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Calculating pH of Weak Acid and Base Solutions

Calculations used to determine pH in solutions of weak acids or bases

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Calculating pH of Weak Acid and Base Solutions

Sodium bicarbonate can be used to help alleviate a bee sting

Credit: Jon Sullivan
Source: http://commons.wikimedia.org/wiki/File:Bees_pollenating_basil.jpg
License: CC BY-NC 3.0

Ouch, that hurts!

Bees are beautiful creatures that help plants flourish. They carry pollen from one plant to another to facilitate plant growth and development. But, they can also be troublesome when they sting you. For people who are allergic to bee venom, this can be a serious, life-threatening problem. For the rest of us, it can be a painful experience. When stung by a bee, one first-aid treatment is to apply a paste of baking soda (sodium bicarbonate) to the stung area. This weak base helps with the itching and swelling that accompanies the bee sting.

Calculating pH of Weak Acid and Base Solutions

The  and  values have been determined for a great many acids and bases, as shown in Tables 21.5 and 21.6. These can be used to calculate the pH of any solution of a weak acid or base whose ionization constant is known.

Sample Problem: Calculating the pH of a Weak Acid

Calculate the pH of a 2.00 M solution of nitrous acid (HNO2). The  for nitrous acid is 4.5 × 10-4.

Step 1: List the known values and plan the problem.


  • initial [HNO2] = 2.00 M


  • pH = ?

First, an ICE table is set up with the variable  used to signify the change in concentration of the substance due to ionization of the acid. Then the  expression is used to solve for  and calculate the pH.

Step 2: Solve.

Concentrations [HNO2] [H+] [NO2]
Initial 2.00 0 0

The  expression and value is used to set up an equation to solve for .

The quadratic equation is required to solve this equation for . However, a simplification can be made because of the fact that the extent of ionization of weak acids is small. The value of  will be significantly less than 2.00, so the "” in the denominator can be dropped.

Since the variable  represents the hydrogen-ion concentration, the pH of the solution can now be calculated.

Step 3: Think about your result.

The pH of a 2.00 M solution of a strong acid would be equal to . The higher pH of the 2.00 M nitrous acid is consistent with it being a weak acid and therefore not as acidic as a strong acid would be.

The procedure for calculating the pH of a solution of a weak base is similar to that of the weak acid in the sample problem. However, the variable  will represent the concentration of the hydroxide ion. The pH is found by taking the negative logarithm to get the pOH, followed by subtracting from 14 to get the pH.


  • The procedure for calculating the pH of a weak acid or base is illustrated.


Perform the calculations at the site below:




  1. What does  stand for in the equation?
  2. What simplifying assumption is made?
  3. What would  stand for if we were calculating pOH?

Image Attributions

  1. [1]^ Credit: Jon Sullivan; Source: http://commons.wikimedia.org/wiki/File:Bees_pollenating_basil.jpg; License: CC BY-NC 3.0


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