Introduction

Natasha Ramroop Singh, PhD

Chemical Bonding and Organic Chemistry

**Figure 0.1.** Chemistry apparatus. ( j4p4n/OpenClipArt) CC0 1.0

Chemistry is the study of matter (anything that has mass and takes up space), its properties, and the changes it undergoes, and it is central to our fundamental understanding of many science-related fields. The field of chemistry can be broadly divided into five main branches:

Organic Chemistry: The study of carbon and carbon-containing compounds—It is also sometimes called the study of the chemistry of life.

Inorganic Chemistry: The study of compounds that do not possess C-H bonds.

Analytical Chemistry: The study of the development of tools to measure various physical and chemical properties of matter.

Physical Chemistry: The study of the physics of the atom, including applications of thermodynamics and quantum mechanics.

Biochemistry: The study of the chemical processes which occur within living things—This field shares much in common with the field of organic chemistry.

Of course, there are many other sub-divisions and iterations of the study of chemistry: environmental chemistry (which takes into consideration the principles of green chemistry and sustainability), petroleum geochemistry, chemical engineering, and many others. If you wish to find some good information on careers in the chemical sciences, you can visit the American Chemical Society’s “Careers & the Chemical Sciences.”

In this text, our focus will be two-fold. Chapters 1–5 focus on physical chemistry, where we look at atomic structure and bonding. Chapters 6–8 will focus on organic chemistry, where we will examine the nomenclature and properties of organic molecules with a focus on biomolecules and pharmaceuticals.

**Figure 0.2.** A chemist at work in the laboratory. (U.S. Army DEVCOM) CC BY 2.0

Learning Objectives

By the end of this section, you will be able to:

Outline the historical development of chemistry.
Provide examples of the importance of chemistry in everyday life.
Describe the scientific method.
Differentiate among hypotheses, theories, and laws.
Provide examples illustrating macroscopic, microscopic, and symbolic domains.

Throughout human history, people have tried to convert matter into more useful forms. Our Stone Age ancestors chipped pieces of flint into useful tools and carved wood into statues and toys. These endeavours involved changing the shape of a substance without changing the substance itself. But as our knowledge increased, humans began to change the composition of the substances as well—clay was converted into pottery, hides were cured to make garments, copper ores were transformed into copper tools and weapons, and grain was made into bread.

Humans began to practise chemistry when they learned to control fire and use it to cook, make pottery, and smelt metals. Subsequently, they began to separate and use specific components of matter. A variety of drugs such as aloe, myrrh, and opium were isolated from plants. Dyes, such as indigo and Tyrian purple, were extracted from plant and animal matter. Metals were combined to form alloys—for example, copper and tin were mixed together to make bronze—and more elaborate smelting techniques produced iron. Alkalis were extracted from ashes, and soaps were prepared by combining these alkalis with fats. Alcohol was produced by fermentation and purified by distillation.

Attempts to understand the behaviour of matter extend back for more than 2500 years. As early as the 6th century BC, Greek philosophers discussed a system in which water was the basis of all things. You may have heard of the Greek postulate that matter consists of four elements: earth, air, fire, and water. Subsequently, an amalgamation of chemical technologies and philosophical speculations were spread from Egypt, China, and the eastern Mediterranean by alchemists, who endeavoured to transform “base metals” such as lead into “noble metals” like gold, and to create elixirs to cure disease and extend life (Figure 1).

A sketch depicts 4 people stirring and handling chemicals. The chemicals are held in a variety of barrels and large cylinders. Several of the containers are being heated over burning embers. A large stove in the laboratory is filled with burning embers. There is also a large chest in the corner that is producing steam.

From alchemy came the historical progressions that led to modern chemistry: the isolation of drugs from natural sources, metallurgy, and the dye industry. Today, chemistry continues to deepen our understanding and improve our ability to harness and control the behaviour of matter. This effort has been so successful that many people do not realize either the central position of chemistry among the sciences or the importance and universality of chemistry in daily life.

