THE FUNDAMENTALS OF MEASUREMENT

The following questions can be interspersed among questions dealing with the
individual chapters of *Chemistry: Structure and Dynamics*, as needed. These questions
presume that a table of standard conversion factors and/or a table of relevant densities
have been attached to the exam under the heading “potentially useful information.”

Units

0-1. The prefix “nano-” is equivalent to multiplying by which of the following?

(a) 10^{-9} (b) 10^{-6} (c) 10^{-3} (d) 10^{3} (e) 10^{9}

Answer: (a)

0-2. How many “Claus”-es are there in a centi-Claus?

(a) 0.01 (b) 0.1 (c) 10 (d) 100

(e) there is only one centi-Claus.

Answer: (a)

0-3. If a nanometer is equal to 10^{-9} meters and a centimeter is 10^{-2} meters, how many
nanometers are there in one centimeter?

(a) 10^{-11} (b) 10^{-7} (c) 10^{7} (d) 10^{11} (e) none of the above

Answer: (c)

0-4. Calculate the derived SI base unit for the following quantities:

(a) speed (b) area (c) volume (d) density

0-5. A gallon in the United States contains 128 oz. Canada once used the imperial gallon which contains 160 oz. Calculate the number of ounces per quart for both a gallon and an imperial gallon if there are always four quarts in a gallon.

Answer: 32 oz/gal; 40 oz/imp gal

Uncertainty/Error

0-6. Calcium carbonate decomposes on heating to form calcium oxide and carbon dioxide.

CaCO_{3}(s) ➝ CaO(s) + CO_{2}(g)

Which of the following would cause the weight loss during the decomposition of a
sample of CaCO_{3} to appear too large?

(a) the CaCO_{3} contained some CaO before it was heated

(b) the crucible was wet when it was weighed before the CaCO_{3} was heated

(c) the crucible was heated for too short a time

(d) the student read the last weight as 40.3047 g instead of the actual value of 30.3047 g

(e) all of these would cause the weight loss to appear too large.

Answer: (b)

Significant Figures

0-7. When 0.10274 grams of sugar are added to 3.05 grams of water, the answer should be reported to how many significant figures?

(a) 2 (b) 3 (c) 4 (d) 5 (e) 6

Answer: (b)

0-8. How many significant figures can be used to describe the speed of a car that travels 20.24 miles in 15.1 minutes?

(a) 1 (b) 2 (c) 3 (d) 4 (e) 5

Answer: (c)

Unit Conversions

0-9. Calculate the height in centimeters of your instructor, assuming that one “George” is exactly 6 feet.

(a) 1.27 cm (b) 5.08 cm (c) 15.24 cm (d) 30.48 cm (e) 182.88 cm

Answer: (e)

0-10. The distance from the Earth to the Sun is 9.2 x 10^{7} miles and the speed of light is
3.0 x 10^{8} m/s. Calculate the time that it takes for light to travel from the Sun to the
Earth.

(a) 0.68 min (b) 3.2 min (c) 8.2 min (d) 16 min (e) 21 min

Answer: (c)

0-11. Water has a density of exactly 1 g/cm^{3} at 4°C. What is the weight of a cubic foot
of water at this temperature.

(a) 0.0672 lb (b) 2.05 lb (c) 3.81 lb (d) 62.4 lb (e) 28,300 lb

Answer: (d)

0-12. Calculate the charge on a single electron if the charge on a mole of electrons is
96,484.56 C and there are 6.022045 x 10^{23} particles in a mole.

(a) 1.602189 x 10^{-19} C (b) 1 C (c) 96,484.56 C (d) 5.810343 x 10^{28} C

(e) none of the above

Answer: (a)

0-13. The new twin-cam Harley-Davidson engine has two cylinders with a total displacement of 88 cubic inches. Calculate the displacement in cubic centimeters to two significant figures.

(a) 4.9 cm^{3} (b) 31 cm^{3} (c) 203.2 cm^{3} (d) 1300 cm^{3} (e) none of the above

Answer: (d)

0-14. A bushel is equal to 4 pecks. There are 8 quarts in a peck and 2 pints in a quart. If
a pint has a volume of 33.6 in^{3} what is the volume of a bushel in cubic inches?

