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#### pH Scale

** The concentration of H+ or OH in aqueous solution can vary over extremely wide ranges, from 1 M or greater to 10−14 M or less.

** To construct a plot of H+ concentration against some variable would be very difficult if the concentration changed from, say, 10−1 M to 10−13 M. This range is common in a titration. It is more convenient to compress the acidity scale by placing it on a logarithm basis.

** The pH of a solution was defined by Sørenson as:

** The minus sign is used because most of the concentrations encountered are less than 1 M, and so this designation gives a positive number. (More strictly, pH is now defined as −log aH+ , but we will use the simpler definition of Equation above)

** In general, pAnything = −log Anything, and this method of notation will be used later for other numbers that can vary by large amounts, or are very large or small (e.g., equilibrium constants).

** Carlsberg Laboratory archives In 1909, Søren Sørenson, head of the chemistry department at Carlsberg Laboratory (Carlsberg Brewery) invented the term pH to describe this effect and defined it as −log[H+].

** The term pH refers simply to (the power of hydrogen).

** In 1924, Søren Sørenson realized that the pH of a solution is a function of the “activity” of the H+ ion, and published a second paper on the subject, defining it as pH = −log aH+.

** A similar definition is made for the hydroxide ion concentration:

So

#### Solved problems

Example (1): Calculate the pH of a 2.0 × 10−3 M solution of HCl.

Solution:

HCl is completely ionized, so

Example(2): Calculate the pOH and the pH of a 5.0 × 10−2 M solution of NaOH at 25C.

Solution:

Example (3): Calculate the pH of a solution prepared by mixing 2.0mL of a strong acid solution of pH 3.00 and 3.0mL of a strong base of pH 10.00.

Solution:

Example (4): The pH of a solution is 9.67. Calculate the hydrogen ion concentration in the solution

Solution:

#### Important Notes for  pH

pH = - log [H+]  , [H+] = 10−pH

[H+] = [OH], the solution is neutral , pH = pOH = 7

[H+] > [OH], the solution is acidic. , pH <7

[H+] < [OH], the solution is alkaline. pH >7

** The hydrogen ion and hydroxide ion concentrations in pure water at 25◦C are each 10−7 M, and the pH of water is 7. A pH of 7 is therefore neutral.

** Values of pH that are greater than this are alkaline, and pH values less than this are acidic. The reverse is true of pOH values. A pOH of 7 is also neutral.

** Note that the product of [H+] and [OH] is always 10−14 at 25C, and the sum of pH and pOH is always 14. If the temperature is other than 25C, then Kw is different from 1.0 × 10−14, and a neutral solution will have other than 10−7 M H+ and OH (see below).

** If the concentration of an acid or base is much less than 10−7 M, then its contribution to the acidity or basicity will be negligible compared with the contribution from water. The pH of a 10−8 M sodium hydroxide solution would therefore not differ significantly from 7. If the concentration of the acid or base is around 10−7 M, then its contribution is not negligible and neither is that from water; hence the sum of the two contributions must be taken. So,
The pH of 10-9 M HCl is not 9!

#### Negative pH

** Some mistakenly believe that it is impossible to have a negative pH. There is no theoretical basis for this.

** A negative pH only means that the hydrogen ion concentration is greater than 1 M.

** In actual practice, a negative pH is uncommon for two reasons:

(1) The First reason: even strong acids may become partially undissociated at high concentrations. For example, 100% H2SO4 is so weakly dissociated that it can be stored in iron containers; more dilute H2SO4 solutions would contain sufficient protons from dissociation to attack and dissolve the iron.

(2) The second reason: has to do with the activity, which we have chosen to neglect for dilute solutions. Since pH is really −log aH+ (this is what a pH meter reading is a measure of), a solution that is 1.1 M in H+ may actually have a positive pH because the activity of the H+ is less than 1.0 M. This is because at these high concentrations, the activity coefficient is less than unity (although at still higher concentrations the activity coefficient may become greater than unity).

** Nevertheless, there is mathematically no basis for not having a negative pH (or a negative pOH), although it may be rarely encountered in situations relevant to analytical chemistry.

Example: 10 M HCl solution should have a pH of −1 and pOH of 15

Example (5): Calculate the pH and pOH of a 1.0 × 10−7 M solution of HCl.

Solution:

Since the hydrogen ions contributed from the ionization of water are not negligible compared to the HCl added

** Note that, owing to the presence of the added H+, the ionization of water is suppressed by 38% by the common ion effect (Le Chˆatelier’s principle). At higher acid (or base) concentrations, the suppression is even greater and the contribution from the water becomes negligible. The contribution from the autoionization of water can be considered negligible if the concentration of protons or hydroxyl ions from an acid or base is 10−6M or greater.

** The calculation in this example is more academic than practical because carbon dioxide from the air dissolved in water substantially exceeds these concentrations, being about 1.2 × 10−5 M carbonic acid. Since carbon dioxide in water forms an acid, extreme care would have to be taken to remove and keep this from the water, to have a solution of 10−7 M acid.

Reference: Analytical chemistry/ Seventh edition / Gary D. Christian, University of Washington, Purnendu K. (Sandy) Dasgupta, University of Texas at Arlington, Kevin A. Schug, University of Texas at Arlington.