Solution: Write the following numbers in standard notation.

Scenes AD represent atomic-scale views of different samples of substances: (a) Under one set of conditions, the substances in A and B mix and the result is depicted in C. Does this represent a chemical or a physical change? (b) Under a second set of conditions, the same substances mix and the result is depicted in D. Does this represent a chemical or a physical change? (c) Under a third set of conditions, the sample depicted in C changes to that in D. Does this represent a chemical or a physical change? (d) When the change in part (c) occurs, does the sample have different chemical properties? Physical properties?

Describe solids, liquids, and gases in terms of how they fill a container. Use your descriptions to identify the physical state (at room temperature) of the following: (a) helium in a toy balloon; (b) mercury in a thermometer; (c) soup in a bowl.

Use your descriptions in the previous problem to identify the physical state (at room temperature) of the following: (a) the air in your room; (b) tablets in a bottle of vitamins; (c) sugar in a packet

Define physical property and chemical property. Identify each type of property in the following statements: (a) Yellow-green chlorine gas attacks silvery sodium metal to form white crystals of sodium chloride (table salt). (b) A magnet separates a mixture of black iron shavings and white sand

Define physical change and chemical change. State which type of change occurs in each of the following statements: (a) Passing an electric current through molten magnesium chloride yields molten magnesium and gaseous chlorine. (b) The iron in discarded automobiles slowly forms reddish brown, crumbly rust.

Which of the following is a chemical change? Explain your reasoning: (a) boiling canned soup; (b) toasting a slice of bread; (c) chopping a log; (d) burning a log.

Which of the following changes can be reversed by changing the temperature: (a) dew condensing on a leaf; (b) an egg turning hard when it is boiled; (c) ice cream melting; (d) a spoonful of batter cooking on a hot griddle?

For each pair, which has higher potential energy? (a) The fuel in your car or the gaseous products in its exhaust (b) Wood in a fire or the ashes after the wood burns

For each pair, which has higher kinetic energy? (a) A sled resting at the top of a hill or a sled sliding down the hill (b) Water above a dam or water falling over the dam

The alchemical, medical, and technological traditions were precursors to chemistry. State a contribution that each made to the development of the science of chemistry.

How did the phlogiston theory explain combustion?

One important observation that supporters of the phlogiston theory had trouble explaining was that the calx of a metal weighs more than the metal itself. Why was that observation important? How did the phlogistonists respond?

Lavoisier developed a new theory of combustion that overturned the phlogiston theory. What measurements were central to his theory, and what key discovery did he make?

How are the key elements of scientific thinking used in the following scenario? While making toast, you notice it fails to pop out of the toaster. Thinking the spring mechanism is stuck, you notice that the bread is unchanged. Assuming you forgot to plug in the toaster, you check and find it is plugged in. When you take the toaster into the dining room and plug it into a different outlet, you find the toaster works. Returning to the kitchen, you turn on the switch for the overhead light and nothing happens.

Why is a quantitative observation more useful than a nonquantitative one? Which of the following are quantitative? (a) The Sun rises in the east. (b) A person weighs one-sixth as much on the Moon as on Earth. (c) Ice floats on water. (d) A hand pump cannot draw water from a well more than 34 ft deep.

Describe the essential features of a well-designed experiment.

Describe the essential features of a scientific model.

When you convert feet to inches, how do you decide which portion of the conversion factor should be in the numerator and which in the denominator?

Write the conversion factor(s) for (a) in2 to m2 (b) km2 to cm2 (c) mi/h to m/s (d) lb/ft3 to g/cm

Write the conversion factor(s) for (a) cm/min to in/s (b) m3 to in3 (c) m/s2 to km/h2 (d) gal/h to L/min

Describe the difference between intensive and extensive properties. Which of the following properties are intensive: (a) mass; (b) density; (c) volume; (d) melting point?

Explain the difference between mass and weight. Why is your weight on the Moon one-sixth that on Earth?