(a) 67.2 in^{3} (b) 134 in^{3} (c) 538 in^{3} (d) 2150 in^{3} (e) none of the above

Answer: (d)

0-15. The measurement system used in the U.S. is clumsy, at best. Consider the fact
that there are 16 ounces in a pound but 32 ounces in a quart. (And that an ounce, by
weight, doesn’t occupy an ounce, by volume.) There are two pints in a quart, eight
quarts in a peck, and four pecks in a bushel. If a pint has a volume of 550.6 cm^{3} and
there are 1000 cm^{3} in a liter, what is the volume of a bushel in L?

(a) Less than 1 L (b) Between 1 and 10 L (c) Between 10 and 25 L

(d) Between 25 and 50 L (e) More than 50 L

Answer: (d)

0-16. A farmer needs to give a 50.0 lb calf a shot of an antibiotic. The bottle is labeled as having 200 mg per mL and says the dosage is 8.0 mg per pound of body weight. The syringe is calibrated in cc's — cubic centimeters. How many cc's should the calf be given? (a) 0.040 cc (b) 2.0 cc (c) 4.0 cc (d) 6.2 cc (e) 25 cc

Answer: (b)

0-17. If the local bars pay $8.75 for a 750 mL bottle of Jack Daniel's, use 1.5 ounces of bourbon to make a drink, and sell drinks for $2.50 each, what fraction of the price of the drink is profit?

(a) less than 25% (b) between 25 and 35% (c) between 35 and 50%

(d) between 50 and 75% (e) more than 75%

Answer: (e)

0-18. List the following in order of increasing speed: lightning that travels at 87,000
miles per hour, an oxygen molecule at room temperature that travels at 440 meters per
second, or light that travels at 5.87851 x 10^{12 }miles per year.

(a) lightning < oxygen molecule < light (b) oxygen molecule < lightning < light

(c) oxygen molecule < light < lightning (d) light < oxygen molecule < lightning (e) light < lightning < oxygen molecule

Answer: (b)

0-19. Calculate the number of fluid ounces in a pint if a milliliter contains 0.0338 fluid ounces and a liter contains 2.1134 pints.

(a) 8 (b) 16 (c) 32 (d) 64 (e) none of the above

Answer: (b)

0-20. Calculate how long it would take for 5 billion people to count out the number of
molecules in a mole (6 x 10^{23}) if each person counted one molecule per second.

(a) 4 years (b) 4000 years (c) 4 million years

(d) 4 billion years (e) 400 billion years

Answer: (c)

0-21. Estimate the fraction of the body weight that is water in an average human body, which has a mass of 70 kilograms and contains 12.5 gallons of water.

(a) less than 25% (b) about 40% (c) about 50% (d) about 70% (e) about 90%

Answer: (d)

0-22. It takes 1000 ft^{3} of natural gas or 293 kilowatt hours of electricity to generate 1.0 x
10^{6} Btu's of energy. What is the ratio of the cost of heating a house with electricity
compared to gas if gas sells for $0.663 per 100 cubic feet and electricity sells for
$0.058/kwh?

Answer: ≈2.5:1

0-23. It takes 13.60 electron volts of energy to remove an electron from a neutral
hydrogen atom in the gas phase. If 1 ev is equal to 1.602 x 10^{-19} J, how much energy, in
kJ, would it take to remove an electron from a mole of hydrogen atoms in the gas
phase?

(a) 1.18 x 10^{-20} kJ (b) 2.18 x 10^{-18 }kJ (c) 7100 J (d) 1,312 kJ/mol (e) 7091 kJ

Answer: (d)

0-24. A 20-pound bag of 20:10:5 fertilizer is 20% N by weight, 10% P_{2}O_{5} by weight, and
5% K_{2}O by weight. If this fertilizer covers 5,000 square feet of lawn, how many grams of
nitrogen are applied per square foot?

(a) 0.00080 g (b) 0.18 g (c) 0.36 g (c) 0.91 g (e) 1.8g

Answer: (c)

0-25. Gold is the most malleable element. An ounce of gold can be beaten into a thin
sheet that covers an area of 300 square feet. Calculate the thickness of this sheet in
centimeters, assuming the density of gold is 19.3 g/cm^{3}. Calculate the thickness of the
sheet in terms of the number of gold atoms if the radius of an individual gold atom is 1.4
x 10^{-8} cm.

