Example: What is the molecular weight of SOCl2?
Solution: To find the molecular weight of SOCl2, add together the atomic weights of each of the atoms.
MOLE
We defined the term mole in Chapter 1, Atomic Structure, but let’s briefly review it. A mole is a quantity of any thing (molecules, atoms, dollar bills, chairs, etc.) equal to the number of particles that are found in 12 grams of carbon-12. That seems like an awfully strange point of comparison, so all you really need to remember is that “mole” is a quick way of indicating that we have an amount of particles equal to Avogadro’s number, 6.022 × 1023. One mole of a compound has a mass in grams equal to the molecular weight of the compound expressed in amu and contains 6.022 × 1023 molecules of that compound. For example, 62 grams of H2CO3 (carbonic acid) represents one mole of the acid compound and contains 6.022 × 1023 molecules of H2CO3. The mass of one mole of a compound, called its molar weight or molar mass, is usually expressed as g/mol. Therefore, the molar mass of H2CO3 is 62 g/mol. You may be accustomed to using the term molecular weight to imply molar mass. Technically this is not correct, but nobody is going to rap your knuckles with a ruler for this minor infraction.
The formula for determining the number of moles of a substance present is
mol = Weight of sample (g)/ Molar weight (g/mol)
Real World
Here we mention Avogadro’s number again and can see that the mole is just a unit of convenience, like the dozen is a convenient unit for eggs.
Example: How many moles are in 9.52 g of MgCl2?
Solution: First, find the molar mass of MgCl2.
1(24.31 g/mol) + 2(35.45 g/mol) = 95.21 g/mol
Now, solve for the number of moles.
EQUIVALENT WEIGHT
Equivalent weight and the related concept of equivalents are a source of confusion for many students. Part of the problem may be the context in which equivalents and equivalent weights are discussed: acid-base reactions, redox reactions, and precipitation reactions, all three of which themselves can be sources of much student confusion and anxiety. So let’s start with some very basic discussion, and then, in later chapters, we will see how these concepts and calculations apply to these three types of reactions.
Bridge
The idea of equivalents is similar to the concept of normality, which we will see when we study Acids and Bases in Chapter 10.
Generally, some compounds or elements have different capacities to act in certain ways, not in terms of their characteristics or behaviors, like electronegativity or ionization energy, but rather the ability of certain elements or compounds to act more potently than others in performing certain reactions. For example, one mole of HCl has the ability to donate one mole of hydrogen ions (H+) in solution, but one mole of H2SO4 has the ability to donate two moles of hydrogen ions, and one mole of H3PO4 has the ability to donate three moles of hydrogen ions. Another example to consider is the difference between Na and Mg: One mole of sodium has the ability to donate one mole of electrons, while one mole of magnesium has the ability to donate two moles of electrons. To find one mole of hydrogen ions for a particular acid-base reaction, we could “source” those protons from one mole of HCl, or we could instead use a half-mole of H2SO4. If we’re using H3PO4, we’d only need one-third of a mole. This is what we mean by “different capacities to act in certain ways.” If we need only one mole of hydrogen ions, it would be a waste to use an entire mole of H3PO4, which could donate three times what we need. We are defining the concept of equivalents: How many moles of the “thing we are interested in” (i.e., protons, hydroxide ions, electrons, or ions) will the number of moles of the compound present produce? One mole of hydrogen ions (one equivalent) will be donated by one mole of HCl, but two moles of hydrogen ions (two equivalents) will be donated by one mole of H2SO4, and three moles of hydrogen ions (three equivalents) will be donated by one mole of H3PO4. Simply put, an equivalent is a mole of charge.
Having discussed the concept of equivalents, we can now introduce a calculation that will be helpful on the MCAT, especially for problems of acid-base chemistry. So far, this discussion has been focused on the mole-to-mole relationship between, say, an acid compound and the hydrogen ions it donates. However, sometimes we need to work in units of mass rather than moles. Just as one mole of HCl will donate one mole (one equivalent) of hydrogen ions, a certain mass amount of HCl will donate one equivalent of hydrogen ions. This amount of compound, measured in grams, that produces one equivalent of the monovalent particle of interest (protons, hydroxide ions, electrons, or ions) is called the gram equivalent weight, and the equation is
Gram equivalent weight = Molar mass/n
where n is the number of protons, hydroxide ions, electrons, or monovalent ions “produced” or “consumed” per molecule of the compound in the reaction. For example, you would need 46 grams of H2SO4 (molar mass = 98 g/mol) to produce one equivalent of hydrogen ions, because each molecule of H2SO4 can donate two hydrogen ions (n = 2). Simply put, an equivalent weight of a compound is the mass that provides one mole of charge.
If the amount of a compound in a reaction is known and you need to determine how many equivalents are present, use the following equation:
Equivalents = Mass of compound (g)/Gram equivalent weight (g)
Finally, we can now introduce the measurement of normality without too much fear of causing the almost-always-fatal head explosion. Normality, as the term suggests, is a measure of concentration. The units for normality are equivalents/liter. A 1 N solution of acid contains a concentration of hydrogen ions equal to 1 mole/liter; a 2 N solution of acid contains a concentration of hydrogen ions equal to 2 moles/liter. The actual concentration of the acidic compound may be the same or different from the normality, because different compounds have different capacities to donate hydrogen ions. In a 1 N acid solution consisting of dissolved HCl, the molarity of HCl is 1 M, because HCl is a monoprotic acid, but if the dissolved acid is H2SO4, then the molarity of H2SO4 in a 1 N acid solution is 0.5 M, because H2SO4 is a diprotic acid. The conversion from normality of acid solution to molarity of acidic compound is
Molarity = Normality/n
where n is the number of protons, hydroxide ions, electrons, or monovalent ions “produced” or “consumed” per molecule of the compound in the reaction.
There is a real benefit to working with equivalents and normality because it allows a direct comparison of quantities of the “thing” you are most interested in. Face it, in an acid-base reaction, you really only care about the hydrogen ion and/or the hydroxide ion. Where they come from is not really your primary concern. So it is very convenient to be able to say that one equivalent of acid (hydrogen ion) will neutralize one equivalent of base (hydroxide ion). The same could not necessarily be said to be true if we were dealing with moles of acidic compound and moles of basic compound. For example, one mole of HCl will not completely neutralize one mole of Ca(OH)2, because one mole of HCl will donate one equivalent of acid but Ca(OH)2 will donate two equivalents of base.