How to Calculate the pH of a Weak Acid?

The term "pH"  defines the quality of the water we drink, but do you know what it means?

Measurement of electrically charged particles is a substance's pH. It helps you to study whether a substance is acidic or it is alkaline (basic). The scale of pH ranges from 0 - 14, where 0 is the most acidic measure and 14 is the most alkaline measure.

• The pH of acidic water is less than 7. The most acidic compounds have a pH of measure 0. Battery acid comes in at this point.

• alkaline water is indicated by a pH of 8.  The lye which is the most alkaline compound has a pH of measure 14.

• Pure water has a pH of 7 and is classified as "neutral" since it lacks both acidic and basic properties.

Calculation of PH of a Weak Acid

pH describes the strength of an acid. Consequently, it is one of the vital topics which must be understood thoroughly by students. While understanding, pH of acids, it is also important as students of chemistry to note how it can be calculated.

This discussion here focuses on the calculation of weak acids. However, before delving into the concept of how to calculate the pH of a weak acid, let us first acquaint you with all the other necessary terms related to acids in the following section.

Acids and Related Components

• Acids – An element that is capable of donating a proton or accepting valence electron pairs to form a bond can be known as acid. 

• Base – An element which is capable of accepting a proton or donating valence electron pairs to form a bond can be known as base.

• Strong Acid – A strong acid is capable of donating a proton or accepting electron pairs more readily. It can quickly ionise or dissociate in a solution. HCl, H2SO4, HI, HBr, HNO3, etc. are a few examples of a strong acid. 

• Weak Acid – Acids which are not capable of dissociating or ionising in the aqueous solution completely are known as a weak acid. For example, H2C2O4, CH3COOH, etc. 

• Strong Base – A strong base is capable of accepting a proton or donating electron pairs more readily. NaOH, LiOH, CsOH, KOH, Ca(OH)2, BaOH2, etc. are a few examples of a strong base. 

• Weak Base – A base which is not capable of completely dissociating or ionising in an aqueous solution is known as a weak base. Ammonia, Pyridine, and Methylamine are a few examples of a weak base. 

• pH Value – pH is the measure of the extent of the acidic and basic property of an element. It is the negative logarithm of (H+) Hydrogen ion approximately. The range of pH scale lies between 0 and 14. A lower pH indicates that the element is acidic in nature, whereas a higher pH indicates it is of basic property. At room temperature, water is neither acidic nor basic and hence shows a pH scale value of 7. 

Interesting fact # pH scale of elements can range below 0 or above 14 as well, for extremely strong acids and strong bases respectively. 

Now that you are familiar with the important terms related to acids, base, and pH, read on to learn the calculation process. 

How to Calculate pH of a Weak Acid? 

The pH equation can be expressed as, 

pH = - log [H+] 

However, one must determine the value of Ka (Acid dissociation constant) to evaluate [H+]. 

Since in weak acids, the dissociation or ionisation process is not fully complete, computing pH for the weak acid is a bit more difficult. Here, try to understand how to find pH of weak acid with an example as discussed below. 

Example 1:

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 –

\[ C_{6}H_{5}COOH \rightarrow H^{+} + C_{6}H_{5}COO^{-}\]

According to the formula for Ka, it can be expressed as –

Ka = [H+] * [B-] /HB . . . . . . . . . (1) Considering as equation1

Where, 

1. [H+] is the Hydrogen ion concentration. 

2. [B-] is conjugate base ion concentration. 

3. HB is un-dissociated or unionised acid molecules concentration. 

[For reaction such as HB → H+ + B-] 

To get a C6H5COO- ion, Benzoic acid ionises 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 gathered values in equation 1 for evaluating Ka. 

Ka = x . x / (C – x) 

Ka = x2 / (C – x) . . . . . . . . . . . (2) Considering as equation2

(C – x) . Ka = x2

Therefore, x2 = (C . Ka – x . Ka) 

x2 + KaX – CKa = 0 . . . . . . . . . . (3) Considering as equation3

Subsequently, you need to solve equation 3 as you solve a quadratic equation to get the following values as shown below – 

x = [-b ± (b2 – 4ac)1/2] / 2a . . . . . . . . . (4) Considering as equation4

x = [-Ka + (Ka2 + 4CKa)1/2] / 2 . . . . . . . . . (5) Considering as equation5

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

Now, putting the value of Ka as 6.5 x10-5 and C as 0.01 M in the 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 or weak 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 x10-4 M. This value is about 770 times weaker than the original concentration of 1 x 10-2. 

Therefore, from equation 2 we have, 

Ka = x2 / (C – x) 

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

So we get, 

Ka = x2 / C

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

x2 = Ka . C 

x2 = (6.5 x10-5) . (0.01)

x2 = 6.5 x10-7

x = 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 

pH = - log [H+] 

Therefore, we can write, pH = - log x

pH = - 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 answer between the two is of approximate 0.02, which is minor. In most cases, you can go with the second method; even though the first one provides more accurate results.  

Multiple-Choice Questions 

1. Choose the appropriate option which is equal to the pKa of the weak acid. 

1. Conjugate base pKb

2. Equilibrium concentration of base. 

3. Relative molecular mass. 

4. A solution with an equal concentration of an acid and conjugate base’s pH value. 

2. Choose the option which holds for an acidic solution at room temperature. 

1. Kw > 1 10-14

2. [H+] > [OH-]

3. pH > 7.00

4. Negative charges solution. 

3. Choose the one which is not an example of the weak acid. 

1. Sulphuric acid. 

2. Lactic acid. 

3. Pyruvic acid. 

4. Carbonic acid. 

Subsequently, go through the calculation steps mentioned above, you will be able to determine how to calculate the pH of a weak acid. To have comprehensive knowledge of this concept, you can visit Vedantu’s website or download our app and refer study notes. The prominent study notes prepared by professional and expert tutors will help you carve new niches in the academic sector.