# 1.E: Essential Ideas of Chemistry (Exercises)

- Page ID
- 78707

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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)## 1.1: Chemistry in Context

### Q1.1.1

Explain how you could experimentally determine whether the outside temperature is higher or lower than 0 °C (32 °F) without using a thermometer.

### S1.1.1

Place a glass of water outside. It will freeze if the temperature is below 0 °C.

### Q1.1.2

Identify each of the following statements as being most similar to a hypothesis, a law, or a theory. Explain your reasoning.

- Falling barometric pressure precedes the onset of bad weather.
- All life on earth has evolved from a common, primitive organism through the process of natural selection.
- My truck’s gas mileage has dropped significantly, probably because it’s due for a tune-up.

### Q1.1.3

Identify each of the following statements as being most similar to a hypothesis, a law, or a theory. Explain your reasoning.

- The pressure of a sample of gas is directly proportional to the temperature of the gas.
- Matter consists of tiny particles that can combine in specific ratios to form substances with specific properties.
- At a higher temperature, solids (such as salt or sugar) will dissolve better in water.

### S1.1.3

(a) law (states a consistently observed phenomenon, can be used for prediction); (b) theory (a widely accepted explanation of the behavior of matter); (c) hypothesis (a tentative explanation, can be investigated by experimentation)

Identify each of the underlined items as a part of either the macroscopic domain, the microscopic domain, or the symbolic domain of chemistry. For any in the symbolic domain, indicate whether they are symbols for a macroscopic or a microscopic feature.

- (a) The mass of a lead pipe is 14 lb.
- (b) The mass of a certain chlorine atom is 35 amu.
- (c) A bottle with a label that reads Al contains aluminum metal.
- (d) Al is the symbol for an aluminum atom.

Identify each of the underlined items as a part of either the macroscopic domain, the microscopic domain, or the symbolic domain of chemistry. For those in the symbolic domain, indicate whether they are symbols for a macroscopic or a microscopic feature.

- (a) A certain molecule contains one H atom and one Cl atom.
- (b) Copper wire has a density of about 8 g/cm
^{3}. - (c) The bottle contains 15 grams of Ni powder.
- (d) A sulfur molecule is composed of eight sulfur atoms.

(a) symbolic, microscopic; (b) macroscopic; (c) symbolic, macroscopic; (d) microscopic

According to one theory, the pressure of a gas increases as its volume decreases because the molecules in the gas have to move a shorter distance to hit the walls of the container. Does this theory follow a macroscopic or microscopic description of chemical behavior? Explain your answer.

The amount of heat required to melt 2 lbs of ice is twice the amount of heat required to melt 1 lb of ice. Is this observation a macroscopic or microscopic description of chemical behavior? Explain your answer.

Macroscopic. The heat required is determined from macroscopic properties.

## 1.2: Phases and Classification of Matter

### Questions

- Why do we use an object's mass, rather than its weight, to indicate the amount of matter it contains?
- What properties distinguish solids from liquids? Liquids from gases? Solids from gases?
- How does a heterogeneous mixture differ from a homogeneous mixture? How are they similar?
- How does a homogeneous mixture differ from a pure substance? How are they similar?
- How does an element differ from a compound? How are they similar?
- How do molecules of elements and molecules of compounds differ? In what ways are they similar?
- How does an atom differ from a molecule? In what ways are they similar?
- Many of the items you purchase are mixtures of pure compounds. Select three of these commercial products and prepare a list of the ingredients that are pure compounds.
- Classify each of the following as an element, a compound, or a mixture:
- copper
- water
- nitrogen
- sulfur
- air
- sucrose
- a substance composed of molecules each of which contains two iodine atoms
- gasoline

- Classify each of the following as an element, a compound, or a mixture:
- iron
- oxygen
- mercury oxide
- pancake syrup
- carbon dioxide
- a substance composed of molecules each of which contains one hydrogen atom and one chlorine atom
- baking soda
- baking powder