For each of the following cases, state whether the density of the object increases, decreases, or remains the same: (a) A sample of chlorine gas is compressed. (b) A lead weight is carried up a high mountain. (c) A sample of water is frozen. (d) An iron bar is cooled. (e) A diamond is submerged in water

Explain the difference between heat and temperature. Does 1 L of water at 65 F have more, less, or the same quantity of energy as 1 L of water at 65 C?

A one-step conversion is sufficient to convert a temperature in the Celsius scale into the Kelvin scale, but not into the Fahrenheit scale. Explain.

The average radius of a molecule of lysozyme, an enzyme in tears, is 1430 pm. What is its radius in nanometers (nm)?

The radius of a barium atom is 2.22 10 m. What is its radius in angstroms ()?

What is the length in inches (in) of a 100.-m soccer field?

The center on your basketball team is 6 ft 10 in tall. How tall is the player in millimeters (mm)?

A small hole in the wing of a space shuttle requires a 20.7-cm patch. (a) What is the patchs area in square kilometers (km )? (b) If the patching material costs NASA $3.25/in, what is the cost of the patch?

The area of a telescope lens is 7903 mm. (a) What is the area in square feet (ft )? (b) If it takes a technician 45 s to polish 135 mm , how long does it take her to polish the entire lens?

Express your body weight in kilograms (kg).

There are 2.60 10 short tons of oxygen in the atmosphere (1 short ton 2000 lb). How many metric tons of oxygen are present (1 metric ton 1000 kg)?

The average density of Earth is 5.52 g/cm . What is its density in (a) kg/m ; (b) lb/ft ?

The speed of light in a vacuum is 2.998 10 m/s. What is its speed in (a) km/h; (b) mi/min?

The volume of a certain bacterial cell is 2.56 m . (a) What is its volume in cubic millimeters (mm3 )? (b) What is the volume of 105 cells in liters (L)?

(a) How many cubic meters of milk are in 1 qt (946.4 mL)? (b) How many liters of milk are in 835 gal (1 gal 4 qt)?

An empty vial weighs 55.32 g. (a) If the vial weighs 185.56 g when filled with liquid mercury (d 13.53 g/cm ), what is its volume? (b) How much would the vial weigh if it were filled with water (d 0.997 g/cm at 25 C)?

An empty Erlenmeyer flask weighs 241.3 g. When filled with water (d 1.00 g/cm ), the flask and its contents weigh 489.1 g. (a) What is the flasks volume? (b) How much does the flask weigh when filled with chloroform (d 1.48 g/cm )?

A small cube of aluminum measures 15.6 mm on a side and weighs 10.25 g. What is the density of aluminum in g/cm ?

A steel ball-bearing with a circumference of 32.5 mm weighs 4.20 g. What is the density of the steel in g/cm3 ( r 3 V of a sphere ; circumference of a circle 2 r)?

Perform the following conversions: (a) 68 F (a pleasant spring day) to C and K (b) 164 C (the boiling point of methane, the main component of natural gas) to K and F (c) 0 K (absolute zero, theoretically the coldest possible temperature) to C and F

Perform the following conversions: (a) 106 F (the body temperature of many birds) to K and C (b) 3410 C (the melting point of tungsten, the highest for any metallic element) to K and F (c) 6.1 10 K (the surface temperature of the Sun) to F and C

A 25.0-g sample of each of three unknown metals is added to 25.0 mL of water in graduated cylinders A, B, and C, and the final volumes are depicted in the circles below. Given their densities, identify the metal in each cylinder: zinc (7.14 g/mL), iron (7.87 g/mL), nickel (8.91 g/mL).

The distance between two adjacent peaks on a wave is called the wavelength. (a) The wavelength of a beam of ultraviolet light is 247 nanometers (nm). What is its wavelength in meters? (b) The wavelength of a beam of red light is 6760 pm. What is its wavelength in angstroms ()?