Chemistry: The Central Science

Chemistry is sometimes referred to as “the central science” due to its interconnectedness with a vast array of other STEM disciplines (STEM stands for areas of study in the science, technology, engineering, and math fields). Chemistry and the language of chemists play vital roles in biology, medicine, materials science, forensics, environmental science, and many other fields (Figure 2). The basic principles of physics are essential for understanding many aspects of chemistry, and there is extensive overlap between many subdisciplines within the two fields, such as chemical physics and nuclear chemistry. Mathematics, computer science, and information theory provide important tools that help us calculate, interpret, describe, and generally make sense of the chemical world. Biology and chemistry converge in biochemistry, which is crucial to understanding the many complex factors and processes that keep living organisms (such as us) alive. Chemical engineering, materials science, and nanotechnology combine chemical principles and empirical findings to produce useful substances, ranging from gasoline to fabrics to electronics. Agriculture, food science, veterinary science, and brewing and winemaking help provide sustenance in the form of food and drink to the world’s population. Medicine, pharmacology, biotechnology, and botany identify and produce substances that help keep us healthy. Environmental science, geology, oceanography, and atmospheric science incorporate many chemical ideas to help us better understand and protect our physical world. Chemical ideas are used to help understand the universe in astronomy and cosmology.

A flowchart shows a box containing chemistry at its center. Chemistry is connected to geochemistry, nuclear chemistry, chemical physics, nanoscience and nanotechnology, materials science, chemical engineering, biochemistry and molecular biology, environmental science, agriculture, and mathematics. Each of these disciplines is further connected to other related fields including medicine, biology, food science, geology earth sciences, toxicology, physics, and computer science.

What are some changes in matter that are essential to daily life? Digesting and assimilating food, synthesizing polymers that are used to make clothing, containers, cookware, and credit cards, and refining crude oil into gasoline and other products are just a few examples. As you proceed through this text, you will discover many different examples of changes in the composition and structure of matter, how to classify these changes and how they occurred, their causes, the changes in energy that accompany them, and the principles and laws involved. As you learn about these things, you will be learning chemistry, the study of the composition, properties, and interactions of matter. The practice of chemistry is not limited to chemistry books or laboratories; it happens whenever someone is involved in changes in matter or in conditions that may lead to such changes.

The Scientific Method

Chemistry is a science based on observation and experimentation. Doing chemistry involves attempting to answer questions and explain observations in terms of the laws and theories of chemistry, using procedures that are accepted by the scientific community. There is no single route to answering a question or explaining an observation, but there is an aspect common to every approach: Each uses knowledge based on experiments that can be reproduced to verify the results. Some routes involve a hypothesis, a tentative explanation of observations that acts as a guide for gathering and checking information. We test a hypothesis by experimentation, calculation, and/or comparison with the experiments of others and then refine it as needed.

Some hypotheses are attempts to explain the behaviour that is summarized in laws. The laws of science summarize a vast number of experimental observations, and describe or predict some facet of the natural world. If such a hypothesis turns out to be capable of explaining a large body of experimental data, it can reach the status of a theory. Scientific theories are well-substantiated, comprehensive, testable explanations of particular aspects of nature. Theories are accepted because they provide satisfactory explanations, but they can be modified if new data become available. The path of discovery that leads from question and observation to law or hypothesis to theory, combined with experimental verification of the hypothesis and any necessary modification of the theory, is called the scientific method (Figure 3).

In this flowchart, the observation and curiosity box has an arrow pointing to a box labeled form hypothesis; make prediction. A curved arrow labeled next connects this box to a box labeled perform experiment; make more observations. Another arrow points back to the box that says form hypothesis; make prediction. This arrow is labeled results not consistent with prediction. Another arrow, labeled results are consistent with prediction points from the perform experiment box to a box labeled contributes to body of knowledge. However, an arrow also points from contributes to body of knowledge back to the form hypothesis; make prediction box. This arrow is labeled further testing does not support hypothesis. There are also two other arrows leading out from contributes to body of knowledge. One arrow is labeled much additional testing yields constant observations. This leads to the observation becomes law box. The other arrow is labeled much additional testing supports hypothesis. This arrow leads to the hypothesis becomes theory box.

The Domains of Chemistry

Chemists study and describe the behaviour of matter and energy in three different domains: macroscopic, microscopic, and symbolic. These domains provide different ways of considering and describing chemical behaviour.

