Chapter Questions
Define the terms chemistry and matter.
Explain what is meant by the scientific method.
What is the difference between a hypothesis and a theory?
Classify each of the following statements as a hypothesis, law, or theory. (a) Beethoven's contribution to music would have been much greater if he had married. (b) An autumn leaf 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.
Classify each of the following statements as a hypothesis, law, or theory. (a) The force acting on an object is equal to its mass times its acceleration. (b) The universe as we know it started with a big bang. (c) There are many civilizations more advanced than ours on other planets.
Identify the elements present in the following molecules (see Table 1.1).
Give an example for each of the following terms: (a) matter,(b) substance, (c) mixture.
Give an example of a homogeneous mixture and an example of a heterogeneous mixture.
Give an example of an element and a compound. How do elements and compounds differ?
What is the number of known elements?
Give the names of the elements represented by the chemical symbols Li, F, P, Cu, As, Zn, Cl, Pt, Mg, U, Al, Si, Ne (see the table inside the front cover).
Give the chemical symbols for the following elements:(a) potassium, (b) tin, (c) chromium, (d) boron, (e) barium,(f) plutonium, (g) sulfur, (h) argon, (i) mercury (see the table inside the 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) seawater,(b) helium gas, (c) sodium chloride (salt), (d) a bottle of soft drink, (e) a milkshake, (f) air in a bottle, (g) concrete.
Identify each of the diagrams shown here as a solid, liquid, gas, r mixture of two substances.
Identify each of the diagrams shown here as an element or a compound.
Name the SI base units that are important in chemistry, and give the SI units for expressing the following: (a) length, (b) volume,(c) mass, (d) time, (e) 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 the density of liquids and solids? For the density of gas? Explain the differences.
What is the difference between mass and weight? If a person weighs 168 lb on Earth, about how much would the person weigh on the moon?
Describe the three temperature scales used in the laboratory and in everyday life: the Fahrenheit, Celsius, and Kelvin scales.
Bromine is a reddish-brown liquid. Calculate its density (in $\mathrm{g} / \mathrm{mL}$ ) if $586 \mathrm{g}$ of the substance occupies $188 \mathrm{mL}$.
The density of ethanol, a colorless liquid that is commonly known as grain alcohol, is $0.798 \mathrm{g} / \mathrm{mL}$. Calculate the mass of $17.4 \mathrm{mL}$ of the liquid.
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?
The density of water at $40^{\circ} \mathrm{C}$ is $0.992 \mathrm{g} / \mathrm{mL}$. What is the volume of $2.50 \mathrm{g}$ of water at this temperature?
The density of platinum ( $\mathrm{Pt}$ ) is $21.5 \mathrm{g} / \mathrm{cm}^{3}$ at $25^{\circ} \mathrm{C}$. What is the volume of $87.6 \mathrm{g}$ of $\mathrm{Pt}$ at this temperature?
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) $77 \mathrm{K}$ the boiling point of liquid nitrogen, (b) $4.2 \mathrm{K}$, the boiling point of liquid helium, (c) 601 K, the melting point of lead.
What is the difference between qualitative data and quantitative data?
Using examples, explain the difference between a physical property and a chemical property.
How does an intensive property differ from an extensive property?
Determine which of the following properties are intensive and which are extensive: (a) length, (b) volume, (c) temperature, (d) mass.
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.
Determine whether the following statements describe chemical or physical properties: (a) Oxygen gas supports combustion.(b) Fertilizers help to increase agricultural production. (c) Water boils below $100^{\circ} \mathrm{C}$ on top of a mountain. (d) Lead is denser than aluminum. (e) Uranium is a radioactive element.
Determine whether each of the following describes 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 salt dissolves in a bowl of soup.