Each of the beakers depicted below contains two liquids that do not dissolve in each other. Three of the liquids are designated A, B, and C, and water is designated W. (a) Which of the liquids is(are) more dense than water and which less dense? (b) If the densities of W, C, and A are 1.0 g/mL, 0.88 g/mL, and 1.4 g/mL, respectively, which of the following densities is possible for liquid B: 0.79 g/mL, 0.86 g/mL, 0.94 g/mL, 1.2 g/mL?

A cylindrical tube 9.5 cm high and 0.85 cm in diameter is used to collect blood samples. How many cubic decimeters (dm ) of blood can it hold (V of a cylinder ? ? r h)?

Copper can be drawn into thin wires. How many meters of 34-gauge wire (diameter 6.304 10 in) can be produced from the copper in 5.01 lb of covellite, an ore of copper that is 66% copper by mass? (Hint: Treat the wire as a cylinder: V of cylinder ? ? r h; d of copper 8.95 g/cm .)

What is an exact number? How are exact numbers treated differently from other numbers in a calculation?

Which procedure(s) decrease(s) the random error of a measurement: (1) taking the average of more measurements; (2) calibrating the instrument; (3) taking fewer measurements? Explain.

A newspaper reported that the attendance at Slippery Rocks home football game was 16,532. (a) How many significant figures does this number contain? (b) Was the actual number of people counted? (c) After Slippery Rocks next home game, the newspaper reported an attendance of 15,000. If you assume that this number contains two significant figures, how many people could actually have been at the game

Underline the significant zeros in the following numbers: (a) 0.41 (b) 0.041 (c) 0.0410 (d) 4.0100 10 4

Underline the significant zeros in the following numbers: (a) 5.08 (b) 508 (c) 5.080 10 3 (d) 0.05080

Round off each number to the indicated number of significant figures (sf): (a) 0.0003554 (to 2 sf); (b) 35.8348 (to 4 sf); (c) 22.4555 (to 3 sf).

Round off each number to the indicated number of significant figures (sf): (a) 231.554 (to 4 sf); (b) 0.00845 (to 2 sf); (c) 144,000 (to 2 sf)

Round off each number in the following calculation to one fewer significant figure, and find the answer:

Round off each number in the following calculation to one fewer significant figure, and find the answer:

Carry out the following calculations, making sure that your answer has the correct number of significant figures: (a) (b) , where r 17.282 mm

Carry out the following calculations, making sure that your answer has the correct number of significant figures: (a) (b) (c) V ? ? r 2 h, where r 6.23 cm and h 4.630 cm

Write the following numbers in scientific notation: (a) 131,000.0 (b) 0.00047 (c) 210,006 (d) 2160.5

Write the following numbers in scientific notation: (a) 282.0 (b) 0.0380 (c) 4270.8 (d) 58,200.9

Write the following numbers in standard notation. Use a terminal decimal point when needed: (a) 5.55 10 3 (b) 1.0070 10 4 (c) 8.85 10 7 (d) 3.004 10 3

Write the following numbers in standard notation. Use a terminal decimal point when needed: (a) 6.500 10 3 (b) 3.46 10 5 (c) 7.5 10 2 (d) 1.8856 10 2

Convert the following into correct scientific notation: (a) 802.5 10 2 (b) 1009.8 10 6 (c) 0.077 10 9

Convert the following into correct scientific notation: (a) 14.3 10 1 (b) 851 10 2 (c) 7500 10 3

Carry out each of the following calculations, paying special attention to significant figures, rounding, and units (J joule, the SI unit of energy; mol mole, the SI unit for amount of substance):

Carry out each of the following calculations, paying special attention to significant figures, rounding, and units: (a) (The term is exact.) (b) (The term 2 is exact.)

Which statements include exact numbers? (a) Angel Falls is 3212 ft high. (b) There are eight known planets in the Solar System. (c) There are 453.59 g in 1 lb. (d) There are 1000 mm in 1 m

Which of the following include exact numbers? (a) The speed of light in a vacuum is a physical constant; to six significant figures, it is 2.99792 10 8 m/s. (b) The density of mercury at 25 C is 13.53 g/mL. (c) There are 3600 s in 1 h. (d) In 2003, the United States had 50 states

How long is the metal strip shown below? Be sure to answer with the correct number of significant figures.