Macro is a Greek word that means “large.” The macroscopic domain is familiar to us: It is the realm of everyday things that are large enough to be sensed directly by human sight or touch. In daily life, this includes the food you eat and the breeze you feel on your face. The macroscopic domain includes everyday and laboratory chemistry, where we observe and measure physical and chemical properties, or changes such as density, solubility, and flammability.

The microscopic domain of chemistry is almost always visited in the imagination. Micro also comes from Greek and means “small.” Some aspects of the microscopic domains are visible through a microscope, such as a magnified image of graphite or bacteria. Viruses, for instance, are too small to be seen with the naked eye, but when we’re suffering from a cold, we’re reminded of how real they are.

However, most of the subjects in the microscopic domain of chemistry—such as atoms and molecules—are too small to be seen even with standard microscopes and often must be pictured in the mind. Other components of the microscopic domain include ions and electrons, protons and neutrons, and chemical bonds, each of which is far too small to see. This domain includes the individual metal atoms in a wire, the ions that compose a salt crystal, the changes in individual molecules that result in a colour change, the conversion of nutrient molecules into tissue and energy, and the evolution of heat as bonds that hold atoms together are created.

The symbolic domain contains the specialized language used to represent components of the macroscopic and microscopic domains. Chemical symbols (such as those used in the periodic table), chemical formulas, and chemical equations are part of the symbolic domain, as are graphs and drawings. We can also consider calculations as part of the symbolic domain. These symbols play an important role in chemistry because they help interpret the behaviour of the macroscopic domain in terms of the components of the microscopic domain. One of the challenges for students learning chemistry is recognizing that the same symbols can represent different things in the macroscopic and microscopic domains, and one of the features that makes chemistry fascinating is the use of a domain that must be imagined to explain behaviour in a domain that can be observed.

A helpful way to understand the three domains is via the essential and ubiquitous substance of water. That water is a liquid at moderate temperatures, will freeze to form a solid at lower temperatures, and boil to form a gas at higher temperatures (Figure 4) are macroscopic observations. But some properties of water fall into the microscopic domain—what we cannot observe with the naked eye. The description of water as comprised of two hydrogen atoms and one oxygen atom, and the explanation of freezing and boiling in terms of attractions between these molecules is within the microscopic arena. The formula H₂O, which can describe water at either the macroscopic or microscopic level, is an example of the symbolic domain. The abbreviations (g) for gas, (s) for solid, and (l) for liquid are also symbolic.

Figure A shows a photo of an iceberg floating in a sea has three arrows. Each arrow points to figure B, which contains three diagrams showing how the water molecules are organized in the air, ice, and sea. In the air, which contains the gaseous form of water, H subscript 2 O gas, the water molecules are disconnected and widely spaced. In the ice, which is the solid form of water, H subscript 2 O solid, the water molecules are bonded together into rings, with each ring containing six water molecules. Three of these rings are connected to each other. In the sea, which is the liquid form of water, H subscript 2 O liquid, the water molecules are very densely packed. The molecules are not bonded together.

Key Concepts and Summary

Chemistry deals with the composition, structure, and properties of matter, and the ways by which various forms of matter may be interconverted. Thus, it occupies a central place in the study and practice of science and technology. Chemists use the scientific method to perform experiments, pose hypotheses, and formulate laws and develop theories, so that they can better understand the behaviour of the natural world. To do so, they operate in the macroscopic, microscopic, and symbolic domains. Chemists measure, analyze, purify, and synthesize a wide variety of substances that are important to our lives.

Exercises

The following questions were retrieved from OpenStax (2019) Chemistry 2e, Chapter 1: “Exercises.”

