Calculate the pH of a Weak Acid

To calculate the pH of a weak acid, it is first important to keep in mind that pH has no units, thus it is required to define it with H⁺ ion concentration. pH is a quantitative measure of acidity or basicity of aqueous or other liquids. The formula to calculate pH of weak acid is:

• The pH value represents whether a substance is acidic, basic, or neutral in nature.
• It is used widely in chemistry, biology, and agronomy.
• The pH value ranges from 0 to 14, the lowest value signifying acidity (any value less than 7) and the highest signifying basicity (any value greater than 7).
• Neutral solutions (such as pure water) have a pH of 7, acidic solutions have a pH of less than 7, and alkaline solutions have a pH of 7.
• The pH of lemon juice is 2.4 and that of household ammonia is 11.5. The normal pH of human blood is 7.4.

Key Terms: Base, Acid, pH value, pH of a weak base, Hydrogen, pH Table, Litmus Paper, Alkaline Solutions, Weak Acids, Strong Acids,  H⁺ ion concentration

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What is pH? 

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pH is the concentration of hydrogen ions (that is, protons) in a substance. pH is an abbreviation of the Potential of Hydrogen. The p in pH stands for ‘potenz’ in German, meaning power. The pH scale was developed in 1923 by the Danish biochemist Søren Peter Lauritz Sørensen for numerical measurement of the acidity or alkalinity of a solution. It is usually measured on a scale of 0-14. pH is reported in "logarithmic units". Each number represents a 10-fold change in the acidity/basicness of the water.

• pH is the negative logarithm of the H⁺ ion concentration.
• The meaning of pH is that it justifies the power of Hydrogen.
• A litmus paper is used as an indicator to specify whether a substance is an acid or base. 
• For instance, Vinegar is an acid and has a pH value of 2.4.

pH Diagram

The litmus paper is an index used to determine whether a substance is an acid or a base. The color of the litmus paper indicates the pH value of what kind of substance is being tested. For example, vinegar is an acid and measures 2.4 on the pH scale. Water with a pH of five is ten times more acidic than water having a pH of six.

pH Formula

It claims that pH equals the negative logarithmic value of hydrogen ion (H⁺) concentration. It does not have any Unit. Thus, the formula of pH can be represented as:

pH of Acids and Bases

A solution with a pH of 0 is known as a strong acid solution. Also, as the pH rises from 0 to 7, the acidity drops, and a solution with a pH of 14 is called a strongly basic solution. When the  pH drops from 14 to 7, the alkalinity drops. The strength of acids and bases depends on the number of H ⁺ and OH ^– ions formed. Acids that provide more H ⁺ ions are known to be strong acids and vice versa. 

The degree of acid and base ionization depends on the acid and base. It helps determine the strength of acids and bases. The strength of the acid also depends on the concentration of hydronium ions (H₃O⁺). You can distinguish between acids and bases by comparing the concentrations of hydronium and hydroxyl ions.

• For acidic solution: [H₃O⁺] > [OH^–]
• For neutral solution: [H₃O⁺] = [OH^–]
• For basic solution: [H₃O⁺] < [OH^–]

Read Also: Chloroauric acid

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pH Table

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The pH values chart for different substances is mentioned below:

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What is Weak Acid?

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In an aqueous solution or water, a weak acid is one that partially dissociates into its ions. However, in water, a strong acid entirely dissociates into its ions. A weak acid's conjugate base is also a weak base. Similarly, a weak base's conjugate acid is also a weak acid.

• Weak acids have a greater pH value than strong acids at the same concentration.
• Strong acids are far less prevalent than weak acids.
• In everyday life, they can be found in vinegar (acetic acid) and lemon juice (citric acid).
• The strength of a weak acid is based on how much it dissociates. 
• Thus, the more it is seen to dissociate, the stronger will be the acid.

Weak Acid Examples

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Calculating pH of Weak Acid

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pH has no units and it can be defined with the help of H⁺ ion concentration. Hence, 

Therefore, the pH of a compound can be shown as,

→ pH = – log(aH ⁺) 

Since weak acids do not completely breakdown in water so calculating the pH value is difficult.

Read More: High-Density Polyethylene structure

Calculation of pH

The calculation of pH of acids and bases can be obtained on the basis of chemical speciation calculation. The solution's nature decides the level of complicacy demanded to evaluate the pH value.Thus, the  pH value of a weak acid with the help of an example is shown below:

Example: Calculate the pH of a Benzoic acid solution of concentration 0.01 M.

Solution: For a 0.01 M concentration of Benzoic acid sample, Ka (Acid dissociation constant) is 6.5 x 10^-5.

Now, a Benzoic acid sample 0.01 M concentration is when mixed with water or aqueous solution,

the dissociation reaction can be expressed as:

According to the formula for Ka, it can be expressed as – Ka = [H⁺] * [B^-] /HB . . . . . . . . . (1)

Considering this as equation 1.