- A sulfur atom and a sulfur molecule are not identical. What is the difference?
- How are the molecules in oxygen gas, the molecules in hydrogen gas, and water molecules similar? How do they differ?
- We refer to astronauts in space as weightless, but not without mass. Why?
- As we drive an automobile, we don't think about the chemicals consumed and produced. Prepare a list of the principal chemicals consumed and produced during the operation of an automobile.
- Matter is everywhere around us. Make a list by name of fifteen different kinds of matter that you encounter every day. Your list should include (and label at least one example of each) the following: a solid, a liquid, a gas, an element, a compound, a homogenous mixture, a heterogeneous mixture, and a pure substance.
- When elemental iron corrodes it combines with oxygen in the air to ultimately form red brown iron(III) oxide which we call rust. (a) If a shiny iron nail with an initial mass of 23.2 g is weighed after being coated in a layer of rust, would you expect the mass to have increased, decreased, or remained the same? Explain. (b) If the mass of the iron nail increases to 24.1 g, what mass of oxygen combined with the iron?
- As stated in the text, convincing examples that demonstrate the law of conservation of matter outside of the laboratory are few and far between. Indicate whether the mass would increase, decrease, or stay the same for the following scenarios where chemical reactions take place:
- Exactly one pound of bread dough is placed in a baking tin. The dough is cooked in an oven at 350 °F releasing a wonderful aroma of freshly baked bread during the cooking process. Is the mass of the baked loaf less than, greater than, or the same as the one pound of original dough? Explain.
- When magnesium burns in air a white flaky ash of magnesium oxide is produced. Is the mass of magnesium oxide less than, greater than, or the same as the original piece of magnesium? Explain.
- Antoine Lavoisier, the French scientist credited with first stating the law of conservation of matter, heated a mixture of tin and air in a sealed flask to produce tin oxide. Did the mass of the sealed flask and contents decrease, increase, or remain the same after the heating?

- Yeast converts glucose to ethanol and carbon dioxide during anaerobic fermentation as depicted in the simple chemical equation here: \[\ce{glucose\rightarrow ethanol + carbon\: dioxide}\]
- If 200.0 g of glucose is fully converted, what will be the total mass of ethanol and carbon dioxide produced?
- If the fermentation is carried out in an open container, would you expect the mass of the container and contents after fermentation to be less than, greater than, or the same as the mass of the container and contents before fermentation? Explain.
- If 97.7 g of carbon dioxide is produced, what mass of ethanol is produced?

### Solutions

2 Liquids can change their shape (flow); solids can’t. Gases can undergo large volume changes as pressure changes; liquids do not. Gases flow and change volume; solids do not.

4.The mixture can have a variety of compositions; a pure substance has a definite composition. Both have the same composition from point to point.

6 Molecules of elements contain only one type of atom; molecules of compounds contain two or more types of atoms. They are similar in that both are comprised of two or more atoms chemically bonded together.

8. Answers will vary. Sample answer: Gatorade contains water, sugar, dextrose, citric acid, salt, sodium chloride, monopotassium phosphate, and sucrose acetate isobutyrate.

11. (a) element; (b) element; (c) compound; (d) mixture, (e) compound; (f) compound; (g) compound; (h) mixture

12. In each case, a molecule consists of two or more combined atoms. They differ in that the types of atoms change from one substance to the next.

14. Gasoline (a mixture of compounds), oxygen, and to a lesser extent, nitrogen are consumed. Carbon dioxide and water are the principal products. Carbon monoxide and nitrogen oxides are produced in lesser amounts.

16. (a) Increased as it would have combined with oxygen in the air thus increasing the amount of matter and therefore the mass. (b) 0.9 g

18. (a) 200.0 g; (b) The mass of the container and contents would decrease as carbon dioxide is a gaseous product and would leave the container. (c) 102.3 g

## 1.3: Physical and Chemical Properties

Classify the six underlined properties in the following paragraph as chemical or physical:

Fluorine is a pale yellow gas that reacts with most substances. The free element melts at −220 °C and boils at −188 °C. Finely divided metals burn in fluorine with a bright flame. Nineteen grams of fluorine will react with 1.0 gram of hydrogen.

Classify each of the following changes as physical or chemical:

- condensation of steam
- burning of gasoline
- souring of milk
- dissolving of sugar in water
- melting of gold

(a) physical; (b) chemical; (c) chemical; (d) physical; (e) physical

Classify each of the following changes as physical or chemical:

- coal burning
- ice melting
- mixing chocolate syrup with milk
- explosion of a firecracker
- magnetizing of a screwdriver

The volume of a sample of oxygen gas changed from 10 mL to 11 mL as the temperature changed. Is this a chemical or physical change?

physical

A 2.0-liter volume of hydrogen gas combined with 1.0 liter of oxygen gas to produce 2.0 liters of water vapor. Does oxygen undergo a chemical or physical change?