A student pours $44.3 \mathrm{g}$ of water at $10^{\circ} \mathrm{C}$ into a beaker containing 115.2 g of water at $10^{\circ} \mathrm{C}$. What are the final mass, temperature, and density of the combined water? The density of water at $10^{\circ} \mathrm{C}$ is $1.00 \mathrm{g} / \mathrm{mL}$
A 37.2 -g sample of lead ( $\mathrm{Pb}$ ) pellets at $20^{\circ} \mathrm{C}$ is mixed with a $62.7-\mathrm{g}$ sample of lead pellets at the same temperature. What are the final mass, temperature, and density of the combined sample? The density of $\mathrm{Pb}$ at $20^{\circ} \mathrm{C}$ is $11.35 \mathrm{g} / \mathrm{cm}^{3}$
Comment on whether each of the following statements represents an exact number: (a) 50,247 tickets were sold at a sporting event, (b) $509.2 \mathrm{mL}$ of water was used to make a birthday cake,(c) 3 dozen eggs were used to make a breakfast, (d) $0.41 \mathrm{g}$ of oxygen was inhaled in each breath, (e) Earth orbits the sun every 365.2564 days.
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.
Distinguish between the terms accuracy and precision. In general, explain why a precise measurement does not always guarantee an accurate result.
Express the following numbers in scientific notation:(a) $0.000000027,$ (b) $356,$ (c) $47,764,$ (d) 0.096
Express the following numbers as decimals: (a) $1.52 \times 10^{-2}$(b) $7.78 \times 10^{-8}$
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) $\left(3.6 \times 10^{-4}\right) \times\left(3.6 \times 10^{6}\right)$
Determine the number of significant figures in each of the following measurements: (a) 4867 mi, (b) 56 mL, (c) 60,104 tons,(d) $2900 \mathrm{g},$ (e) $40.2 \mathrm{g} / \mathrm{cm}^{3},$ (f) $0.0000003 \mathrm{cm},$ (g) $0.7 \mathrm{min}$(h) $4.6 \times 10^{19}$ atoms.
Determine the number of significant figures in each of the following measurements: (a) 0.006 L, (b) 0.0605 dm, (c) 60.5 $\mathrm{mg},(\mathrm{d}) 605.5 \mathrm{cm}^{2},(\mathrm{e}) 9.60 \times 10^{3} \mathrm{g},(\mathrm{f}) 6 \mathrm{kg},(\mathrm{g}) 60 \mathrm{m}$
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) $4.51 \mathrm{cm} \times 3.6666 \mathrm{cm}$
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) $7.310 \mathrm{km} \div 5.70 \mathrm{km}$(b) $\left(3.26 \times 10^{-3} \mathrm{mg}\right)-\left(7.88 \times 10^{-5} \mathrm{mg}\right)$(c) $\left(4.02 \times 10^{6} \mathrm{dm}\right)+\left(7.74 \times 10^{7} \mathrm{dm}\right)$
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)$; \mathrm{B}(86.9,87.1,87.2) ; \mathrm{C}(87.6,87.8,87.9)$The true volume is $87.0 \mathrm{mL}$. Comment on the precision and the accuracy of each student's results.
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)$; \mathrm{Z}(31.9,32.2,32.1) .$ 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) $22.6 \mathrm{m}$ to decimeters,(b) $25.4 \mathrm{mg}$ to kilograms, (c) $556 \mathrm{mL}$ 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) $28.3 \mu \mathrm{g}$ 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 is $3.00 \times 10^{8} \mathrm{m} / \mathrm{s}$.)
A slow jogger runs a mile in 13 min. Calculate the speed in(a) in/s, (b) $\mathrm{m} / \mathrm{min},(\mathrm{c}) \mathrm{km} / \mathrm{h}(1 \mathrm{mi}=1609 \mathrm{m} ; 1 \text { in }=2.54 \mathrm{cm})$
A 6.0 -ft person weighs 168 lb. Express this person's height in meters and weight in kilograms ( $1 \mathrm{lb}=453.6 \mathrm{g} ; 1 \mathrm{m}=3.28 \mathrm{ft}$ ).
