# How to Calculate the pH for Weak Acids and Bases

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

** The amount of ionization being dependent on the strength of the acid or the base.

** A “

**strong**” electrolyte is completely dissociated, while a “

**weak**” electrolyte is partially dissociated.

** Table blow shows lists some common electrolytes, some strong and some weak:

** Hydrochloric acid is a strong acid, and in water, its ionization is complete:

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

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

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**Calculation of pH for weak acids**

** 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 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:

**Example (1): Calculate the pH and pOH of a 1.00 × 10**

^{−3}M 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 error in calculation 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, 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 unit 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 in view 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 obviously justified); this is generally permissible except for very dilute (<10

^{−6}M) or very weak (K

_{a}< 10

^{−12}) acids.

####
**Calculation of pH for 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.*

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