Explain the difference between extensive properties and intensive properties.

The value of an extensive property depends upon the amount of matter being considered, whereas the value of an intensive property is the same regardless of the amount of matter being considered.

Identify the following properties as either extensive or intensive.

- volume
- temperature
- humidity
- heat
- boiling point

The density (d) of a substance is an intensive property that is defined as the ratio of its mass (m) to its volume (V).

\(\mathrm{density=\dfrac{mass}{volume}}\) \(\mathrm{d=\dfrac{m}{V}}\)

Considering that mass and volume are both extensive properties, explain why their ratio, density, is intensive.

Being extensive properties, both mass and volume are directly proportional to the amount of substance under study. Dividing one extensive property by another will in effect “cancel” this dependence on amount, yielding a ratio that is independent of amount (an intensive property).

## 1.4: Measurements

Is one liter about an ounce, a pint, a quart, or a gallon?

Is a meter about an inch, a foot, a yard, or a mile?

about a yard

Indicate the SI base units or derived units that are appropriate for the following measurements:

- (a) the length of a marathon race (26 miles 385 yards)
- (b) the mass of an automobile
- (c) the volume of a swimming pool
- (d) the speed of an airplane
- (e) the density of gold
- (f) the area of a football field
- (g) the maximum temperature at the South Pole on April 1, 1913

Indicate the SI base units or derived units that are appropriate for the following measurements:

- (a) the mass of the moon
- (b) the distance from Dallas to Oklahoma City
- (c) the speed of sound
- (d) the density of air
- (e) the temperature at which alcohol boils
- (f) the area of the state of Delaware
- (g) the volume of a flu shot or a measles vaccination

(a) kilograms; (b) meters; (c) kilometers/second; (d) kilograms/cubic meter; (e) kelvin; (f) square meters; (g) cubic meters

Give the name and symbol of the prefixes used with SI units to indicate multiplication by the following exact quantities.

- (a) 10
^{3} - (b) 10
^{−2} - (c) 0.1
- (d) 10
^{−3} - (e) 1,000,000
- (f) 0.000001

Give the name of the prefix and the quantity indicated by the following symbols that are used with SI base units.

- (a) c
- (b) d
- (c) G
- (d) k
- (e) m
- (f) n
- (g) p
- (h) T

(a) centi-, \(\times\) 10^{−2}; (b) deci-, \(\times\) 10^{−1}; (c) Giga-, \(\times\) 10^{9}; (d) kilo-, \(\times\) 10^{3}; (e) milli-, \(\times\) 10^{−3}; (f) nano-, \(\times\) 10^{−9}; (g) pico-, \(\times\) 10^{−12}; (h) tera-, \(\times\) 10^{12}

A large piece of jewelry has a mass of 132.6 g. A graduated cylinder initially contains 48.6 mL water. When the jewelry is submerged in the graduated cylinder, the total volume increases to 61.2 mL.

- (a) Determine the density of this piece of jewelry.
- (b) Assuming that the jewelry is made from only one substance, what substance is it likely to be? Explain.

Visit this PhET density simulation and select the Same Volume Blocks.

- (a) What are the mass, volume, and density of the yellow block?
- (b) What are the mass, volume and density of the red block?
- (c) List the block colors in order from smallest to largest mass.
- (d) List the block colors in order from lowest to highest density.
- (e) How are mass and density related for blocks of the same volume?

(a) 8.00 kg, 5.00 L, 1.60 kg/L; (b) 2.00 kg, 5.00 L, 0.400 kg/L; (c) red < green < blue < yellow; (d) If the volumes are the same, then the density is directly proportional to the mass.

Visit this PhET density simulation and select Custom Blocks and then My Block.

- (a) Enter mass and volume values for the block such that the mass in kg is
*less than*the volume in L. What does the block do? Why? Is this always the case when mass < volume? - (b) Enter mass and volume values for the block such that the mass in kg is
*more than*the volume in L. What does the block do? Why? Is this always the case when mass > volume? - (c) How would (a) and (b) be different if the liquid in the tank were ethanol instead of water?
- (d) How would (a) and (b) be different if the liquid in the tank were mercury instead of water?

