Calculating the pH of Weak Acid and Base Solutions

– In this subject, we will discuss Calculating the pH of Weak Acid and Base Solutions

Total and partial ionization

– When an acid or base is dissolved in water, it will dissociate, or ionize According to the equations: 

– The amount of ionization is dependent on the strength of the acid or the base.

– A strong electrolyte is completely dissociated, while a weak electrolyte is partially dissociated.

– The table below shows lists some common electrolytes, some strong and some weak:

Calculating the pH of Weak Acid

– Acetic acid is a weak acid, which ionizes only partially in water (a few percent):

– The ionization constant can be used to calculate the amount ionized and, from this, the pH.

– The acidity constant for acetic acid at 25^◦C is 1.75 × 10⁻⁵:

– When acetic acid ionizes, it dissociates to equal portions of H⁺ and OAc⁻ by such an amount that the computation on the left side of the Equation above will always be equal to 1.75 × 10⁻⁵:

– If the original concentration of acetic acid is C and the concentration of ionized acetic acid species (H⁺ and OAc⁻) is x, then the final concentration for each species at equilibrium is given by:

Solved Problem for Calculating the pH of weak Acid

Example (1): Calculate the pH and pOH of a 1.00 × 10⁻³M solution of acetic acid.

Solution: 

Note: 

– The solution is that of a quadratic equation.

– If less than about 10 or 15% of the acid is ionized, the expression may be simplified by neglecting x compared with C (10⁻³ M in this case).

– This is an arbitrary (and not very demanding) criterion.

– The simplification applies if K_a is smaller than about 0.01C, that is, smaller than 10⁻⁴ at C = 0.01 M, 10⁻³ at C = 0.1 M, and so forth.

– Under these conditions, the calculation error is 5% or less (results come out too high), and within the probable accuracy of the equilibrium constant.

– Our calculation simplifies to: 

– The simplification in the calculation does not lead to serious errors, particularly since equilibrium constants are often not known to a high degree of accuracy (frequently no better than ±10%).

– In the above example, the solution of the quadratic equation results in [H⁺] = 1.26 × 10⁻⁴ M (5% less) and pH = 3.91.

– This pH is within 0.03 units of that calculated using the simplification, which is near the limit of accuracy to which pH measurements can be made.

– It is almost certainly as close a calculation as is justified because of the experimental errors in K_a or K_b values and the fact that we are using concentrations rather than activities in the calculations.

– In our calculations, we also neglected the contribution of hydrogen ions from the ionization of water (which was justified); this is generally permissible except for very dilute (<10⁻⁶ M) or very weak (K_a < 10⁻¹²) acids.

Calculating the pH of Weak bases

– Ammonia is a weak base, which ionizes only partially in water:

– The ionization constant can be used to calculate the amount ionized and, from this, the pOH.

– The acidity constant for ammonia at 25^◦C is 1.75 × 10⁻⁵:

Example (2): The basicity constant K_b for ammonia is 1.75 × 10⁻⁵ at 25^◦C. (It is only coincidental that this is equal to K_a for acetic acid.) Calculate the pH and pOH for a 1.00 × 10⁻³ M solution of ammonia.

Solution:

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.