pH and pOH

The hydrogen ion concentration of a solution varies from approximately 1 in a 1 M solution of a strong acid to about 1×10-14 in a 1 M solution of a strong base, and the calculations often become unwieldy. To alleviate this difficulty, Sörensen suggested a simplified method of expressing hydrogen ion concentration. He established the term pH to represent the hydrogen ion potential, and he defined it as the common logarithm of the reciprocal of the hydrogen ion concentration:

$$ pH=log\frac{1}{[H_3O^+]} $$

According to the rules of logarithms, this equation can be written as:

$$ pH=-log[H_3O^+] $$

The pH of a solution can be considered in terms of a numerical scale ranging from 0 to 14, which quantitatively expresses the degree of acidity (7 to 0) and alkalinity (7 to 14). The value 7, at which the hydrogen and hydroxyl ion concentrations are approximately equal at room temperature, is referred to as the neutral point, or neutrality. The neutral pH at 0°C is 7.47, and at 100°C, it is 6.15.

The pOH

The pOH, similar to the pH scale, represents the concentration of hydroxide ions (OH–) in a solution. It is calculated as the negative logarithm of the hydroxide ion concentration:

$$ pOH=-log[OH^-] $$

This measure helps indicate the basicity of a solution, with lower pOH values corresponding to higher basicity. The pOH scale typically ranges from 0 to 14. Lower pOH values indicate a higher concentration of hydroxide ions, meaning the solution is more basic, while higher pOH values indicate a lower concentration, suggesting acidity.

For example, a solution with a pOH of 0 is strongly basic, while a pOH of 14 is acidic. In water at a neutral pH (pH 7), the pOH is also 7, reflecting an equilibrium between hydrogen ions (H+) and hydroxide ions (OH–).

The Relationship Between pH and pOH

The Relationship Between pH and pOH can be easily derived from the expression for the water dissociation constant (Kw) :

$$ K_w=[H^+][OH^-] $$

By applying the negative logarithm to both sides, we find:

$$ -log(K_w)=-log([H^+][OH^-]) $$

According to the rules of logarithms, this equation can be written as:

$$ -log(K_w)=(-log[H^+])+(-log[OH^-]) $$

Then,

$$ pK_w=pH+pOH $$

At 25°C, the sum of pH and pOH in a solution always equals 14. This balance allows chemists to determine one value if they know the other. For example, if a solution has a pH of 5, its pOH would be 9.

Reference:

  • Sinko, P. (2011). Martin’s Physical Pharmacy and Pharmaceutical Sciences. Baltimore, : Lippincott Williams & Wilkins, a Wolters Kluwer business.

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