Visit this PhET density simulation and select Mystery Blocks.

- (a) Pick one of the Mystery Blocks and determine its mass, volume, density, and its likely identity.
- (b) Pick a different Mystery Block and determine its mass, volume, density, and its likely identity.
- (c) Order the Mystery Blocks from least dense to most dense. Explain.

(a) (b) Answer is one of the following. A/yellow: mass = 65.14 kg, volume = 3.38 L, density = 19.3 kg/L, likely identity = gold. B/blue: mass = 0.64 kg, volume = 1.00 L, density = 0.64 kg/L, likely identity = apple. C/green: mass = 4.08 kg, volume = 5.83 L, density = 0.700 kg/L, likely identity = gasoline. D/red: mass = 3.10 kg, volume = 3.38 L, density = 0.920 kg/L, likely identity = ice; and E/purple: mass = 3.53 kg, volume = 1.00 L, density = 3.53 kg/L, likely identity = diamond. (c) B/blue/apple (0.64 kg/L) < C/green/gasoline (0.700 kg/L) < D/red/ice (0.920 kg/L) < E/purple/diamond (3.53 kg/L) < A/yellow/gold (19.3 kg/L)

## 1.5: Measurement Uncertainty, Accuracy, and Precision

Express each of the following numbers in scientific notation with correct significant figures:

- (a) 711.0
- (b) 0.239
- (c) 90743
- (d) 134.2
- (e) 0.05499
- (f) 10000.0
- (g) 0.000000738592

Express each of the following numbers in exponential notation with correct significant figures:

- (a) 704
- (b) 0.03344
- (c) 547.9
- (d) 22086
- (e) 1000.00
- (f) 0.0000000651
- (g) 0.007157

(a) 7.04 \(\times\) 10^{2}; (b) 3.344 \(\times\) 10^{−2}; (c) 5.479 \(\times\) 10^{2}; (d) 2.2086 \(\times\) 10^{4}; (e) 1.00000 \(\times\) 10^{3}; (f) 6.51 \(\times\) 10^{−8}; (g) 7.157 \(\times\) 10^{−3}

Indicate whether each of the following can be determined exactly or must be measured with some degree of uncertainty:

- (a) the number of eggs in a basket
- (b) the mass of a dozen eggs
- (c) the number of gallons of gasoline necessary to fill an automobile gas tank
- (d) the number of cm in 2 m
- (e) the mass of a textbook
- (f) the time required to drive from San Francisco to Kansas City at an average speed of 53 mi/h

Indicate whether each of the following can be determined exactly or must be measured with some degree of uncertainty:

- (a) the number of seconds in an hour
- (b) the number of pages in this book
- (c) the number of grams in your weight
- (d) the number of grams in 3 kilograms
- (e) the volume of water you drink in one day
- (f) the distance from San Francisco to Kansas City

(a) exact; (b) exact; (c) uncertain; (d) exact; (e) uncertain; (f) uncertain

How many significant figures are contained in each of the following measurements?

- (a) 38.7 g
- (b) 2 \(\times\) 10
^{18}m - (c) 3,486,002 kg
- (d) 9.74150 \(\times\) 10
^{−4}J - (e) 0.0613 cm
^{3} - (f) 17.0 kg
- (g) 0.01400 g/mL

How many significant figures are contained in each of the following measurements?

- (a) 53 cm
- (b) 2.05 \(\times\) 10
^{8}m - (c) 86,002 J
- (d) 9.740 \(\times\) 10
^{4}m/s - (e) 10.0613 m
^{3} - (f) 0.17 g/mL
- (g) 0.88400 s

(a) two; (b) three; (c) five; (d) four; (e) six; (f) two; (g) five

The following quantities were reported on the labels of commercial products. Determine the number of significant figures in each.