(a) about 4 atoms (b) about 400 atoms (c) about 4000 atoms

(d) about 400,000 atoms (e) about 4,000,000 atoms

Answer: (b)

0-26. LD_{50} for a drug is the dose that will be lethal for 50% of the population given that
amount of drug. LD_{50} for aspirin in rats is 1.75 grams per kilogram of body weight. How
many aspirin tablets weighing 325 mg each would the average 70-kg human have to
consume to achieve this dose?

(a) about 4 tablets (b) about 40 tablets (c) about 400 tablets

(d) about 4000 tablets (e) about 400,000 tablets

Answer: (c)

0-27. In 1773, Benjamin Franklin observed that one teaspoon of oil spilled on a pond
near London spread out to form a film that covered an area of about 22,000 ft^{2}. If a
teaspoon of oil has a volume of about 5 cm^{3}, and we assume that the oil spread out to
form a film roughly one molecule tall, calculate the average height of an oil molecule.

(a) 2.5 x 10^{-8} cm (b) 2.5 10^{-7} cm (c) 2.5 x 10^{-5} cm

(d) 2.5 x 10^{-3} cm (e) 2.5 cm

Answer: (b)

0-28. At a chemistry conference several years ago, they organized a 100-trillion
angstrom (100 x 10^{12} Å) race. If 1 Å is 10^{-8} cm, roughly how long would it take someone
who can run a mile in four minutes to run a 100-trillion angstrom race?

(a) Less than 5 minutes (b) between 5 and 10 minutes

(c) between 10 and 20 minutes (d) between 20 and 30 minutes

(e) More than 30 minutes

Answer: (d)

0-29. It costs $9.00 per month to rent the water cooler in my office and $5.00 per 5-gallon bottle of water. I use 1.40 L of this water each time I make coffee, I make coffee five times a week, and the average month has 4.28 weeks. I use decaffeinated Kona coffee from Hawaii that costs me about $25.00 per month. Estimate the average cost of the water and water cooler per month and compare it to the cost of the coffee. (Note that it would cost me more than $100 per month, if I bought Starbucks coffee from the Union.)

(a) I average less than $10.00 per month for the water/water cooler and the coffee is much more expensive.

(b) I average between $10 and $15.00 per month for the water/water cooler and the coffee is much more expensive.

(c) I average between $15 and $20.00 per month for the water/water cooler and the coffee is more expensive.

(d) I average between $20 and $25.00 per month for the water/water cooler and the coffee is somewhat more expensive.

(e) I average more than $25.00 per month for the water/water cooler and the coffee is actually less expensive than the water/water cooler.

Answer: (c)

0-30. Theory predicts that hydrogen should become metallic under extreme pressure,
such as the pressure at the center of Jupiter and Saturn. Until recently, this
transformation had not been observed in the laboratory, even when hydrogen was
compressed to 340 gigapascals (GPa). Instead of compressing hydrogen in a diamond
anvil cell at room temperature, scientists at the Lawrence Livermore National
Laboratory simultaneously compressed and heated the element – up to 300 GPa and
40,000 K [*Science*, 281, 1178 (1998)] They used deuterium (^{2}H) rather than hydrogen
because it is more dense and, therefore, easier to compress. They found that
deuterium begins to behave like a metal at pressures as low as 60 GPa if the
temperature is high enough. What is 60 GPa in atm? (Hint: 1 atm = 101.325 kPa; SI
multipliers increase in the order kilo, mega, giga, tera ...)

(a) 1.0 x 10^{-4} atm (b) 5.9 x 10^{3} atm (c) 5.9 x 10^{6} atm (d) 5.9 x 10^{9} atm

(e) none of the above

Answer: (e)

0-31. The reagent grade “ethyl alcohol” we use the lab has a density of 0.7892 g/mL at
20°C. (Never confuse this with the ethyl alcohol served at the local bars because lab
alcohol contains both methyl and isopropyl alcohol contaminants that are dangerous to
consume.) The formula for ethyl alcohol is CH_{3}CH_{2}OH and the molecular weight is
46.07 g/mol. Calculate the volume of reagent grade ethyl alcohol that contains 1.50
moles of the alcohol.