The current speed limit in some states in the United States is55 mph. What is the speed limit in kilometers per hour ( $1 \mathrm{mi}=$ $1609 \mathrm{m}) ?$
For a fighter jet to take off from the deck of an aircraft carrier, it must reach a speed of $62 \mathrm{m} / \mathrm{s}$. Calculate the speed in miles per hour.
The "normal" lead content in human blood is about 0.40 part per million (that is, $0.40 \mathrm{g}$ 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 $6.0 \times 10^{3} \mathrm{g}$ of blood (the amount in an average adult) if the lead content is $0.62 \mathrm{ppm} ?$
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 $3.00 \times 10^{8} \mathrm{m} / \mathrm{s}$ ), $(\mathrm{b}) 32.4$ yd to centimeters, $(\mathrm{c}) 3.0 \times 10^{10}$$\mathrm{cm} / \mathrm{s}$ to $\mathrm{ft} / \mathrm{s}$
Carry out the following conversions: (a) $185 \mathrm{nm}$ to meters,(b) 4.5 billion years (roughly the age of Earth) to seconds (assume 365 days in a year), (c) $71.2 \mathrm{cm}^{3}$ to cubic meters,(d) $88.6 \mathrm{m}^{3}$ to liters.
Aluminum is a lightweight metal (density $=2.70 \mathrm{g} / \mathrm{cm}^{3}$ ) used in aircraft construction, high-voltage transmission lines, beverage cans, and foils. What is its density in $\mathrm{kg} / \mathrm{m}^{3} ?$
The density of ammonia gas under certain conditions is $0.625 \mathrm{g} / \mathrm{L} .$ Calculate its density in $\mathrm{g} / \mathrm{cm}^{3}$
(a) Carbon monoxide (CO) is a poisonous gas because it binds very strongly to the oxygen carrier hemoglobin in blood. A concentration of $8.00 \times 10^{2}$ ppm by volume of carbon monoxide is considered lethal to humans. Calculate the volume in liters occupied by carbon monoxide in a room that measures $17.6 \mathrm{~m}$ long, $8.80 \mathrm{~m}$ wide, and $2.64 \mathrm{~m}$ high at this concentration.(b) Prolonged exposure to mercury (Hg) vapor can cause neurological disorder and respiratory problems. For safe air quality control, the concentration of mercury vapor must be under $0.050 \mathrm{mg} / \mathrm{m}^{3}$. Convert this number to g/L. (c) The general test for type II diabetes is that the blood sugar (glucose) level should be below $120 \mathrm{mg}$ per deciliter $(\mathrm{mg} / \mathrm{dL})$. Convert this number to micrograms per milliliter ( $\mu \mathrm{g} / \mathrm{mL}$ ).
The average time it takes for a molecule to diffuse a distance of$x \mathrm{cm}$ is given by$$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 $5.7 \times 10^{-7} \mathrm{cm}^{2} / \mathrm{s},$ 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 $1 \mathrm{kg}$ and contains about $10^{11}$ cells. Assuming that each cell is completely filled with water (density $=$ $1 \mathrm{g} / \mathrm{mL}),$ calculate the length of one side of such a cell if it were a cube. If the cells are spread out into a thin layer that is a single cell thick, what is the surface area in square meters?
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.
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) salt (sodium chloride), (g) mercury,(h) gold, (i) air.
In $2004,$ about 95.0 billion $1 \mathrm{b}$ 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, $8.53 \mathrm{cm} ;$ width,$2.4 \mathrm{cm} ;$ height, $1.0 \mathrm{cm} ;$ mass, $52.7064 \mathrm{g}$. 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 $10.0 \mathrm{cm}$ (volume of a sphere with a radius $r$ is $V=4 / 3 \pi r^{3} ;$ density of gold $=19.3 \mathrm{g} / \mathrm{cm}^{3},$ (b) a cube of platinum of edge length $\left.0.040 \mathrm{mm} \text { (density }=21.4 \mathrm{g} / \mathrm{cm}^{3}\right),(\mathrm{c}) 50.0 \mathrm{mL}$ ofethanol (density $=0.798 \mathrm{g} / \mathrm{mL}$ ).