- (a) 0.0055 g active ingredients
- (b) 12 tablets
- (c) 3% hydrogen peroxide
- (d) 5.5 ounces
- (e) 473 mL
- (f) 1.75% bismuth
- (g) 0.001% phosphoric acid
- (h) 99.80% inert ingredients

Round off each of the following numbers to two significant figures:

- (a) 0.436
- (b) 9.000
- (c) 27.2
- (d) 135
- (e) 1.497 \(\times\) 10
^{−3} - (f) 0.445

(a) 0.44; (b) 9.0; (c) 27; (d) 140; (e) 1.5 \(\times\) 10^{−3}; (f) 0.44

Round off each of the following numbers to two significant figures:

- (a) 517
- (b) 86.3
- (c) 6.382 \(\times\) 10
^{3} - (d) 5.0008
- (e) 22.497
- (f) 0.885

Perform the following calculations and report each answer with the correct number of significant figures.

- (a) 628 \(\times\) 342
- (b) (5.63 \(\times\) 10
^{2}) \(\times\) (7.4 \(\times\) 10^{3}) - (c)
- \(\dfrac{28.0}{13.483}\)
- (d) 8119 \(\times\) 0.000023
- (e) 14.98 + 27,340 + 84.7593
- (f) 42.7 + 0.259

(a) 2.15 \(\times\) 10^{5}; (b) 4.2 \(\times\) 10^{6}; (c) 2.08; (d) 0.19; (e) 27,440; (f) 43.0

Perform the following calculations and report each answer with the correct number of significant figures.

- (a) 62.8 \(\times\) 34
- (b) 0.147 + 0.0066 + 0.012
- (c) 38 \(\times\) 95 \(\times\) 1.792
- (d) 15 – 0.15 – 0.6155
- (e) \(8.78\times\left(\dfrac{0.0500}{0.478}\right)\)
- (f) 140 + 7.68 + 0.014
- (g) 28.7 – 0.0483
- (h) \(\dfrac{(88.5−87.57)}{45.13}\)

Consider the results of the archery contest shown in this figure.

- (a) Which archer is most precise?
- (b) Which archer is most accurate?
- (c) Who is both least precise and least accurate?

Classify the following sets of measurements as accurate, precise, both, or neither.

- (a) Checking for consistency in the weight of chocolate chip cookies: 17.27 g, 13.05 g, 19.46 g, 16.92 g
- (b) Testing the volume of a batch of 25-mL pipettes: 27.02 mL, 26.99 mL, 26.97 mL, 27.01 mL
- (c) Determining the purity of gold: 99.9999%, 99.9998%, 99.9998%, 99.9999%

## 1.6: Mathematical Treatment of Measurement Results

Write conversion factors (as ratios) for the number of:

- yards in 1 meter
- liters in 1 liquid quart
- pounds in 1 kilogram

(a) \(\mathrm{\dfrac{1.0936\: yd}{1\: m}}\); (b) \(\mathrm{\dfrac{0.94635\: L}{1\: qt}}\); (c) \(\mathrm{\dfrac{2.2046\: lb}{1\: kg}}\)

Write conversion factors (as ratios) for the number of:

- (a) kilometers in 1 mile
- (b) liters in 1 cubic foot
- (c) grams in 1 ounce

The label on a soft drink bottle gives the volume in two units: 2.0 L and 67.6 fl oz. Use this information to derive a conversion factor between the English and metric units. How many significant figures can you justify in your conversion factor?

\(\mathrm{\dfrac{2.0\: L}{67.6\: fl\: oz}=\dfrac{0.030\: L}{1\: fl\: oz}}\)

Only two significant figures are justified.

The label on a box of cereal gives the mass of cereal in two units: 978 grams and 34.5 oz. Use this information to find a conversion factor between the English and metric units. How many significant figures can you justify in your conversion factor?

Soccer is played with a round ball having a circumference between 27 and 28 in. and a weight between 14 and 16 oz. What are these specifications in units of centimeters and grams?

68–71 cm; 400–450 g

A woman's basketball has a circumference between 28.5 and 29.0 inches and a maximum weight of 20 ounces (two significant figures). What are these specifications in units of centimeters and grams?

How many milliliters of a soft drink are contained in a 12.0-oz can?

355 mL

A barrel of oil is exactly 42 gal. How many liters of oil are in a barrel?

The diameter of a red blood cell is about 3 \(\times\) 10^{−4} in. What is its diameter in centimeters?

8 \(\times\) 10^{−4} cm

The distance between the centers of the two oxygen atoms in an oxygen molecule is 1.21 \(\times\) 10^{−8} cm. What is this distance in inches?

