Calculation of pH to know the acidity and basicity of a solution

pH = – log [H ₃ O ⁺ ]

For a strong acid, such as hydrochloric acid (HCl), with a molarity of 0.02 M or mol/L, the hydronium ion concentration will be the same as that of the acid, since it is fully ionized, as is shown in the following equation.

HCl -> H ₃ O ⁺ + Cl ^–

Therefore, the pH can be calculated:

pH = – log [H ₃ O ⁺ ] = – log [0.02] = 1.69

For a weak acid, such as acetic acid (CH ₃ COOH) and most organic acids, the concentration of the acid does not match that of the hydronium ions because the acid is partially dissociated, giving an equilibrium . Therefore, it is necessary to know both the concentration of the acid and the degree of dissociation to know the pH of the solution.

Thus, for example, for a weak acid, such as acetic, with a concentration of 0.02 M and a degree of dissociation of 5%, the concentration of hydronium ions, and therefore, the pH, can be calculated as follows:

pH = – log [H ₃ O ⁺ ] = – log [ C alpha ] = – log (0.02 (5/100)) = 3

Calculation of hydronium ion concentration from pH

The concentration of hydronium ions can be calculated from the pH by doing the reverse mathematical operation to the one used to calculate the pH:

pH = – log [H ₃ O ⁺ ]

[H ₃ O ⁺ ] = 10  ^–pH

That is why, for a pH = 6.3; the hydronium ion concentration would be:

6.3 = – log [H ₃ O ⁺ ]

– 6.3 = log [H ₃ O ⁺ ]

[H ₃ O ⁺ ] = 10 ^{– 6.3} = 5,011.10 ^-7

pOH calculation

To know the pOH , that is, the degree of basicity of an aqueous solution , it is necessary to know the concentration of hydroxide ions in a strong base solution, or the concentration of a weak base together with its degree of dissociation. Following as an example what was done with the concentration of hydronium anions, for a strong base such as sodium hydroxide (NaOH) with a concentration of 0.02 M it can be said that:

pOH = – log [OH ^– ]

pOH = –log [0.02] = 1.69

The ratio of pOH to pH is equal to:

pH + pOH = 14

pH + 1.69 = 14

pH = 14 – 1.69 = 12.21

It is also possible to calculate the hydroxide ion concentration from a pOH value, thus for example for a pOH value of 2.56:

2.56 = – log [OH ^– ]

– 2.56 = log [OH ^– ]

[OH ^– ] = 10 ^-2.56 = 2.75.10 ^-3 M

Practical examples

Example 1 . Calculate the pH for a solution whose concentration of hydronium anions is [H ₃ O ⁺ ] = 1.4.10  ^-5  M.

Solution

pH = -log [H ₃ O ⁺ ]
pH = -log [1.4.10  ^-5 ]
pH = 4.85

Example 2 . Calculate the concentration of [H ₃ O ⁺ ] from a pH of 8.5.

Solution

[H ₃ O ⁺ ] = 10  ^-pH
[H ₃ O ⁺ ] = 10  ^-8.5
[H ₃ O ⁺ ] = 3.2.10  ^-9  M

Example 3 . Calculate the pH of a solution, if the concentration of H ₃ O ⁺ is 0.0001 moles per liter.

Solution

pH = –log(0.0001) = 4

Example 4 . Find the pH of a 0.03 M solution of hydrochloric acid, HCl.

Hydrochloric acid is a strong acid that dissociates according to a 1:1 molar ratio into hydronium ions and chloride anions. Therefore, the concentration of hydronium ions is exactly the same as the concentration of the acid solution.

Answer

[H ₃ O ⁺ ]= 0.03 M

pH = – log (0.03)
pH = 1.5

When performing calculations to calculate pH, you should always check that your answers make sense. An acid should have a pH much lower than 7 (usually 1-3), while a base has a high pH value (usually around 11-13). Although in theory it is possible to calculate a negative pH, in practice the pH values ​​must be between 0 and 14. This means that a pH greater than 14 indicates that some type of error must have occurred.

Sources

• Calculating_pH and pOH. (2021). Retrieved 17 March 2021, from https://www.chem.purdue.edu/gchelp/howtosolveit/Equilibrium/Calculating_pHandpOH.htm