Volume 1

Valence • Exercises
1.9.1. Valence. You have already seen quite a number of chemical formulas in this course. How do we know that table salt has the formula NaCl? The composition and ratio of the elements in NaCl and other compounds have been determined experimentally. But why is it that in NaCl there is one chlorine atom per each sodium atom, whereas in MgCl2 there are two Cl atoms per magnesium, and in AlCl3 the aluminum atom is combined with three Cl atoms? Can we predict such ratios of atoms in molecules? We can, but for that we need to know the valences of the elements a given molecule is made up of.

The valence of a chemical element is its capacity to combine with a certain number of atoms of other elements. Does this sound confusing? I would not be surprised if it did. I got interested in chemistry when I was about 10 years old. I confess that back then it is the concept of valence that represented a problem for me. That "childhood problem" of mine later on prompted me to think frequently about how to explain the idea of valence simply and clearly.

Picture atoms of various elements as small objects such as colorful balls that have a different number of "hands" (Figure 1-28). They can hold hands with one another. By holding hands they come together to form molecules. Some atoms have only one hand, some have two, and some three, four, or even more. Hydrogen (H) has only one hand, and so do fluorine (F), chlorine (Cl), sodium (Na), potassium (K), and some other elements. Oxygen (O), magnesium (Mg), calcium (Ca), and barium (Ba) all have two hands. Aluminum (Al) and nitrogen (N) have three hands, whereas carbon (C) has four (Figure 1-28).
Figure 1-28. Representation of atoms of selected elements as balls with a different number of hands.

When a "one-handed" hydrogen atom (H) shakes and holds hands with a fluorine atom (F), which is also "one-handed", a molecule of HF (hydrogen fluoride) is formed (Figure 1-29). Hydrogen and fluorine cannot form any other molecules such as H2F or H3F or H4F or HF4 just because H has only one hand and F has only one hand. Similarly, table salt, sodium chloride has the formula NaCl because both Na and Cl have only one hand each (Figure 1-29). The certain number of "hands" for each element explains the law of definite composition, stating that regardless of its origin and method of preparation, a chemical compound always contains its component elements in a fixed ratio (subsection 1.6.3).
Figure 1-29. "Handshaking" between H and F and between Na and Cl, elements that all have a valence of 1 (one "hand").

Oxygen (O) is always divalent, which means its valence equals 2 (two "hands"). Thus, an oxygen atom can "shake and hold hands" with two monovalent ("one-handed") hydrogen atoms (Figure 1-30) to form a molecule of water (H2O). As the valence of nitrogen is 3, it bonds to three hydrogen atoms to yield a molecule of ammonia (NH3). In the molecule of methane (CH4), the tetravalent (valence = 4), "four-handed" carbon atom is bonded to four hydrogen atoms.
Figure 1-30. Molecules formed by hydrogen, H (valence = 1) and (a) oxygen, O (valence = 2), (b) nitrogen, N (valence = 3), and (c) carbon, C (valence = 4).

The number of "hands" an element has represents its capacity to combine with a certain number of atoms of other elements, which is valence (see above). Each handholding in Figures 1-29 and 1-30 portrays a chemical bond between two atoms. Of course, chemists do not draw holding hands to portray chemical bonds. We just draw lines between representations of atoms to indicate that they are bonded to each other. We will learn about different types of chemical bonds in Volume 2 of this course.

Knowing the valences of chemical elements allows us to make reliable predictions of the composition (formulas) for a broad variety of compounds. For example, it has been experimentally established that the compound that silicon (Si) forms with oxygen (O) is SiO2 (silicon dioxide). Can we determine the valence of silicon from this formula? Yes, we can. Given the formula SiO2 and that the valence of oxygen is 2, we conclude that a Si atom has four "hands" to come together with two O atoms. Therefore, the valence of Si is 4 or, in other words, Si is tetravalent. Consequently, silicon is predicted to form compounds of the formulas SiH4, SiF4, and SiCl4 with the "one-handed" atoms of H, F, and Cl. These formulas are all correct, as has been established experimentally.

Valence numbers (the number of "hands") for some elements are presented in Table 1.

Table 1. Valence numbers for selected elements.
In Table 1, some symbols of the elements are black and some red. The ones in black are for those elements that exhibit only one valence. For example, the valence of hydrogen, fluorine, and sodium is always 1. For oxygen (O), calcium (Ca), and zinc (Zn), it is always 2 and for aluminum (Al), it is always 3. However, iron (Fe) can be divalent and trivalent, and copper can be monovalent and divalent. We know this from the facts that both CuCl and CuCl2 are well-known stable compounds, and so are FeCl2 and FeCl3. Both CuCl and CuCl2 are copper chlorides. To distinguish between the two when writing their chemical names, the valence is specified as a Roman numeral in parentheses after the name of the element exhibiting more than one valence. Consequently, the name for CuCl is "copper (I) chloride" and for CuCl2 "copper (II) chloride". Similarly, "iron (II) chloride" is the name for FeCl2 and "iron (III) chloride" for FeCl3. The names are pronounced as follows: copper-one-chloride, copper-two-chloride, iron-two-chloride, and iron-three-chloride.

There are also fascinating old common names for copper and iron chlorides, reflecting the valences of Cu and Fe. Copper (I) chloride is called cuprous chloride and copper (II) chloride cupric chloride. Similarly, the old names for FeCl2 and FeCl3 are ferrous chloride and ferric chloride, respectively. These names are still in use today.

Why do different elements have a different number of "hands", or, more scientifically, different valences? We will learn that in the next module (Volume 2) of our course. Meanwhile, let us do a few simple exercises.

1.9.2. Exercises. When doing these exercises, think in terms of "hands" the elements have (Table 1).

1. The valence of indium (In) is always 3. Knowing the valences of chlorine (1) and oxygen (2), what are the subscripts x, y, and z in the formulas of (a) indium chloride InClx and (b) indium oxide InyOz? Answer

2. Using the valence numbers in Table 1, write chemical formulas for compounds of oxygen with the following elements: K, Ba, Al, C, P, and Cr for all valences of these elements. Answer