing temperature in degrees Fahrenheit. (c) The temperature on the surface of the sun is about \(6300^{\circ} \mathrm{C}\). What is this temperature in degrees Fahrenheit? (d) The ignition temperature of paper is \(451^{\circ} \mathrm{F}\). What is the temperature in degrees Celsius?

Convert the following temperatures to kelvin: (a) \(113^{\circ} \mathrm{C}\), the melting point of sulfur, (b) \(37^{\circ} \mathrm{C}\), the normal body temperature, (c) \(357^{\circ} \mathrm{C}\), the boiling point of mercury.

Convert the following temperatures to degrees Celsius: (a) 77 K, the boiling point of liquid nitrogen, (b) 4.2 K, the boiling point of liquid helium, (c) 601 K, the melting point of lead.

What is the advantage of using scientific notation over decimal notation?

Define significant figure. Discuss the importance of using the proper number of significant figures in measurements and calculations.

Express the following numbers in scientific notation: (a) 0.0000000.27, (b) 356, (c) 47,764, (d) 0.096.

Express the following numbers as decimals: (a) \(1.52 \times 10^{-2}\), (b) \(7.78 \times 10^{-8}\)

A pycnometer is a device for measuring the density of liquids. It is a glass flask with a close-fitting ground glass stopper having a capillary hole through it. (a) The volume of the pycnometer is determined by using distilled water at \(20^{\circ} \mathrm{C}\) with a known density of 0.99820 g/mL. First, the water is filled to the rim. With the stopper in place, the fine hole allows the excess liquid to escape. The pycnometer is then carefully dried with filter paper. Given that the masses of the empty pycnometer and the same one filled with water are 32.0764 g and 43.1195 g, respectively, calculate the volume of the pycnometer. (b) If the mass of the pycnometer filled with ethanol at \(20^{\circ} \mathrm{C}\) is 40.8051 g, calculate the density of ethanol. (c) Pycnometers can also be used to measure the density of solids. First, small zinc granules weighing 22.8476 g are placed in the pycnometer, which is then filled with water. If the combined mass of the pycnometer plus the zinc granules and water is 62.7728 g, what is the density of zinc?

In 1849 a gold prospector in California collected a bag of gold nuggets plus sand. Given that the density of gold and sand are \(19.3\mathrm{\ g}/\mathrm{cm}^3\) and \(2.95\ \mathrm{g}/\mathrm{cm}^3\) respectively, and that the density of the mixture is \(4.17\mathrm{\ g}/\mathrm{cm}^3\). calculate the percent by mass of gold in the mixture.

The average time it takes for a molecule to diffuse a distance of \(x \ cm\) is given by \(t=\frac{x^{2}}{2 D}\) where \(t\) is the time in seconds and \(D\) is the diffusion coefficient. Given that the diffusion coefficient of glucose is \(5.7\times10^{-7}\mathrm{\ cm}^2/\mathrm{s}\), calculate the time it would take for a glucose molecule to diffuse \(10\ \mu\mathrm{m}\), which is roughly the size of a cell.

A human brain weighs about 1 kg and contains about \(10^{11}\) cells. Assuming that each cell is completely filled with water (density = 1 g/mL), calculate the length of one side of such a cell if it were a cube. If the cells are spread out in a thin layer that is a single cell thick, what is the surface area in square meters?

(a) Carbon monoxide (CO) is a poisonous gas because it binds very strongly to the oxygen carrier hemoglobin in blood. A concentration of \(8.00\times10^2\ ppm\) by volume of carbon monoxide is considered lethal to humans. Calculate the volume in liters occupied by carbon monoxide in a room that measures 17.6 m long, 8.80 m wide, and 2.64 m high at this concentration. (b) Prolonged exposure to mercury (Hg) vapor can cause neurological disorders and respiratory problems. For safe air quality control, the concentration of mercury vapor must be under \(0.050\ \mathrm{mg}/\mathrm{m}^3\). Convert this number to g/L. (c) The general test for type II diabetes is that the blood sugar (glucose) level should be below 120 mg per deciliter (mg/dL). Convert this number to micrograms per milliliter \((\mu \mathrm{g} / \mathrm{mL})\).

