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Several categories of substances can be considered Lewis acids: 1. positive ions 2. having less than a full octet in the valence shell 3. polar double bonds (one end) 4. expandable valence shells Several categories of substances can be considered Lewis bases: 1. negative ions 2. one of more unshared pairs in the valence shell 3. polar double bonds (the other end) 4. the presence of a double bond Sören Sörenson and the pH scale I. Short Historical Introduction In the late 1880's, Svante Arrhenius proposed that acids were substances that delivered hydrogen ion to the solution. He has also pointed out that the law of mass action could be applied to ionic reactions, such as an acid dissociating into hydrogen ion and a negatively charged anion. This idea was followed up by Wilhelm Ostwald, who calculated the dissociation constants (the modern symbol is Ka) of many weak acids. Ostwald also showed that the size of the constant is a measure of an acid's strength. By 1894, the dissociation constant of water (today called Kw) was measured to the modern value of 1 x 10¯14 . In 1904, H. Friedenthal recommended that the hydrogen ion concentration be used to characterize solutions. He also pointed out that alkaline (modern word = basic) solutions could also be characterized this way since the hydroxyl concentration was always 1 x 10¯14 ÷ the hydrogen ion concentration. Many consider this to be the real introduction of the pH scale. III. The Introduction of pH Sörenson defined pH as the negative logarithm of the hydrogen ion concentration. pH = - log [H + ] Remember that sometimes H3O + is written, so pH = - log [H3O + ] means the same thing. So let's try a simple problem: The [H + ] in a solution is measured to be 0.010 M. What is the pH? The solution is pretty straightforward. Plug the [H + ] into the pH definition: pH = - log 0.010 An alternate way to write this is: pH = - log 10¯2 Since the log of 10¯2 is -2, we have: pH = - (- 2) Which, of course, is 2.
Let's discuss significant figures and pH. Another sample problem: Calculate the pH of a solution in which the [H3O + ] is 1.20 x 10¯3 M. For the solution, we have: pH = - log 1.20 x 10¯3 This problem can be done very easily using your calculator. However, be warned about putting numbers into the calculator. So you enter (-), log, 1.20, X10 n , (-), 3, enter. The answer, to the proper number of significant digits is: 2.921. III. Significant Figures in pH Here is the example problem: Calculate the pH of a solution where the [H + ] is 0.00100 M. (This could also be a pOH problem. The point being made is the same.) OK, you say, that's pretty easy, the answer is 3. After all, 0.00100 is 10¯3 and the negative log of 10¯3 is 3. You would be graded wrong!! Why? Because the pH is not written to reflect the number of significant figures in the concentration. Notice that there are three sig figs in 0.00100. (Hopefully you remember significant figures, since you probably studied them months ago before getting to acid base stuff. THEY ARE STILL IMPORTANT!) So, our pH value should also reflect three significant figures. However, there is a special rule to remember with pH (and pOH) values. The whole number portion DOES NOT COUNT when figuring out how many digits to write down. Let's phrase that another way: in a pH (and a pOH), the only place where significant figures are contained is in the decimal portion. So, the correct answer to the above problem is 3.000. Three sig figs and they are all in the decimal portion, NOT (I repeat NOT) in the whole number portion. Practice Problems Convert each hydrogen ion concentration into a pH. Identify each as an acidic pH or a basic pH. 1. 0.0015 2. 5.0 x 10¯9 3. 1.0 4. 3.27 x 10¯4 5. 1.00 x 10¯12 6. 0.00010
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