A cylindrical glass tube $12.7 \mathrm{cm}$ in length is filled with mercury (density $=13.6 \mathrm{g} / \mathrm{mL}$ ). The mass of mercury needed to fill the tube is $105.5 \mathrm{g}$. Calculate the inner diameter of the tube (volume of a cylinder of radius $r$ and length $h$ is $V=\pi r^{2} h$ ).
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 $56.12 \mathrm{g}$ and 87.39 g, respectively, and the density of water is 0.9976 g/cm $^{3}$, calculate the volume of the flask in cubic centimeters.
The speed of sound in air at room temperature is about $343 \mathrm{m} / \mathrm{s}$. Calculate this speed in miles per hour $(1 \mathrm{mi}=1609 \mathrm{m})$
A piece of silver (Ag) metal weighing $194.3 \mathrm{g}$ is placed in a graduated cylinder containing $242.0 \mathrm{mL}$ of water. The volume of water now reads $260.5 \mathrm{mL}$. From these data calculate the density of silver.
The experiment described in Problem 1.79 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 has a mass of $1.20 \times 10^{4} \mathrm{g}$, and its volume is $1.05 \times 10^{3} \mathrm{cm}^{3} .$ 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 to $\pm 0.1^{\circ} \mathrm{F}$, whereas those in the doctor's office may be accurate to $\pm 0.1^{\circ} \mathrm{C}$. 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: percent error $=\frac{| \text { true value }-\text { experimental value } |}{\text { true value }} \times 100 \%$The vertical lines indicate absolute value. 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 $2.0 \times 10^{-11} \mathrm{g}$ per liter of air. If the current price of $50 \mathrm{g}$ 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 $\left(-117.3^{\circ} \mathrm{C}\right)$ and the boiling point of ethanol $\left(78.3^{\circ} \mathrm{C}\right)$ are taken as $0^{\circ} \mathrm{S}$ and $100^{\circ} \mathrm{S},$ 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 $25^{\circ} \mathrm{C}$ ?
A resting adult requires about $240 \mathrm{mL}$ of pure oxygen per minute and breathes about 12 times every minute. If inhaled air contains20 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 $1.87,$ calculate the total volume (in liters) of air an adult breathes in a day. (b) In a city with heavy traffic, the air contains $2.1 \times 10^{-6} \mathrm{L}$ of carbon monoxide (a poisonous gas) per liter. Calculate the average daily intake of carbon monoxide in liters by a person.
The total volume of seawater is $1.5 \times 10^{21}$ L. Assume that seawater contains 3.1 percent sodium chloride by mass and that its density is $1.03 \mathrm{g} / \mathrm{mL} .$ Calculate the total mass of sodium chloride in kilograms and in tons $(1 \text { ton }=2000 \mathrm{lb} ; 1 \mathrm{lb}=453.6 \mathrm{g})$
Magnesium (Mg) is a valuable metal used in alloys, in batteries, and in the manufacture of chemicals. It is obtained mostly from seawater, which contains about $1.3 \mathrm{g}$ of $\mathrm{Mg}$ for every kilogram of seawater. Referring to Problem $1.89,$ calculate the volume of seawater (in liters) needed to extract $8.0 \times 10^{4}$ tons of $\mathrm{Mg},$ which is roughly the annual production in the United States.
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 $=0.9986 \mathrm{g} / \mathrm{mL}$ ). The readings are $860.2 \mathrm{g}$ and $820.2 \mathrm{g},$ 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 buoyancy of air.)
The surface area and average depth of the Pacific Ocean are $1.8 \times 10^{8} \mathrm{km}^{2}$ and $3.9 \times 10^{3} \mathrm{m},$ 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 $(1 \mathrm{lb}=16$ oz;$1 \mathrm{lb}=453.6 \mathrm{g}) ?$
Osmium (Os) is the densest element known (density $=$22.57 g/cm $^{3}$ ). Calculate the mass in pounds and in kilograms of an Os sphere $15 \mathrm{cm}$ in diameter (about the size of a grapefruit) (volume of a sphere of radius $r$ is $\frac{4}{3} \pi r^{3}$ ).