A bank teller is asked to assemble "one-dollar" sets of coins for his clients. Each set is made of three quarters, one nickel, and two dimes. The masses of the coins are: quarter: 5.645 g; nickel: 4.967 g; dime: 2.316 g. What is the maximum number of sets that can be assembled from 33.871 kg of quarters, 10.432 kg of nickels, and 7.990 kg of dimes? What is the total mass (in g) of the assembled sets of coins?

A graduated cylinder is filled to the 40.00-mL mark with a mineral oil. The masses of the cylinder before and after the addition of the mineral oil are 124.966 g and 159.446 g, respectively. In a separate experiment, a metal ball bearing of mass 18.713 g is placed in the cylinder and the cylinder is again filled to the 40.00-mL mark with the mineral oil. The combined mass of the ball bearing and mineral oil is 50.952 g. Calculate the density and radius of the ball bearing. [The volume of a sphere of radius r is \((4 / 3) \pi r^{3}\)]

Express the answers to the following calculations in scientific notation: (a) \(145.75+\left(2.3 \times 10^{-1}\right)\) (b) \(79,500 \div\left(2.5 \times 10^{2}\right)\) (c) \(\left(7.0 \times 10^{-3}\right)-\left(8.0 \times 10^{-4}\right)\) (d) \(\left(1.0 \times 10^{4}\right) \times\left(9.9 \times 10^{6}\right)\)

Express the answers to the following calculations in scientific notation: (a) \(0.0095+\left(8.5 \times 10^{-3}\right)\) (b) \(653 \div\left(5.75 \times 10^{-8}\right)\) (c) \(850,000-\left(9.0 \times 10^{5}\right)\) (d) \(\left(3.6 \times 10^{-4}\right) \times\left(3.6 \times 10^{6}\right)\)

What is the number of significant figures in each of the following measurements? (a) 4867 mi (b) 56 mL (c) 60,104 tons (d) 2900 g (e) \(40.2\mathrm{\ g}/\mathrm{cm}^3\) (f) 0.0000003 cm (g) 0.7 min (h) \(4.6 \times 10^{19}\) atoms

How many significant figures are there in each of the following? (a) 0.006 L, (b) 0.0605 dm, (c) 60.5 mg, (d) \(605.5\mathrm{\ cm}^2\), (e) \(960\times10^{-3}\ g\), (f) 6 kg, (g) 60 m.

Carry out the following operations as if they were calculations of experimental results, and express each answer in the correct units with the correct number of significant figures: (a) \(5.6792 \mathrm{~m}+0.6 \mathrm{~m}+4.33 \mathrm{~m}\) (b) \(3.70 \mathrm{~g}-2.9133 \mathrm{~g}\) (c) \(4.51 \mathrm{~cm} \times 3.6666 \mathrm{~cm}\) (d) \(\left(3 \times 10^{4} \mathrm{~g}+6.827 \mathrm{~g}\right) /\left(0.043 \mathrm{~cm}^{3}-0.021 \mathrm{~cm}^{3}\right)\)

Carry out the following operations as if they were calculations of experimental results, and express each answer in the correct units with the correct number of significant figures: (a) \(7.310\mathrm{\ km}\div5.70\mathrm{\ km}\) (b) \(\left(3.26 \times 10^{-3} \ \mathrm{mg}\right)-\left(7.88 \times 10^{-5} \ \mathrm{mg}\right)\) (c) \(\left(4.02 \times 10^{6} \ \mathrm{dm}\right)+\left(7.74 \times 10^{7} \ \mathrm{dm}\right)\) (d) \((7.8m-0.34\ m)/(1.15s+0.82\ s)\)

Three students (\(A\), \(B\), and \(C\)) are asked to determine the volume of a sample of ethanol. Each student measures the volume three times with a graduated cylinder. The results in milliliters are: \(A\) (87.1, 88.2, 87.6); \(B\) (86.9, 87.1, 87.2); \(C\) (87.6, 87.8, 87.9). The true volume is 87.0 mL. Comment on the precision and the accuracy of each student’s results.

Comment on whether each of the following is a homogeneous mixture or a heterogeneous mixture: (a) air in a closed bottle and (b) air over New York City.

Chlorine is used to disinfect swimming pools. The accepted concentration for this purpose is 1 ppm chlorine, or 1 g of chlorine per million grams of water. Calculate the volume of a chlorine solution (in milliliters) a homeowner should add to her swimming pool if the solution contains 6.0 percent chlorine by mass and there are \(2.0 \times 10^{4}\) gallons of water in the pool. (1 gallon = 3.79 L; density of liquids = 1.0 g/mL.)

