Atoms and Molecules

An atom is the smallest particle of an element that has the properties of that element. Consider the element gold, for example. Imagine cutting a gold nugget in half, then cutting one of the halves in half and repeating this process until a piece of gold remained that was so small that it could not be cut in half (regardless of how tiny your knife may be). This minimally sized piece of gold is an atom (from the Greek atomos, meaning “indivisible”) (Figure 3). This atom would no longer be gold if it were divided any further.

The first suggestion that matter is composed of atoms is attributed to the Greek philosophers Leucippus and Democritus, who developed their ideas in the 5th century BCE. However, it was not until the early nineteenth century that John Dalton (1766–1844), a British school teacher with a keen interest in science, supported this hypothesis with quantitative measurements. Since then, repeated experiments have confirmed many aspects of this hypothesis and it has become one of the central theories of chemistry. Other aspects of Dalton’s atomic theory are still used but with minor revisions (details of Dalton’s theory are provided in the chapter on atoms and molecules).

An atom is so small that its size is difficult to imagine. One of the smallest things we can see with our unaided eye is a single thread of a spider web: These strands are about 1/10,000 of a centimeter (0.0001 cm) in diameter. Although the cross-section of one strand is almost impossible to see without a microscope, it is huge on an atomic scale. A single carbon atom in the web has a diameter of about 0.000000015 centimeter and it would take about 7,000 carbon atoms to span the diameter of the strand. To put this in perspective, if a carbon atom were the size of a dime, the cross-section of one strand would be larger than a football field. This would require about 150 million “dimes” or carbon atoms to cover it. (Figure 4) shows increasingly close microscopic and atomic-level views of ordinary cotton.

An atom is so light that its mass is also difficult to imagine. A billion lead atoms (1,000,000,000 atoms) masses about 3 × 10⁻¹³ grams, a mass that is far too light to be measured on even the world’s most sensitive balances. It would require over 300,000,000,000,000 lead atoms (300 trillion, or 3 × 10¹⁴) to be measured and they would mass only 0.0000001 gram.

It is rare to find collections of individual atoms. Only a few elements, such as the gases helium, neon and argon, consist of a collection of individual atoms that move about independently of one another. Other elements, such as the gas states of hydrogen, nitrogen, oxygen and chlorine, are composed of units that consist of pairs of atoms (Figure 5). One form of the element phosphorus consists of units composed of four phosphorus atoms. The element sulfur exists in various forms, one of which consists of units composed of eight sulfur atoms. These units are called molecules. A molecule consists of two or more atoms joined by strong forces called chemical bonds. The atoms in a molecule move around as a unit, much like the cans of soda in a six-pack or a bunch of keys joined together on a single key ring. A molecule may consist of two or more identical atoms, as in the molecules found in the elements hydrogen, oxygen and sulfur or it may consist of two or more different atoms, as in the molecules found in water. Each water molecule is a unit that contains two hydrogen atoms and one oxygen atom. Each glucose molecule is a unit that contains 6 carbon atoms, 12 hydrogen atoms and 6 oxygen atoms. Like atoms, molecules are incredibly small and light. If an ordinary glass of water were enlarged to the size of the earth, the water molecules inside it would be about the size of golf balls.

Classifying Matter

We can classify matter into several categories. Two broad categories are pure substances  and mixtures. A pure substance has a constant composition. All specimens of a pure substance have exactly the same makeup and properties. Any sample of sucrose (table sugar) consists of 42.1% carbon, 6.5% hydrogen and 51.4% oxygen by mass. Any sample of sucrose also has the same physical properties, such as melting point, color and sweetness, regardless of the source from which it is isolated.

We can divide pure substances into two classes: elements and compounds. Pure substances that cannot be broken down into simpler substances by chemical changes are called elements. Iron, silver, gold, aluminum, sulfur, oxygen, and copper are familiar examples of the more than 100 known elements. Of these, about 90 occur naturally on the earth and two dozen or so have been created in laboratories.