Is a 197-lb weight lifter light enough to compete in a class limited to those weighing 90 kg or less?

yes; weight = 89.4 kg

A very good 197-lb weight lifter lifted 192 kg in a move called the clean and jerk. What was the mass of the weight lifted in pounds?

Many medical laboratory tests are run using 5.0 μL blood serum. What is this volume in milliliters?

5.0 \(\times\) 10^{−3} mL

If an aspirin tablet contains 325 mg aspirin, how many grams of aspirin does it contain?

Use scientific (exponential) notation to express the following quantities in terms of the SI base units in [link]:

- (a) 0.13 g
- (b) 232 Gg
- (c) 5.23 pm
- (d) 86.3 mg
- (e) 37.6 cm
- (f) 54 μm
- (g) 1 Ts
- (h) 27 ps
- (i) 0.15 mK

(a) 1.3 \(\times\) 10^{−4} kg; (b) 2.32 \(\times\) 10^{8} kg; (c) 5.23 \(\times\) 10^{−12} m; (d) 8.63 \(\times\) 10^{−5} kg; (e) 3.76 \(\times\) 10^{−1} m; (f) 5.4 \(\times\) 10^{−5} m; (g) 1 \(\times\) 10^{12} s; (h) 2.7 \(\times\) 10^{−11} s; (i) 1.5 \(\times\) 10^{−4} K

Complete the following conversions between SI units.

- (a) 612 g = ________ mg
- (b) 8.160 m = ________ cm
- (c) 3779 μg = ________ g
- (d) 781 mL = ________ L
- (e) 4.18 kg = ________ g
- (f) 27.8 m = ________ km
- (g) 0.13 mL = ________ L
- (h) 1738 km = ________ m
- (i) 1.9 Gg = ________ g

Gasoline is sold by the liter in many countries. How many liters are required to fill a 12.0-gal gas tank?

45.4 L

Milk is sold by the liter in many countries. What is the volume of exactly 1/2 gal of milk in liters?

A long ton is defined as exactly 2240 lb. What is this mass in kilograms?

1.0160 \(\times\) 10^{3} kg

Make the conversion indicated in each of the following:

- (a) the men’s world record long jump, 29 ft 4¼ in., to meters
- (b) the greatest depth of the ocean, about 6.5 mi, to kilometers
- (c) the area of the state of Oregon, 96,981 mi
^{2}, to square kilometers - (d) the volume of 1 gill (exactly 4 oz) to milliliters
- (e) the estimated volume of the oceans, 330,000,000 mi
^{3}, to cubic kilometers. - (f) the mass of a 3525-lb car to kilograms
- (g) the mass of a 2.3-oz egg to grams

Make the conversion indicated in each of the following:

- (a) the length of a soccer field, 120 m (three significant figures), to feet
- (b) the height of Mt. Kilimanjaro, at 19,565 ft the highest mountain in Africa, to kilometers
- (c) the area of an 8.5 t 11-inch sheet of paper in cm
^{2} - (d) the displacement volume of an automobile engine, 161 in.
^{3}, to liters - (e) the estimated mass of the atmosphere, 5.6 t 10
^{15}tons, to kilograms - (f) the mass of a bushel of rye, 32.0 lb, to kilograms
- (g) the mass of a 5.00-grain aspirin tablet to milligrams (1 grain = 0.00229 oz)

- (a) 394 ft
- (b) 5.9634 km
- (c) 6.0 \(\times\) 10
^{2} - (d) 2.64 L
- (e) 5.1 \(\times\) 10
^{18}kg - (f) 14.5 kg
- (g) 324 mg

Many chemistry conferences have held a 50-Trillion Angstrom Run (two significant figures). How long is this run in kilometers and in miles? (1 Å = 1 \(\times\) 10^{−10} m)

A chemist’s 50-Trillion Angstrom Run (see Exercise) would be an archeologist’s 10,900 cubit run. How long is one cubit in meters and in feet? (1 Å = 1 \(\times\) 10^{−8} cm)

0.46 m; 1.5 ft/cubit

The gas tank of a certain luxury automobile holds 22.3 gallons according to the owner’s manual. If the density of gasoline is 0.8206 g/mL, determine the mass in kilograms and pounds of the fuel in a full tank.