An aluminum cylinder is 10.0 cm in length and has a radius of 0.25 cm. If the mass of a single Al atom is \(4.48\times10^{-23}\mathrm{\ g}\), calculate the number of Al atoms present in the cylinder. The density of aluminum is \(2.70\mathrm{\ g}/\mathrm{cm}^3\)

A chemist in the nineteenth century prepared an unknown substance. In general, do you think it would be more difficult to prove that it is an element or a compound? Explain.

Bronze is an alloy made of copper (Cu) and tin (Sn). Calculate the mass of a bronze cylinder of radius 6.44 cm and length 44.37 cm. The composition of the bronze is 79.42 percent Cu and 20.58 percent Sn and the densities of Cu and Sn are 8.94 \(\mathrm{g} / \mathrm{cm}^{3}\) and 7.31 \(\mathrm{g} / \mathrm{cm}^{3}\), respectively. What assumption should you make in this calculation?

You are given a liquid. Briefly describe steps you would take to show whether it is a pure substance or a homogeneous mixture.

A chemist mixes two liquids \(A\) and \(B\) to form a homogeneous mixture. The densities of the liquids are 2.0514 g/mL for \(A\) and 2.6678 g/mL for \(B\). When she drops a small object into the mixture, she finds that the object becomes suspended in the liquid; that is, it neither sinks nor floats. If the mixture is made of 41.37 percent \(A\) and 58.63 percent \(B\) by volume, what is the density of the metal? Can this procedure be used in general to determine the densities of solids? What assumptions must be made in applying this method?

Tums is a popular remedy for acid indigestion. A typical Tums tablet contains calcium carbonate plus some inert substances. When ingested, it reacts with the gastric juice (hydrochloric acid) in the stomach to give off carbon dioxide gas. When a 1.328-g tablet reacted with 40.00 mL of hydrochloric acid (density: 1.140 g/mL), carbon dioxide gas was given off and the resulting solution weighed 46.699 g. Calculate the number of liters of carbon dioxide gas released if its density is 1.81 g/L.

A 250-mL glass bottle was filled with 242 mL of water at 20°C and tightly capped. It was then left outdoors overnight, where the average temperature was -5°C. Predict what would happen. The density of water at 20°C is 0.998 \(g/cm^3\) and that of ice at -5°C is 0.916 \(g/cm^3\)

Estimate the volume of blood in an adult in liters.

How far (in feet) does light travel in one nanosecond?

Estimate the distance (in miles) covered by an NBA player in a professional basketball game.

Estimate the total amount of ocean water in liters.

In water conservation, chemists spread a thin film of a certain inert material over the surface of water to cut down on the rate of evaporation of water in reservoirs. This technique was pioneered by Benjamin Franklin three centuries ago. Franklin found that 0.10 mL of oil could spread over the surface of water about \(40\mathrm{\ m}^2\) in area. Assuming that the oil forms a monolayer, that is, a layer that is only one molecule thick, estimate the length of each oil molecule in nanometers. \(\left(1\mathrm{\ nm}=1\times10^{-9}\mathrm{\ m}.\right)\)

The circumference of an NBA-approved basketball is 29.6 in. Given that the radius of Earth is about 6400 km, how many basketballs would it take to circle around the equator with the basketballs touching one another? Round off your answer to an integer with three significant figures.

What is the mass of one mole of ants? (Useful information: A mole is the unit used for atomic and subatomic particles. It is approximately \(6 \times 10^{23}\). A 1-cm-long ant weighs about 3 mg.)

How much time (in years) does an 80-year-old person spend sleeping during his or her life span?

Estimate the daily amount of water (in gallons) used indoors by a family of four in the United States.

Public bowling alleys generally stock bowling balls from 8 to 16 lb, where the mass is given in whole numbers. Given that regulation bowling balls have a diameter of 8.6 in, which (if any) of these bowling balls would you expect to float in water?

Fusing "nanofibers" with diameters of 100-300 nm gives junctures with very small volumes that would potentially allow the study of reactions involving only a few molecules. Estimate the volume in liters of the junction formed between two such fibers with internal diameters of 200 nm. The scale reads \(1\ \mu\mathrm{m}\).

Estimate the annual consumption of gasoline by passenger cars in the United States.