Chemistry in Context

Explain how you could experimentally determine whether the outside temperature is higher or lower than 0 °C (32 °F) without using a thermometer.
Identify each of the following statements as being most similar to a hypothesis, a law, or a theory. Explain your reasoning.
1. Falling barometric pressure precedes the onset of bad weather.
2. All life on Earth has evolved from a common, primitive organism through the process of natural selection.
3. My truck’s gas mileage has dropped significantly, probably because it’s due for a tune-up.
Identify each of the following statements as being most similar to a hypothesis, a law, or a theory. Explain your reasoning.
1. The pressure of a sample of gas is directly proportional to the temperature of the gas.
2. Matter consists of tiny particles that can combine in specific ratios to form substances with specific properties.
3. At a higher temperature, solids (such as salt or sugar) will dissolve better in water.
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.
1. The mass of a lead pipe is 14 lb.
2. The mass of a certain chlorine atom is 35 amu.
3. A bottle with a label that reads Al contains aluminum metal.
4. 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.
1. A certain molecule contains one H atom and one Cl atom.
2. Copper wire has a density of about 8 g/cm³.
3. The bottle contains 15 grams of Ni powder.
4. A sulfur molecule is composed of eight sulfur atoms.
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 behaviour? Explain your answer.
The amount of heat required to melt 2 lb 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 behaviour? Explain your answer.

Phases and Classification of Matter

Why is an object’s mass, rather than its weight, used 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:
1. Copper
2. Water
3. Nitrogen
4. Sulfur
5. Air
6. Sucrose
7. A substance composed of molecules, each of which contains two iodine atoms
8. Gasoline
Classify each of the following as an element, a compound, or a mixture:
1. Iron
2. Oxygen
3. Mercury oxide
4. Pancake syrup
5. Carbon dioxide
6. A substance composed of molecules, each of which contains one hydrogen atom and one chlorine atom
7. Baking soda
8. 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?
Why are astronauts in space said to be “weightless,” but not “massless”?
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 15 different kinds of matter that you encounter every day. Your list should include (and label at least one example of) each of 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, called rust.
1. 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.
2. 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:
1. 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.
2. 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.
3. 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:
$glucose⟶ethanol+carbon dioxide$
1. If 200 g of glucose is fully converted, what will be the total mass of ethanol and carbon dioxide produced?
2. 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.
3. If 97.7 g of carbon dioxide is produced, what mass of ethanol is produced?

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 gram of hydrogen.
Classify each of the following changes as physical or chemical:
1. Condensation of steam
2. Burning of gasoline
3. Souring of milk
4. Dissolving of sugar in water
5. Melting of gold
Classify each of the following changes as physical or chemical:
1. Coal burning
2. Ice melting
3. Mixing chocolate syrup with milk
4. Explosion of a firecracker
5. 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?
A 2-L volume of hydrogen gas combined with 1 L of oxygen gas to produce 2 L of water vapour. Does oxygen undergo a chemical or physical change?
Explain the difference between extensive properties and intensive properties.
Identify the following properties as either extensive or intensive.
1. Volume
2. Temperature
3. Humidity
4. Heat
5. 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).
${\rm{density = }}\frac{{{\rm{mass}}}}{{{\rm{volume}}}}{\rm{ d = }}\frac{{\rm{m}}}{{\rm{v}}}$
Considering that mass and volume are both extensive properties, explain why their ratio, density, is intensive.

