Due to the large range of proton concentration values ([H+]) in aqueous solution (typically from 10-15 to 10 M), a logarithmic scale of acidity makes the most sense to put the values into manageable numbers. The pH scale of acidity defines pH as the negative common logarithm of the concentration of H+: pH = - log [H+].
Before proceeding with our discussion on pH, let's review some properties of Logarithms (affectionately called "logs"). A common logarithm is a function that computes what exponent would be on 10 to obtain the input number. For example, the logarithm of 100 (written "log 100") is 2 because 102 = 100. Likewise, log 1,000,000 = 6. To add logs, multiply their arguments: log 100 + log 1000 = log (100 x 1000) = log (100,000) = 5. To subtract logs, divide their arguments: log 100 - log 1000 = log (100/1000) = log (0.1) = - 1. Given those simple rules, you can now manipulate logs well enough to do any problem involving logs in acid-base chemistry. For this section of chemistry, you will get to know and love the log key on your calculator almost as much as you did in kinetics.
The pH scale in water is centered around 7, which is called neutral pH. This value is not randomly selected, but rather it comes from the fact that the [H+] in pure water is 10-7 (recall that K w = 10-14). An acidic solution has a pH value less than 7 because [H+] is greater than that of pure water. A basic solution has a pH greater than 7 because there is a lower [H+] than that of pure water (and consequently a larger [OH-]).
Chemists use a pOH scale analogous to the pH acidity scale to gage hydroxide ion concentrations of aqueous solutions. pOH is defined as the negative common logarithm of the concentration of OH-: pOH = - log [OH- ]. In the pOH scale, 7 is neutral, less than 7 is basic, and greater than 7 is acidic. A useful relationship (which you should be able to derive using the definition of K w) is that pH + pOH = 14. This formula will allow you to readily convert between values of pH and pOH. A comparison of the pH and pOH scales is provided in . Note that because K w is constant, the product of [H+] and [OH-] is always equal to 10-14.
As you have probably guessed by now, the prefix "p" in front of a symbol means "take the negative log". We have defined pH and pOH as values to describe the acidic or basic strength of solutions. Now we can talk about pK a (- log K a) and pK b (- log K b) as measures of acidity and basicity, respectively, for standard acids and bases. An acid with a pK a less than zero is called a strong acid because it almost completely dissociates in water, giving an aqueous solution a relatively low pH. Acids with pK a's greater than zero are called weak acids because they only partially dissociate in water, to make solutions with larger pH's than those strong acids produce at the same concentration. Similarly, bases with pK b's less than zero are strong bases and bases with pK b's greater than zero are called weak bases.
Now that we have the tools to be able to describe the acidity and basicity of compounds with known pK a's, let's analyze trends in acidity and basicity to reach an intuitive understanding of those trends.
First, let's consider the acidity of the halogen acids--HF, HCl, HBr, and HI-- collectively abbreviated HX as shown in , where X represents the halogen. From the data in the figure below, you can see that the major factor affecting the acidity of halogen acids is the strength of the H-X bond. Intuitively, a larger electronegativity difference should lead to a stronger acid due to the polarization of electrons away from hydrogen. However, the trend in bond strength is enough to overrule that competing trend in electronegativity. The smaller the halogen, the closer in size it is to the proton and the greater the orbital overlap; so HF is most the strongly bonded and weakly acidic of the halogen acids.
Generalizing that result, we can say that when the an H-A bond is strong, the acid is weak. Experimental confirmation of this postulate comes from the oxyacid series of compounds. An oxyacid is a molecule of the form AOn(OH)m, where A is a non-metal. Pauling and Ricci derived the following approximate equation for oxyacid acidity from experimental observations:
pK a = 8 - 9f + 4n
The variable f is the formal charge on A when all oxygens are singly bound to A. The variable n represents the number of O atoms bound to A that are not bound to an H. A general trend, summarized in the Pauling-Ricci rule above, is that the more electron withdrawing (more electropositive) the non- metal center, the stronger the acid due to a weakening of the O-H bond.
In summary, we note the following trend regarding acidity: hydrogens are more weakly bound to more electronegative groups, and this produces stronger acids. By using the relationship K w = K a * K b, you should be able to figure out that we need only to discuss the acidity of compounds to describe basicity. From the above discussion, we can deduce that bases with weaker conjugate acids are more basic than those with stronger conjugate acids. Therefore, bases that form stronger bonds to H will have larger K b's and are stronger bases.