As an instructor is preparing for an experiment, he requires 225 g phosphoric acid. The only container readily available is a 150-mL Erlenmeyer flask. Is it large enough to contain the acid, whose density is 1.83 g/mL?

Yes, the acid's volume is 123 mL.

To prepare for a laboratory period, a student lab assistant needs 125 g of a compound. A bottle containing 1/4 lb is available. Did the student have enough of the compound?

A chemistry student is 159 cm tall and weighs 45.8 kg. What is her height in inches and weight in pounds?

62.6 in (about 5 ft 3 in.) and 101 lb

In a recent Grand Prix, the winner completed the race with an average speed of 229.8 km/h. What was his speed in miles per hour, meters per second, and feet per second?

Solve these problems about lumber dimensions.

(a) To describe to a European how houses are constructed in the US, the dimensions of “two-by-four” lumber must be converted into metric units. The thickness \(\times\) width \(\times\) length dimensions are 1.50 in. \(\times\) 3.50 in. \(\times\) 8.00 ft in the US. What are the dimensions in cm \(\times\) cm \(\times\) m?

(b) This lumber can be used as vertical studs, which are typically placed 16.0 in. apart. What is that distance in centimeters?

(a) 3.81 cm \(\times\) 8.89 cm \(\times\) 2.44 m; (b) 40.6 cm

The mercury content of a stream was believed to be above the minimum considered safe—1 part per billion (ppb) by weight. An analysis indicated that the concentration was 0.68 parts per billion. What quantity of mercury in grams was present in 15.0 L of the water, the density of which is 0.998 g/ml? \(\mathrm{\left(1\: ppb\: Hg=\dfrac{1\: ng\: Hg}{1\: g\: water}\right)}\)

Calculate the density of aluminum if 27.6 cm^{3} has a mass of 74.6 g.

2.70 g/cm^{3}

Osmium is one of the densest elements known. What is its density if 2.72 g has a volume of 0.121 cm^{3}?

Calculate these masses.

(a) What is the mass of 6.00 cm^{3} of mercury, density = 13.5939 g/cm^{3}?

(b) What is the mass of 25.0 mL octane, density = 0.702 g/cm^{3}?

(a) 81.6 g; (b) 17.6 g

Calculate these masses.

- (a) What is the mass of 4.00 cm
^{3}of sodium, density = 0.97 g/cm? - (b) What is the mass of 125 mL gaseous chlorine, density = 3.16 g/L?

Calculate these volumes.

- (a) What is the volume of 25 g iodine, density = 4.93 g/cm
^{3}? - (b) What is the volume of 3.28 g gaseous hydrogen, density = 0.089 g/L?

(a) 5.1 mL; (b) 37 L

Calculate these volumes.

- (a) What is the volume of 11.3 g graphite, density = 2.25 g/cm
^{3}? - (b) What is the volume of 39.657 g bromine, density = 2.928 g/cm
^{3}?

Convert the boiling temperature of gold, 2966 °C, into degrees Fahrenheit and kelvin.

5371 °F, 3239 K

Convert the temperature of scalding water, 54 °C, into degrees Fahrenheit and kelvin.

Convert the temperature of the coldest area in a freezer, −10 °F, to degrees Celsius and kelvin.

−23 °C, 250 K

Convert the temperature of dry ice, −77 °C, into degrees Fahrenheit and kelvin.

Convert the boiling temperature of liquid ammonia, −28.1 °F, into degrees Celsius and kelvin.

−33.4 °C, 239.8 K

The label on a pressurized can of spray disinfectant warns against heating the can above 130 °F. What are the corresponding temperatures on the Celsius and kelvin temperature scales?

The weather in Europe was unusually warm during the summer of 1995. The TV news reported temperatures as high as 45 °C. What was the temperature on the Fahrenheit scale?

113 °F

## Contributors and Attributions

Paul Flowers (University of North Carolina - Pembroke), Klaus Theopold (University of Delaware) and Richard Langley (Stephen F. Austin State University) with contributing authors. Textbook content produced by OpenStax College is licensed under a Creative Commons Attribution License 4.0 license. Download for free at http://cnx.org/contents/85abf193-2bd...a7ac8df6@9.110).