Measurements

Is one litre about an ounce, a pint, a quart, or a gallon?
Is a metre about an inch, a foot, a yard, or a mile?
Indicate the SI base units or derived units that are appropriate for the following measurements:
1. The length of a marathon race (26 miles 385 yards)
2. The mass of an automobile
3. The volume of a swimming pool
4. The speed of an airplane
5. The density of gold
6. The area of a football field
7. 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:
1. The mass of the moon
2. The distance from Dallas to Oklahoma City
3. The speed of sound
4. The density of air
5. The temperature at which alcohol boils
6. The area of the state of Delaware
7. The volume of a flu shot or a measles vaccination
Give the name and symbol of the prefixes used with SI units to indicate multiplication by the following exact quantities.
1. 10³
2. 10⁻²
3. 0.1
4. 10⁻³
5. 1,000,000
6. 0.000001
Give the name of the prefix and the quantity indicated by the following symbols that are used with SI base units.
1. c
2. d
3. G
4. k
5. m
6. n
7. p
8. T
A large piece of jewellery has a mass of 132.6 g. A graduated cylinder initially contains 48.6 mL water. When the jewellery is submerged in the graduated cylinder, the total volume increases to 61.2 mL.
1. Determine the density of this piece of jewellery.
2. Assuming that the jewellery is made from only one substance, what substance is it likely to be? Explain.
Visit SimBucket’s “Density Lab” simulation and click the “Turn Fluid into Water” button to adjust the density of liquid in the beaker to 1 g/mL.
1. Use the water displacement approach to measure the mass and volume of the unknown material (select the green block with question marks).
2. Use the measured mass and volume data from step (a) to calculate the density of the unknown material.
3. Link out to the link provided.
4. Assuming this material is a copper-containing gemstone, identify its three most likely identities by comparing the measured density to the values tabulated at AJS Gems’ “Gemstone Density” guide.
5. How are mass and density related for blocks of the same volume?
Visit the density simulation and click the “reset” button to ensure all simulator parameters are at their default values.
1. Use the water displacement approach to measure the mass and volume of the red block.
2. Use the measured mass and volume data from step (a) to calculate the density of the red block.
3. Use the vertical green slide control to adjust the fluid density to values well above, then well below, and finally nearly equal to the density of the red block, reporting your observations.
Visit the density simulation and click the “Turn Fluid into Water” button to adjust the density of liquid in the beaker to 1. g/mL. Change the block material to foam, and then wait patiently until the foam block stops bobbing up and down in the water.
1. The foam block should be floating on the surface of the water (that is, only partially submerged). What is the volume of water displaced?
2. Use the water volume from part (a) and the density of water (1 g/mL) to calculate the mass of water displaced.
3. Remove and weigh the foam block. How does the block’s mass compare to the mass of displaced water from part (b)?

Measurement Uncertainty, Accuracy, and Precision

Express each of the following numbers in scientific notation with correct significant figures:
1. 711.0
2. 0.239
3. 90743
4. 134.2
5. 0.05499
6. 10000.0
7. 0.000000738592
Express each of the following numbers in exponential notation with correct significant figures:
1. 704
2. 0.03344
3. 547.9
4. 22086
5. 1000.00
6. 0.0000000651
7. 0.007157
Indicate whether each of the following can be determined exactly or must be measured with some degree of uncertainty:
1. The number of eggs in a basket
2. The mass of a dozen eggs
3. The number of gallons of gasoline necessary to fill an automobile gas tank
4. The number of cm in 2 m
5. The mass of a textbook
6. The time required to drive from San Francisco to Kansas City at an average speed of 53 mph
Indicate whether each of the following can be determined exactly or must be measured with some degree of uncertainty:
1. The number of seconds in an hour
2. The number of pages in this book
3. The number of grams in your weight
4. The number of grams in 3 kilograms
5. The volume of water you drink in one day
6. The distance from San Francisco to Kansas City
How many significant figures are contained in each of the following measurements
1. 38.7 g
2. 2 × 10¹⁸ m
3. 3,486,002 kg
4. 9.7415 $\times$ 10⁻⁴ J
5. 0.0613 cm³
6. 17.0 kg
7. 0.01400 g/mL
How many significant figures are contained in each of the following measurements
1. 53 cm
2. 2.05 $\times$ 10⁸ m
3. 86,002 J
4. 9.740 $\times$ 10⁴ m/s
5. 10.0613 m³
6. 0.17 g/mL
7. 0.88400 s
The following quantities were reported on the labels of commercial products. Determine the number of significant figures in each.
1. 0.0055 g active ingredients
2. 12 tablets
3. 3% hydrogen peroxide
4. 5.5 ounces
5. 473 mL
6. 1.75% bismuth
7. 0.001% phosphoric acid
8. 99.80% inert ingredients
Round off each of the following numbers to two significant figures:
1. 0.436
2. 9.000
3. 27.2
4. 135
5. 1.497 $\times$ 10⁻³
6. 0.445
Round off each of the following numbers to two significant figures:
1. 517
2. 86.3
3. 6.382 $\times$ 10³
4. 5.0008
5. 22.497
6. 0.885
Perform the following calculations and report each answer with the correct number of significant figures.
1. 628 $\times$ 342
2. (5.63 $\times$ 10²) $\times$ (7.4 $\times$ 10³)
3. $\frac{{28.0}}{{13.483}}$
4. 8119 $\times$ 0.000023
5. 14.98 + 27,340 + 84.7593
6. 42.7 + 0.259
Perform the following calculations and report each answer with the correct number of significant figures.
1. 62.8 $\times$ 34
2. 0.147 + 0.0066 + 0.012
3. 38 $\times$ 95 $\times$ 1.792
4. 15 – 0.15 – 0.6155
5. $8.78{\rm{ \times }}\left( {\frac{{0.0500}}{{0.478}}} \right)$
6. 140 + 7.68 + 0.014
7. 28.7 – 0.0483
8. $\frac{{\left( {88.5 - 87.57} \right)}}{{45.13}}$
Consider the results of the archery contest shown in this figure.
1. Which archer is most precise?
2. Which archer is most accurate?
3. Who is both least precise and least accurate?
Classify the following sets of measurements as accurate, precise, both, or neither.
1. Checking for consistency in the weight of chocolate chip cookies: 17.27 g, 13.05 g, 19.46 g, 16.92 g
2. Testing the volume of a batch of 25-mL pipettes: 27.02 mL, 26.99 mL, 26.97 mL, 27.01 mL
3. Determining the purity of gold: 99.9999%, 99.9998%, 99.9998%, 99.9999%