(a) 24.2 mL (b) 54.5 mL (c) 87.6 mL (d) 389 mL (e) none of the above

Answer: (c)

0-32. One of the risk factors for diabetes is an elevated value of the body mass index (BMI). This is calculated by dividing the weight of the patient in kilograms by the square of the patient’s height in meters. Typical BMI charts cover a range of heights between 4'10" and 6'2", a weight range between 120 and 320 pounds, and BMI values between 15 and 67. Borderline BMI values are 27-29; anyone with a BMI over 30 is likely to be “obese.” Let’s assume that one of your relatives is 6'0" tall and that he weighs 200 pounds. If he asked for advice, what would you tell him?

(a) He has a BMI less than 15, and his only problem is he should gain some weight.

(b) His BMI is between 15 and 20, and he should be in great shape.

(c) His BMI is between 20 and 25 and he’s doing “O.K.”

(d) His BMI is more than 25, but less than 30, and he’s on the borderline.

(e) His BMI is 30, or more, and he ought to either gain a few inches or lose a few pounds.

Answer: (d)

Graphical Treatment of Data

0-33. The following data show how the pressure of a gas depends on its volume when
the amount of gas and the temperature of the gas are held constant. Which of the
following would give a straight line that would fit the equation *y* = *mx* + *b*?

Pressure (atm): 0.0586 0.0856 0.142 0.289

Volume (L): 1.28 0.876 0.528 0.259

(a) only P vs V (b) only P vs 1/V (c) both P vs V and P vs 1/V

(d) both P vs 1/V and V vs 1/P (e) P vs V, P vs 1/V, and V vs 1/P

Answer: (d)

0-34. The following data show how the volume of a gas depends on its temperature
when the amount of gas and the pressure of the gas are held constant. Which of the
following would give a straight line that would fit the equation *y* = *mx* + *b*?

Volume (mL): 246 295 332 390 443

Temperature (°C) 27 87 132 202 267

(a) only V vs T (b) only V vs 1/T (c) both V vs T and V vs 1/T

(d) both V vs 1/T and T vs 1/V (e) V vs T, V vs 1/T, and T vs 1/V

Answer: (a)

Density

0-35. The density of sugar is 1.59 g/mL. Calculate the volume of a teaspoon of sugar if this quantity of sugar weighs 4.50 grams.

(a) 0.140 mL (b) 0.353 mL (c) 2.83 mL (d) 6.09 mL (e) 7.16 mL

Answer: (c)

0-36. The iron in steel has a density of 7.86 g/cm^{3}. When iron rusts, it forms hydrated
Fe_{2}O_{3} that has a density of 5.12 g/cm^{3}. What happens to the volume as iron rusts?

(a) it expands (b) it contracts (c) the volume must remain the same

Answer: (a)

0-37. The first silver dollar minted in the Americas was 3.95 cm in diameter and
contained 27.07 grams of silver. If the density of silver is 10.5 g/cm^{3}, what was the
height of each coin?

(a) 0.00791 cm (b) 0.0316 cm (c) 0.0526 cm (d) 0.210 cm (e) none of these

Answer: (d)

0-38. The density of water in pounds per cubic foot is 62.4 lb/ft^{3}. If a 2 ft^{3} bag of mulch
sold at the local lawn care center weighs 30 lbs, which of the following correctly
describes what happens when this mulch is poured on water?

(a) the mulch will sink because it is less dense than water

(b) the mulch will sink because it is more dense than water

(c) the mulch will float because it is less dense than water

(d) the mulch will float because it is more dense than water

(e) there is no way of predicting what will happen

Answer: (c)

0-39. A sample of sucrose (C_{12}H_{22}O_{11}) that weighs 9.35 g is placed in a 15.00 mL flask.
The remaining volume of the flask is filled with benzene — a liquid in which sucrose
does not dissolve. The density of benzene is 0.879 g/cm^{3}. The sucrose and benzene
together weigh 17.33 g. What is the density of sucrose?