These organic solvents are used to clean compact discs: Solvent Density (g/mL) at 20 C Chloroform 1.492 Diethyl ether 0.714 Ethanol 0.789 Isopropanol 0.785 Toluene 0.867 (a) If a 15.00-mL sample of CD cleaner weighs 11.775 g at 20 C, which solvent is most likely to be present? (b) The chemist analyzing the cleaner calibrates her equipment and finds that the pipet is accurate to 0.02 mL, and the balance is accurate to 0.003 g. Is this equipment precise enough to distinguish between ethanol and isopropanol?

A laboratory instructor gives a sample of amino-acid powder to each of four students, I, II, III, and IV, and they weigh the samples. The true value is 8.72 g. Their results for three trials are I: 8.72 g, 8.74 g, 8.70 g II: 8.56 g, 8.77 g, 8.83 g III: 8.50 g, 8.48 g, 8.51 g IV: 8.41 g, 8.72 g, 8.55 g (a) Calculate the average mass from each set of data, and tell which set is the most accurate. (b) Precision is a measure of the average of the deviations of each piece of data from the average value. Which set of data is the most precise? Is this set also the most accurate? (c) Which set of data is both the most accurate and most precise? (d) Which set of data is both the least accurate and least precise?

The following dartboards illustrate the types of errors often seen in measurements. The bulls-eye represents the actual value, and the darts represent the data. (a) Which experiments yield the same average result? (b) Which experiment(s) display(s) high precision? (c) Which experiment(s) display(s) high accuracy? (d) Which experiment(s) show(s) a systematic error?

Two blank potential energy diagrams appear below. Beneath each diagram are objects to place in the diagram. Draw the objects on the dashed lines to indicate higher or lower potential energy and label each case as more or less stable: (a) Two balls attached to a relaxed or a compressed spring. (b) Two positive charges near or apart from each other

The scenes below illustrate two different mixtures. When mixture A at 273 K is heated to 473 K, mixture B results. (a) How many different chemical changes occur? (b) How many different physical changes occur?

Bromine is used to prepare the pesticide methyl bromide and flame retardants for plastic electronic housings. It is recovered from seawater, underground brines, and the Dead Sea. The average concentrations of bromine in seawater (d 1.024 g/mL) and the Dead Sea (d 1.22 g/mL) are 0.065 g/L and 0.50 g/L, respectively. What is the mass ratio of bromine in the Dead Sea to that in seawater?

An Olympic-size pool is 50.0 m long and 25.0 m wide. (a) How many gallons of water (d 1.0 g/mL) are needed to fill the pool to an average depth of 4.8 ft? (b) What is the mass (in kg) of water in the pool?

At room temperature (20 C) and pressure, the density of air is 1.189 g/L. An object will float in air if its density is less than that of air. In a buoyancy experiment with a new plastic, a chemist creates a rigid, thin-walled ball that weighs 0.12 g and has a volume of 560 cm3 . (a) Will the ball float if it is evacuated? (b) Will it float if filled with carbon dioxide (d 1.830 g/L)? (c) Will it float if filled with hydrogen (d 0.0899 g/L)? (d) Will it float if filled with oxygen (d 1.330 g/L)? (e) Will it float if filled with nitrogen (d 1.165 g/L)? (f) For any case that will float, how much weight must be added to make the ball sink?

Asbestos is a fibrous silicate mineral with remarkably high tensile strength. But it is no longer used because airborne asbestos particles can cause lung cancer. Grunerite, a type of asbestos, has a tensile strength of 3.5 10 2 kg/mm2 (thus, a strand of grunerite with a 1-mm2 cross-sectional area can hold up to 3.5 10 2 kg). The tensile strengths of aluminum and Steel No. 5137 are 2.5 10 4 lb/in2 and 5.0 10 4 lb/in2 , respectively. Calculate the cross-sectional area (in mm2 ) of wires of aluminum and of Steel No. 5137 that have the same tensile strength as a fiber of grunerite with a cross- sectional area of 1.0 m 2 .