Mathematical Treatment of Measurement Results

Write conversion factors (as ratios) for the number of:
1. Yards in 1 metre
2. Litres in 1 liquid quart
3. Pounds in 1 kilogram
Write conversion factors (as ratios) for the number of:
1. Kilometres in 1 mile
2. Litres in 1 cubic foot
3. 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?
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 inches and a weight between 14 and 16 ounces. What are these specifications in units of centimetres and grams?
A woman’s basketball has a circumference between 28.5 and 29 inches and a maximum weight of 20 ounces (two significant figures). What are these specifications in units of centimetres and grams?
How many millilitres of a soft drink are contained in a 12-oz can?
A barrel of oil is exactly 42 gal. How many litres 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 centimetres?
The distance between the centres 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 weightlifter light enough to compete in a class limited to those weighing 90 kg or less?
A very good 197-lb weightlifter 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 millilitres?
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 Table 1.2 of Chemistry 2e.
1. 0.13 g
2. 232 Gg
3. 5.23 pm
4. 86.3 mg
5. 37.6 cm
6. 54 μm
7. 1 Ts
8. 27 ps
9. 0.15 mK
Complete the following conversions between SI units.
1. 612 g = ________ mg
2. (8.160 m = ________ cm
3. 3779 μg = ________ g
4. 781 mL = ________ L
5. 4.18 kg = ________ g
6. 27.8 m = ________ km
7. 0.13 mL = ________ L
8. 1738 km = ________ m
9. 1.9 Gg = ________ g
Gasoline is sold by the litre in many countries. How many litres are required to fill a 12-gal gas tank?
Milk is sold by the litre in many countries. What is the volume of exactly 1/2 gal of milk in litres?
A long tonne is defined as exactly 2240 lb. What is this mass in kilograms?
Make the conversion indicated in each of the following:
1. The men’s world record long jump, 29 ft 4¼ in., to metres
2. The greatest depth of the ocean, about 6.5 mi, to kilometres
3. The area of the state of Oregon, 96,981 mi², to square kilometres
4. The volume of 1 gill (exactly 4 oz) to millilitres
5. The estimated volume of the oceans, 330,000,000 mi³, to cubic kilometres
6. The mass of a 3525-lb car to kilograms
7. The mass of a 2.3-oz egg to grams
Make the conversion indicated in each of the following:
1. The length of a soccer field, 120 m (three significant figures), to feet
2. The height of Mt. Kilimanjaro, the highest mountain in Africa at 19,565 ft, to kilometres
3. The area of an 8.5×11-inch sheet of paper in cm²
4. The displacement volume of an automobile engine, 161 in.³, to litres
5. The estimated mass of the atmosphere, 5.6 × 10¹⁵ tonnes, to kilograms
6. The mass of a bushel of rye, 32.0 lb, to kilograms
7. The mass of a 5-grain aspirin tablet to milligrams (1 grain = 0.00229 oz)
Many chemistry conferences have held a 50-trillion angstrom run (two significant figures). How long is this run in kilometres and in miles? (1 Å = 1 × 10⁻¹⁰ m)
A chemist’s 50-trillion angstrom run (see Exercise 78) would be an archeologist’s 10,900 cubit run. How long is one cubit in metres and in feet? (1 Å = 1 × 10⁻⁸ cm)
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?
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?
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, metres per second, and feet per second?
Solve these problems about lumber dimensions.
1. 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 × width × length dimensions are 1.5 in × 3.5 in. × 8 ft in the US. What are the dimensions in cm × cm × cm?
2. This lumber can be used as vertical studs, which are typically placed 16.0 in. apart. What is that distance in centimetres?
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 L of the water, the density of which is 0.998 g/mL? $\left( {1{\rm{ ppb Hg = }}\frac{{1{\rm{ ng Hg}}}}{{1{\rm{ g water}}}}} \right)$
Calculate the density of aluminum if 27.6 cm³ has a mass of 74.6 g.
Osmium is one of the densest elements known. What is its density if 2.72 g has a volume of 0.121 cm³?
Calculate these masses.
1. What is the mass of 6 cm³ of mercury, density = 13.5939 g/cm³?
2. What is the mass of 25 mL octane, density = 0.702 g/cm³?
Calculate these masses.
1. What is the mass of 4 cm³ of sodium, density = 0.97 g/cm³ ?
2. What is the mass of 125 mL gaseous chlorine, density = 3.16 g/L?
Calculate these volumes.
1. What is the volume of 25 g iodine, density = 4.93 g/cm³?
2. What is the volume of 3.28 g gaseous hydrogen, density = 0.089 g/L?
Calculate these volumes.
1. What is the volume of 11.3 g graphite, density = 2.25 g/cm³?
2. What is the volume of 39.657 g bromine, density = 2.928 g/cm³?
Convert the boiling temperature of gold, 2966 °C, into degrees Fahrenheit and kelvin.
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.
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.
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?

