# pH Scale: Definition, formula, Notes, Solved problems

– In this subject, we will discuss the pH Scale: Definition, formula, Notes, Solved problems

## 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 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

If  [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:

– It has to do with the activity, which we have chosen to neglect for dilute solutions.

– Since pH is −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

## Solved Problem

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 10−6 M 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.