Pure substances that can be broken down by chemical changes are called compounds. This breakdown may produce either elements or other compounds, or both. Mercury(II) oxide, an orange, crystalline solid, can be broken down by heat into the elements mercury and oxygen (Figure 6). When heated in the absence of air, the compound sucrose is broken down into the element carbon and the compound water. (The initial stage of this process, when the sugar is turning brown, is known as caramelization—this is what imparts the characteristic sweet and nutty flavor to caramel apples, caramelized onions, and caramel). Silver chloride is a white solid that can be broken down into its elements, silver and chlorine, by the absorption of light. This property is the basis for the use of this compound in photographic films and photochromic eyeglasses (those with lenses that darken when exposed to light).

The properties of combined elements are different from those in the free, or uncombined, state. For example, white crystalline sugar (sucrose) is a compound resulting from the chemical combination of the element carbon, which is a black solid in one of its uncombined forms, and the two elements hydrogen and oxygen, which are colorless gases when uncombined. Free sodium, an element that is a soft, shiny, metallic solid, and free chlorine, an element that is a yellow-green gas, combine to form sodium chloride (table salt), a compound that is a white, crystalline solid.

A mixture is composed of two or more types of matter that can be present in varying amounts and can be separated by physical changes, such as evaporation (you will learn more about this later). A mixture with a composition that varies from point to point is called a heterogeneous mixture. Italian dressing is an example of a heterogeneous mixture (Figure 7a). Its composition can vary because we can make it from varying amounts of oil, vinegar and herbs. It is not the same from point to point throughout the mixture—one drop may be mostly vinegar, whereas a different drop may be mostly oil or herbs because the oil and vinegar separate and the herbs settle. Other examples of heterogeneous mixtures are chocolate chip cookies (we can see the separate bits of chocolate, nuts and cookie dough) and granite (we can see the quartz, mica, feldspar and more).

A homogeneous mixture, also called a solution, exhibits a uniform composition and appears visually the same throughout. An example of a solution is a sports drink, consisting of water, sugar, coloring, flavoring, and electrolytes mixed together uniformly (Figure 7b). Each drop of a sports drink tastes the same because each drop contains the same amounts of water, sugar and other components. Note that the composition of a sports drink can vary—it could be made with somewhat more or less sugar, flavoring or other components, and still be a sports drink. Other examples of homogeneous mixtures include air, maple syrup, gasoline and a solution of salt in water.

Although there are just over 100 elements, tens of millions of chemical compounds result from different combinations of these elements. Each compound has a specific composition and possesses definite chemical and physical properties by which we can distinguish it from all other compounds. In addition, of course, there are innumerable ways to combine elements and compounds to form different mixtures. A summary of how to distinguish between the various major classifications of matter is shown in (Figure 8).

Eleven elements make up about 99% of the earth’s crust and atmosphere (Table 1). Oxygen constitutes nearly one-half and silicon about one-quarter of the total quantity of these elements. A majority of elements on earth are found in chemical combinations with other elements; about one-quarter of the elements are also found in the free state.

Conversion of Temperature Units

We use the word temperature to refer to the hotness or coldness of a substance. One way we measure a change in temperature is to use the fact that most substances expand when their temperature increases and contract when their temperature decreases. The mercury or alcohol in a common glass thermometer changes its volume as the temperature changes. Because the volume of the liquid changes more than the volume of the glass, we can see the liquid expand when it gets warmer and contract when it gets cooler.

To mark a scale on a thermometer, we need a set of reference values: Two of the most commonly used are the freezing and boiling temperatures of water at a specified atmospheric pressure. On the Celsius scale, 0 °C is defined as the freezing temperature of water and 100 °C as the boiling temperature of water. The space between the two temperatures is divided into 100 equal intervals, which we call degrees. On the Fahrenheit scale, the freezing point of water is defined as 32 °F and the boiling temperature as 212 °F. The space between these two points on a Fahrenheit thermometer is divided into 180 equal parts (degrees).

Defining the Celsius and Fahrenheit temperature scales as described in the previous paragraph results in a slightly more complex relationship between temperature values on these two scales than for different units of measure for other properties. Most measurement units for a given property are directly proportional to one another (y = mx). Using familiar length units as one example:

$\text{length in feet} = \left(\dfrac{\SI{1}{ft}}{\SI{12}{in}}\right) \times \text{ length in inches}$

where y = length in feet, x = length in inches, and the proportionality constant, m, is the conversion factor. The Celsius and Fahrenheit temperature scales, however, do not share a common zero point, and so the relationship between these two scales is a linear one rather than a proportional one (y = mx + b). Consequently, converting a temperature from one of these scales into the other requires more than simple multiplication by a conversion factor, m, it also must take into account differences in the scales’ zero points (b).