Solutions

Answers to Odd-Numbered Exercises

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

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

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

7. Macroscopic—The heat required is determined from macroscopic properties.

9. 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.

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

13. 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.

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

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

19. 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.

21. 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.

23. (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

25. (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

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

29. physical

31. 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.

33. 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).

35. about a yard

37. (a) kilograms; (b) metres; (c) metres/second; (d) kilograms/cubic metre; (e) kelvin; (f) square metres; (g) cubic metres

39. (a) centi-, × 10⁻²; (b) deci-, × 10⁻¹; (c) Giga-, × 10⁹; (d) kilo-, × 10³; (e) milli-, × 10⁻³; (f) nano-, $\times$ 10⁻⁹; (g) pico-, $\times$ 10⁻¹²; (h) tera-, × 10¹²

41. (a) m = 18.58 g, V = 5.7 mL; (b) d = 3.3 g/mL; (c) dioptase (copper cyclosilicate, d = 3.28—3.31 g/mL); malachite (basic copper carbonate, d = 3.25—4.10 g/mL); Paraiba tourmaline (sodium lithium boron silicate with copper, d = 2.82—3.32 g/mL)

43. (a) displaced water volume = 2.8 mL; (b) displaced water mass = 2.8 g; (c) The block mass is 2.76 g, essentially equal to the mass of displaced water (2.8 g) and consistent with Archimedes’ principle of buoyancy.

45. (a) 7.04 $\times$ 10²; (b) 3.344 $\times$ 10⁻²; (c) 5.479 $\times$ 10²; (d) 2.2086 $\times$ 10⁴; (e) 1.00000 $\times$ 10³; (f) 6.51 $\times$ 10⁻⁸; (g) 7.157 $\times$ 10⁻³

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

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

51. (a) 0.44; (b) 9.0; (c) 27; (d) 140; (e) 1.5 × 10⁻³; (f) 0.44

53. (a) 2.15 $\times$ 10⁵; (b) 4.2 $\times$ 10⁶; (c) 2.08; (d) 0.19; (e) 27,440; (f) 43.0

55. (a) Archer X; (b) Archer W; (c) Archer Y

57. (a) $\frac{{1.0936{\rm{ yd}}}}{{1{\rm{ m}}}}$ (b) $\frac{{0.94635{\rm{ L}}}}{{1{\rm{ qt}}}}$ (c) $\frac{{2.2046{\rm{ lb}}}}{{1{\rm{ kg}}}}$