Where [H⁺] is the Hydrogen ion concentration. [B^-] is conjugate base ion concentration.

HB is an un-dissociated or unionized acid molecule concentration. [For reaction such as HB → H⁺ + B^-]

To get a C₆H₅COO^- ion, Benzoic acid ionizes one H⁺ ion, so we can write [H⁺] = [C₆H₅COO^-].

Let us now consider the H⁺ ions concentration which can dissociate from HB as ‘x’.

From the above consideration, we can write HB = C – x (wherein C is the concentration at the beginning of the reaction).

Now, putting these values in equation 1 for evaluating:

K_a = x . x / (C – x) K_a = x² / (C – x) . . . . . . (2)

Considering as equation 2

(C – x) . K_a = x²

Therefore, x² = (C . K_a – x . K_a) x² + K_aX – CK_a = 0 . . . . . . (3)

Considering as equation 3, we need to take the quadratic equation to get the following values. Thus, x =\( \frac{- b \pm \sqrt{ b^2 – 4ac }}{ 2a }\) . . . . . .  (4)

Considering the above as equation 4. Thus,

x = [-K_a + (K_a² + 4CK_a)^1/2] / 2 . . . . . . (5)

Considering as equation 5

This leaves us with two equations to calculate the value of x. Its value cannot be negative as it signifies the ion concentration in the solution.

Now, putting the value of Ka as 6.5 x 10^-5 and C as 0.01 M in equation 5,

We have, x = [(-6.5 x 10^-5) + {(6.5 x 10^-5)² + 4 . (0.01) . (6.5 x 10^-5)}^1/2] / 2 

On solving this or simplifying this, we have x = [-6.5 x 10^-5 + 1.6 X 10^-3] / 2 x = [1.5 X 10^-3] / 2

Finally, X = 7.7 x 10^-4

Now, to answer how to find pH of a weak acid, put these values in the pH equation which can be expressed as pH = – log [H⁺]

Putting the value of H⁺,

We have pH = - log x Putting the value of x, we have, pH = – log [7.7 x10^-4]

Further, pH = - (-3.11) = + 3.11

Therefore, you can calculate using this method and quickly tell that 0.01 M concentration of Benzoic acid has a pH value of 3.11.

Alternate Method

To know how to calculate the pH of a weak acid, you can also follow this process below.

It gives an approximate value of pH for weak acids and can be calculated more quickly.

For weak acids, the degree of dissociation or ionisation is nominal.

For instance, here Benzoic acid of concentration 0.01 M was dissociated by a mere value of 7.7 x 10^-4 M.

This value is about 770 times weaker than the original concentration of 1 x 10^-2.

Therefore, from equation 2:

we have, K_a = x² / (C – x)

Since the dissociation is nominal in the case of weak acids, the value of (C – x) will be almost equal to C.

So we get, K_a = x² / C

This saves you from another complicated step of solving the quadratic equation, and we can write –

x² = K_a.C x² = (6.5 x10^-5) . (0.01)x² = 6.5 x10^-7x = 8.06 x 10^-4

Now, to answer how to calculate the pH of a weak acid, put these values in the pH equation which can be expressed as:

Therefore, we can write, pH = - log xpH = - log (8.06 x 10^-4)

Therefore, pH = - (-3.09) = 3.09.

This is a rather simple method for calculating the pH of the weak acid.

The difference in answers between the two is approximately 0.02, which is very minor in comparison. In most cases, you can go with the second method; even though the first one provides more accurate results.

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Solved Examples Related to pH

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Ques: Which one of the following will turn red litmus paper blue

1. Vinegar
2. Lemon juice
3. Baking soda solution
4. Aerated cold drinks

Ans: c) Baking soda solution

Explanation: Since Bases turn red litmus paper blue, acids turn blue litmus paper red and baking soda is basic in nature so it turns red litmus paper to blue.

Ques: pH is a measure of which factor:

1. Ion concentration
2. Hydrogen-ion concentration
3. Density
4. Concentration of Solute

Ans: b) Hydrogen-ion Concentration

Ques: The neutral value of pH scale is?

1. Less than 5
2. Equal to 7
3. Less than 8
4. Less than 10

Ans: b) Equal to 7

Ques:  Who had invented the pH Scale?

1. S.P.L Sorenson
2. Benjamin Franklin
3. Henry Moseley
4. Wilhelm Rontgen

Ans: a) S.P.L Sorenson

Read More: List of Strong Acids

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Things to Remember

• pH can be defined as the concentration of hydrogen ions in a substance.
• pH is an abbreviation of the Hydrogen Potentials.
• If the pH value is lower than 7, the solution is acidic.
• If pH is 7, the solution is neutral.
• If pH is higher than 7, the solution is basic.
• The pH value of weak acids decreases with an increase in temperature due to increased ionization. 
• The pH value of a weak base increases with an increase in temperature due to ionization or an increase in [OH] ion concentration.

Check out: Importance of pH testing in everyday life