The linear equation relating Celsius and Fahrenheit temperatures is easily derived from the two temperatures used to define each scale. Representing the Celsius temperature as x and the Fahrenheit temperature as y, the slope, m, is computed to be:

$m = \dfrac{\Delta y}{\Delta x} = \dfrac{\SI{212}{\degree F} – \SI{32}{\degree F}}{\SI{100}{\degree C} – \SI{0}{\degree C}} = \dfrac{\SI{180}{\degree F}}{\SI{100}{\degree C}} = \dfrac{\SI{9}{\degree F}}{\SI{5}{\degree C}} $

The y-intercept of the equation, b, is then calculated using either of the equivalent temperature pairs, (100 °C, 212 °F) or (0 °C, 32 °F), as:

$b = y-mx = \SI{32}{\degree F} – \left(\dfrac{\SI{9}{\degree F}}{\SI{5}{\degree C}}\right) \times \SI{0}{\degree C} = \SI{32}{\degree F}$

The equation relating the temperature scales is then:

$T_{\si{\degree F}} = \left(\dfrac{\SI{9}{\degree F}}{\SI{5}{\degree C}} \times T_{\si{\degree C}} \right) + \SI{32}{\degree C}$

An abbreviated form of this equation that omits the measurement units is:

$T_{\si{\degree F}} = \left(\dfrac{9}{5} \times T_{\si{\degree C}} \right) + 32$

Rearrangement of this equation yields the form useful for converting from Fahrenheit to Celsius:

$T_{\si{\degree C}} = \dfrac{5}{9}(T_{\si{\degree F}}-32)$

As mentioned earlier in this chapter, the SI unit of temperature is the kelvin (K). Unlike the Celsius and Fahrenheit scales, the kelvin scale is an absolute temperature scale in which 0 (zero) K corresponds to the lowest temperature that can theoretically be achieved. The early 19th-century discovery of the relationship between a gas’s volume and temperature suggested that the volume of a gas would be zero at −273.15 °C. In 1848, British physicist William Thompson, who later adopted the title of Lord Kelvin, proposed an absolute temperature scale based on this concept (further treatment of this topic is provided in this text’s chapter on gases).

The freezing temperature of water on this scale is 273.15 K and its boiling temperature 373.15 K. Notice the numerical difference in these two reference temperatures is 100, the same as for the Celsius scale, and so the linear relation between these two temperature scales will exhibit a slope of $1 \frac{\si{K}}{\si{\degree C}}$ Following the same approach, the equations for converting between the kelvin and Celsius temperature scales are derived to be:

$T_{\si{K}} = T_{\si{\degree C}}+273.15$

$T_{\si{\degree C}} = T_{\si{K}}-273.15$

The 273.15 in these equations has been determined experimentally, so it is not exact. Figure 1 shows the relationship among the three temperature scales. Recall that we do not use the degree sign with temperatures on the kelvin scale.

Although the kelvin (absolute) temperature scale is the official SI temperature scale, Celsius is commonly used in many scientific contexts and is the scale of choice for nonscience contexts in almost all areas of the world. Very few countries (the U.S. and its territories, the Bahamas, Belize, Cayman Islands, and Palau) still use Fahrenheit for weather, medicine, and cooking.

Conversion from Celsius

Normal body temperature has been commonly accepted as 37.0 °C (although it varies depending on time of day and method of measurement, as well as among individuals). What is this temperature on the kelvin scale and on the Fahrenheit scale?

Solution

$\si{K} = \si{\degree C} + 273.15 = 37.0 + 273.2 = 310.2 \si{K}$

$\si{\degree F} = \dfrac{9}{5} \si{\degree C} + 32.0 = \left(\dfrac{9}{5} \times 37.0 \right) +32.0 = 66.6+32.0 = 98.6 \si{\degree F}$

Check Your Learning

Convert 80.92 °C to K and °F.

ANSWER:

354.07 K, 177.7 °F