(a) 0.532 g/cm^{3} (b) 0.623 g/cm^{3} (c) 1.03 g/cm^{3}

(d) 1.16 g/cm^{3} (e) 1.58 g/cm^{3}

Answer: (e)

0-40. The following liquids don’t mix with water. Which of these liquids would float on top of water?

(I) benzene, C_{6}H_{6}, d = 0.877 g/cm^{3}

(II) carbon disulfide, CS_{2}, d = 1.263 g/cm^{3}

(III) chloroform, CHCl_{3}, d = 1.483 g/cm^{3}

(IV) ether, (C_{2}H_{5})_{2}O, d = 0.714 g/cm^{3}

(V) gasoline, d = 0.675 g/cm^{3}

(a) I, IV and V (b) II and III (c) I, II and III

(d) none of these liquids would float on top of water

(e) all of these liquids would float on top of water.

Answer: (a)

0-41. If a beaker that contains 250 mL of chloroform (CHCl_{3}) weighs 524 grams, what is
the weight of the beaker? (CHCl_{3}: d = 1.483 g/cm^{3})

(a) about 50 g (b) about 100 g (c) about 150 g

(d) about 250 g (e) about 500 g

Answer: (c)

0-42. A student was given three pieces of metal that looked like brass. Sample I had a
volume of 17.3 mL and weighed 154.3 g, sample II had a volume of 28.4 mL and
weighed 547.2 g, and sample III had a volume of 22.2 mL and weighed 186.1 g. Which
sample(s) was(were) brass? (Brass: d ≈ 8 g/cm^{3})

(a) only I (b) I and II (c) I and III (d) II and III

(e) all of these samples were brass

Answer: (c)

Temperature

0-43. Until recently, materials had to be cooled to temperatures on the order of 4 K to become superconducting. A ceramic has been discovered that becomes superconducting at 92 K. Which of the following temperatures corresponds to 92 K?

(a) 32°F (b) -181°C (c) 212° (d) 181°C (e) 365°C

Answer: (b)

0-44. Normal body temperature is 98.6°F. What is the equivalent temperature in kelvin?

(a) 236 K (B) 293 K (c) 310 K (d) 393 K (e) 418 K

Answer: (c)

0-45. At what temperature are the readings on the Celsius and Fahrenheit scales the same? At what temperature are the magnitudes the same but the signs different?

Answer: -40°C = -40°F; -11.4°C = 11.4°F

0-46. What is the melting point of table salt (NaCl) in degrees Fahrenheit, if salt melts at 801°C?

(a) 463°F (b) 477°F (c) 1441°F (d) 1474° (e) 1499°F

Answer: (d)

0-47. Fahrenheit defined 0^{o} as the lowest temperature that could be achieved by adding
salt to ice and found that ice by itself freezes at 32^{o} on this scale. Unfortunately,
Fahrenheit's measurements were wrong. The lowest temperature that can be achieved
by adding salt to ice is -21.2°C. Calculate the equivalent temperature on the Fahrenheit
scale.

(a) -38.2°F (b) -11.8°F (c) -6.2°F (d) 20°F (e) 32°F

Answer: (c)

0-48. The Kelvin scale is an absolute temperature scale on which one unit, or one kelvin, is equal to one unit, or one degree, on the Celsius scale. The Rankin scale is an absolute temperature scale on which one unit is equal to one degree on the Fahrenheit scale. Calculate the temperature on the Fahrenheit scale that corresponds to zero on the Rankin scale.

Answer: -459.7°

Extensive/Intensity Quantities

0-49. Which of the following is not an extensive quantity?

(a) mass (b) volume (c) temperature (d) time (e) length

Answer: (c)

0-50. Which of the following is not correct?

(a) Extensive quantities, such as mass and volume depend on the size of the sample

(b) Intensive quantities are characteristic properties of a substance, which do not depend on the size of the sample

(c) The ratio of a pair of extensive quantities, which both depend on the size of the sample, is often an intensive quantity that is a characteristic property of the substance.

(d) Density is an extensive quantity

(e) Temperature is an intensive quantity

Answer: (d)

0-51. All of the following are intensive quantities that can be calculated by dividing one extensive quantity into another, except:

(a) density (b) temperature (c) time

(d) all of these are intensive quantities

(e) none of these are intensive quantities

Answer: (b)