Calculate the percent error for the following measurements:(a) The density of alcohol (ethanol) is found to be $0.802 \mathrm{g} / \mathrm{mL}$ (true value $=0.798 \mathrm{g} / \mathrm{mL}$ ). (b) The mass of gold in an earring is analyzed to be $0.837 \mathrm{g}$ (true value $=0.864 \mathrm{g}$ ).
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 1997 ) is $3 \min 44.39$ 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 $7.3 \times 10^{2} \mathrm{K}$. Convert this temperature to degrees Celsius and degrees Fahrenheit.
Chalcopyrite, the principal ore of copper (Cu), contains 34.63 percent Cu by mass. How many grams of $\mathrm{Cu}$ can be obtained from $5.11 \times 10^{3} \mathrm{kg}$ of the ore?
It has been estimated that $8.0 \times 10^{4}$ tons of gold (Au) have been mined. Assume gold costs $\$ 625$ per ounce. What is the total worth of this quantity of gold?
A 1.0 -mL volume of seawater contains about $4.0 \times 10^{-12} \mathrm{g}$ of gold. The total volume of ocean water is $1.5 \times 10^{21}$ L. Calculate the total amount of gold (in grams) that is present in seawater and the worth of the gold in dollars (see Problem 1.100 ). With so much gold out there, why hasn't someone become rich by mining gold from the ocean?
Measurements show that $1.0 \mathrm{g}$ of iron (Fe) contains $1.1 \times 10^{22}$ Fe atoms. How many Fe atoms are in $4.9 \mathrm{g}$ of $\mathrm{Fe}$, which is the total amount of iron in the body of an average adult?
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 (mass of Earth $\left.=5.9 \times 10^{21} \text { tons; } 1 \text { ton }=2000 \mathrm{lb} ; 1 \mathrm{lb}=453.6 \mathrm{g}\right)$
The radius of a copper (Cu) atom is roughly $1.3 \times 10^{-10} \mathrm{m}$. How many times can you divide evenly a 10 -cm-long piece of 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 $9.5 \mathrm{kg}$ 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 $5000 \mathrm{mi}$ 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 $3.636 \mathrm{g} .$ What is the thickness of the foil in millimeters (density of $\left.\mathrm{Al}=2.699 \mathrm{g} / \mathrm{cm}^{3}\right) ?$
Comment on whether each of the following is a homogeneous mixture or a heterogeneous mixture: (a) air in a closed bottle, (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 (gal) of water in the pool (1 gal $=3.79$ L; density of liquids $=1.0 \mathrm{g} / \mathrm{mL}$ ).
The world's total petroleum reserve is estimated at $2.0 \times$ $10^{22}$ joules [a joule ( $\mathrm{J}$ ) is the unit of energy where $1 \mathrm{J}=$ $\left.1 \mathrm{kg} \cdot \mathrm{m}^{2} / \mathrm{s}^{2}\right] .$ At the present rate of consumption, $1.8 \times 10^{20}$ joules per year (J/yr), how long would it take to exhaust the supply?