59. $\frac{{2.0{\rm{ L}}}}{{67.6{\rm{ fl oz}}}} = \frac{{0.030{\rm{ L}}}}{{1{\rm{ fl oz}}}}$

61. 68–71 cm; 400–450 g

63. 355 mL

65. 8 $\times$ 10⁻⁴ cm

67. yes; weight = 89.4 kg

69. 5.0 $\times$ 10⁻³ mL

71. (a) 1.3 $\times$ 10⁻⁴ kg; (b) 2.32 $\times$ 10⁸ 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 $\times$ 10¹² s; (h) 2.7 $\times$ 10⁻¹¹ s; (i) 1.5 $\times$ 10⁻⁴ K

73. 45.4 L

75. 1.0160 $\times$ 10³ kg

77. (a) 394 ft; (b) 5.9634 km; (c) 6.0 $\times$ 10²; (d) 2.64 L; (e) 5.1 $\times$ 10¹⁸ kg; (f) 14.5 kg; (g) 324 mg

79. 0.46 m; 1.5 ft/cubit

81. Yes, the acid’s volume is 123 mL.

83. 62.6 in. (about 5 ft 3 in.) and 101 lb

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

87. 2.70 g/cm³

89. (a) 81.6 g; (b) 17.6 g

91. (a) 5.1 mL; (b) 37 L

93. 5371 °F, 3239 K

95. −23 °C, 250 K

97. −33.4 °C, 239.8 K

99. 113 °F

Glossary

chemistry: study of the composition, properties, and interactions of matter

hypothesis: tentative explanation of observations that acts as a guide for gathering and checking information

law: statement that summarizes a vast number of experimental observations, and describes or predicts some aspect of the natural world

macroscopic domain: realm of everyday things that are large enough to sense directly by human sight and touch

microscopic domain: realm of things that are much too small to be sensed directly

scientific method: path of discovery that leads from question and observation to law or hypothesis to theory, combined with experimental verification of the hypothesis and any necessary modification of the theory

symbolic domain: specialized language used to represent components of the macroscopic and microscopic domains, such as chemical symbols, chemical formulas, chemical equations, graphs, drawings, and calculations

theory: well-substantiated, comprehensive, testable explanation of a particular aspect of nature

Media Attributions

Figure 0.1: Chemistry items by j4p4n via OpenClipArt is used under a CC0 1.0 license.
Figure 0.2: Laboratory broadens student’s horizons by U.S. Army Combat Capabilities Development Command via Flickr is used under a CC BY 2.0 license.
Figure 1: Chemical Heritage Foundation/Science History Institute. (2015, March 11). Figure 1.2 [Digital image]. In OpenStax/Rice University, Chemistry. (Section 1.1). https://openstax.org/books/chemistry/pages/1-1-chemistry-in-context. Public domain.
Figure 2: OpenStax/Rice University. (2015, March 11). Figure 1.3 [Digital image]. In Chemistry. (Section 1.1). https://openstax.org/books/chemistry/pages/1-1-chemistry-in-context CC BY 4.0
Figure 3: OpenStax/Rice University. (2015, March 11). Figure 1.4 [Digital image]. In Chemistry. (Section 1.1). https://openstax.org/books/chemistry/pages/1-1-chemistry-in-context CC BY 4.0
Figure 4: OpenStax/Rice University. (2015, March 11). Figure 1.5 [Digital image]. In Chemistry. (Section 1.1). https://openstax.org/books/chemistry/pages/1-1-chemistry-in-context CC BY 4.0 (Derivative of image by Gorkaazk [username]. Iceberg bat [Digital image]. Wikimedia Commons. https://commons.wikimedia.org/wiki/File:Iceberg_bat.jpg. Used under a CC BY 3.0 license.)

References

OpenStax/Rice University. (2015, March 11). Chemistry. BC Campus. https://openstax.org/details/books/chemistry/ CC BY 4.0.

OpenStax/Rice University. (2019, February 14). Chemistry 2e. https://openstax.org/details/books/chemistry-2e CC BY 4.0.

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