In chemistry, all substances have a charge, something that determines how the substance interacts with other substances. The charge is determined by the number of protons and the number of electrons.
The charge of a substance is based on the number of protons, \(p\), and the number of electrons, \(e\), present in the substance. If the charge is represented by \(C\), then for any substance in chemistry,
$$C = p - e$$
This is a fundamental concept that plays a role in many more complicated aspects of chemistry.
Generally a Periodic Table will be helpful for solving these types of problems. Also, it is important to recognize the atomic number of an element. This is the number that represents the "order" of the elements, and also how many protons the element has. An atom that gains a nonzero charge is known as an ion. If it is positively charged it is known as a cation, and if it is negatively charged it is known as an anion.
Before proceeding, it is helpful to recognize some notation that is used very frequently in chemistry.
For a known or unknown element:
If the symbol has an exponent with "+" following some positive integer, it is positively charged with the magnitude of the charge being the number present. If there is no number the magnitude is 1.
Example 1a: \(Cr^{3+}\) is a Chromium cation with a charge of \(+3\).
On the other hand, if the symbol has an exponent with "-" following some positive integer, it is negatively charged with the magnitude of the charge being the number present. Again, if there is no number present the magnitude of the charge is 1.
Example 1b: \(S^{2-}\) is a Sulfide ion with a charge of \(-2\).
If no exponent is present at all, either the charge is irrelevant to the problem being discussed or the charge is zero.
Example 2: What is the charge of a Tungsten ion with 68 electrons?
Solution: Reference to a periodic table will tell you that Tungsten has an atomic number of 74, and thus it has 74 protons. The difference in protons in electrons gives a charge of \(74 + (-68) = 6\).
The concept of finding the charge of an ion is very straightforward. However, the formula presented earlier has many slightly different uses that are somewhat trickier to identify and execute. The next few examples illustrate some of these types of problems.
Example 3: If the Phosphate ion is \(PO_4^{3-}\), then how many protons and how many electrons are in the entire molecule?
Solution: The number of protons is based on the atomic numbers of Phosphorus and Oxygen. We sum the number of protons in each atom to get the number of protons:
$$15 + 4(8) = 15 + 32 = 47$$
Therefore \(p = 47\), and since we know the charge is \(-3\), we can find the number of electrons with the charge equation:
$$-3 = 47 - e \Rightarrow$$ $$e = 50$$
So there are \(50\) electrons in the entire ion.
Example 4: An ion has 87 protons and 86 electrons. What is the ion?
Solution: Here \(p = 87\) and \(e = 86\), so
$$C = 87 - 86 = 1$$
Therefore the charge of the ion is \(+1\). Since there are 87 protons, the atomic number is 87. Referencing a periodic table identifies this element as Francium. Therefore this is a +1 Francium ion.
The noble gases are a special set of elements on the periodic table. They are all on the rightmost column on the table. In order, these elements are: Helium, Neon, Argon, Krypton, Xenon, and Radon.
The reason these are so special is that these atoms have a particular number of electrons readily available for most reactions (known as an atom's core electrons) that makes it less likely for these atoms to react with other substances. As a result these atoms are called inert. Also, noble gases, besides Helium, all have eight core electrons.
At this point you, the reader, may be wondering what this has to do with charge. It means that the atoms are less likely to gain or lose electrons, and thus remain neutral substances. Therefore they are less likely to become ions (either positively or negatively charged).
Example 5: Why is it unusual for Argon to have 17 electrons?
Solution: Argon is a noble gas, and as an atom it has 18 electrons. If an Argon has 17 electrons, it must be an ion, because Argon must have 18 protons (18 is Argon's atomic number). As stated above, noble gases are unlikely to form ions, so \(Ar^{+}\) is unusual.