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$0.10 \mathrm{mL}$ 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 $\left(1 \mathrm{nm}=1 \times 10^{-9} \mathrm{m}\right)$
Fluoridation is the process of adding fluorine compounds to drinking water to help fight tooth decay. A concentration of $1 \mathrm{ppm}$ of fluorine is sufficient for the purpose (1 ppm means one part per million, or 1 g of fluorine per 1 million g of water). The compound normally chosen for fluoridation is sodium fluoride, which is also added to some toothpastes. Calculate the quantity of sodium fluoride in kilograms needed per year for a city of 50,000 people if the daily consumption of water per person is 150 gal. What percent of the sodium fluoride is "wasted" if each person uses only $6.0 \mathrm{L}$ of water a day for drinking and cooking (sodium fluoride is 45.0 percent fluorine by mass; 1 gal $=3.79$ L; 1 year $=365$ days; 1 ton $=2000 \mathrm{lb} ; 1 \mathrm{lb}=453.6 \mathrm{g} ; \text { density of water }=1.0 \mathrm{g} / \mathrm{mL}) ?$
A gas company in Massachusetts charges $\$ 1.30$ for $15.0 \mathrm{ft}^{3}$ of natural gas. (a) Convert this rate to dollars per liter of gas. (b) If it takes $0.304 \mathrm{ft}^{3}$ of gas to boil a liter of water, starting at room temperature $\left(25^{\circ} \mathrm{C}\right),$ how much would it cost to boil a $2.1-\mathrm{L}$ kettle of water?
Pheromones are compounds secreted by females of many insect species to attract mates. Typically, $1.0 \times 10^{-8} \mathrm{g}$ of a pheromone is sufficient to reach all targeted males within a radius of $0.50 \mathrm{mi}$. Calculate the density of the pheromone (in grams per liter) in a cylindrical air space having a radius of $0.50 \mathrm{mi}$ and a height of $40 \mathrm{ft} .$ (Volume of a cylinder of radius $r$ and height $h$ is $\pi r^{2} h$ )
A bank teller is asked to assemble $\$ 1$ sets of coins for his clients. Each set is made up of three quarters, one nickel, and two dimes. The masses of the coins are quarter, $5.645 \mathrm{g} ;$ nickel, $4.967 \mathrm{g} ;$ and dime, 2.316 g. What is the maximum number of sets that can be assembled from $33.871 \mathrm{kg}$ of quarters, $10.432 \mathrm{kg}$ of nickels, and $7.990 \mathrm{kg}$ of dimes? What is the total mass (in grams) 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 $124.966 \mathrm{g}$ and $159.446 \mathrm{g},$ respectively. In a separate experiment, a metal ball bearing of mass $18.713 \mathrm{g}$ 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 $50.952 \mathrm{g}$. Calculate the density and radius of the ball bearing (volume of a sphere of radius $r$ is $^{4} / 3 \pi r^{3}$ ).
Bronze is an alloy made of copper (Cu) and tin (Sn). Calculate the mass of a bronze cylinder of radius $6.44 \mathrm{cm}$ and length $44.37 \mathrm{cm} .$ The composition of the bronze is 79.42 percent $\mathrm{Cu}$ 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?
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.
A chemist mixes two liquids $A$ and $B$ to form a homogeneous mixture. The densities of the liquids are $2.0514 \mathrm{g} / \mathrm{mL}$ for $\mathrm{A}$ and $2.6678 \mathrm{g} / \mathrm{mL}$ for $\mathrm{B}$. 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 object? Can this procedure be used in general to determine the densities of solids? What assumptions must be made in applying this method?
You are given a liquid. Briefly describe the steps you would take to show whether it is a pure substance or a homogeneous mixture.
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 $1.328-\mathrm{g}$ tablet reacted with $40.00 \mathrm{mL}$ of hydrochloric acid (density $=$ $1.140 \mathrm{g} / \mathrm{mL}),$ carbon dioxide gas was given off and the resulting solution weighed $46.699 \mathrm{g} .$ Calculate the number of liters of carbon dioxide gas released if its density is $1.81 \mathrm{g} / \mathrm{L}$
A $250-\mathrm{mL}$ glass bottle was filled with $242 \mathrm{mL}$ of water at $20^{\circ} \mathrm{C}$ and tightly capped. It was then left outdoors overnight, where the average temperature was $-5^{\circ} \mathrm{C}$. Predict what would happen. The density of water at $20^{\circ} \mathrm{C}$ is $0.998 \mathrm{g} / \mathrm{cm}^{3}$ and that of ice at $-5^{\circ} \mathrm{C}$ is $0.916 \mathrm{g} / \mathrm{cm}^{3}$