Drugs called COX-2 inhibitors (e.g., Vioxx, Bextra, and Celebrex) were thought to relieve the pain and inflammation of osteoarthritis without the stomach bleeding and ulcers nonsteroidal anti-inflammatory drugs (NSAIDs) cause. In a 12- month trial, Vioxx caused fewer gastrointestinal side effects than the NSAID ibuprofen. However, a study of the recurrence of colon polyps after three years of Vioxx found an increased risk for heart attack and stroke beginning after 18 months of treatment. As a result, Vioxx was withdrawn from the market, and an FDA panel concluded that COX-2 inhibitors as a class have increased cardiovascular risk that varies by drug and dose. The FDA then caused the withdrawal of Bextra and required a warning label on Celebrex. Based on this information, list (a) an observation, (b) a hypothesis, (c) an experiment, and (d) a theory.

Earths oceans have an average depth of 3800 m, a total area of 3.63 108 km2 , and an average concentration of dissolved gold of 5.8 10 9 g/L. (a) How many grams of gold are in the oceans? (b) How many m3 of gold are in the oceans? (c) Assuming the price of gold is $370.00/troy oz, what is the value of gold in the oceans (1 troy oz 31.1 g; d of gold 19.3 g/cm3 )?

Brass is an alloy of copper and zinc. Varying the mass percentages of the two metals produces brasses with different properties. A brass called yellow zinc has high ductility and strength and is 34%37% zinc by mass. (a) Find the mass range (in g) of copper in 185 g of yellow zinc. (b) What is the mass range (in g) of zinc in a sample of yellow zinc that contains 46.5 g of copper?

Liquid nitrogen is obtained from liquefied air and is used industrially to prepare frozen foods. It boils at 77.36 K. (a) What is this temperature in C? (b) What is this temperature in F? (c) At the boiling point, the density of the liquid is 809 g/L and that of the gas is 4.566 g/L. How many liters of liquid nitrogen are produced when 895.0 L of nitrogen gas is liquefied at 77.36 K?

The speed of sound varies according to the material. Sound travels at 5.4 103 cm/s through rubber and at 1.97 104 ft/s through granite. Calculate each of these speeds in m/s.

If a raindrop weighs 0.52 mg on average and 5.1 10 raindrops fall on a lawn every minute, what mass (in kg) of rain falls on the lawn in 1.5 h?

A jogger runs at an average speed of 5.9 mi/h. (a) How fast is she running in m/s? (b) How many kilometers does she run in 98 min? (c) If she starts a run at 11:15 am, what time is it after she covers 4.75 10 4 ft?

Scenes A and B depict changes in matter at the atomic scale: Scenes A and B depict changes in matter at the atomic scale: (a) Which show(s) a physical change? (b) Which show(s) a chemical change? (c) Which result(s) in different physical properties? (d) Which result(s) in different chemical properties? (e) Which result(s) in a change in state?

Nutritional tables give the potassium content of a standard apple (about 3 apples/lb) as 159 mg. How many grams of potassium are in 3.25 kg of apples?

Describe, in general terms, the changes in potential energy and kinetic energy as an automobile (a) starts moving, (b) climbs a hill, (c) descends a hill, and (d) comes to a stop

If a temperature scale were based on the freezing point (5.5 C) and boiling point (80.1 C) of benzene and the temperature difference between these points was divided into 50 units (called X), what would be the freezing and boiling points of water in X? (See Figure 1.12, p. 25.)

Earths surface area is 5.10 108 km2 , and its crust has a mean thickness of 35 km and mean density of 2.8 g/cm3 . The two most abundant elements in the crust are oxygen (4.55 105 g/ metric ton, t) and silicon (2.72 10 5 g/t), and the two rarest nonradioactive elements are ruthenium and rhodium, each with an abundance of 1 10 4 g/t. What is the total mass of each of these elements in Earths crust (1 t 1000 kg)?