Calculate Ph of Weak Acid

Introduction

Acidic and basic compounds are always fascinating things for scientists at that time. The colour change experiment using litmus paper is commonly used for the identification of the strength of acid and bases. But it does not give proper data on the acidity and basicity of chemical compounds.

The proper identification of the acidity of a chemical compound is very necessary. In the year 1909, the chemist Søren Sørensen introduced the concept of pH from the old theories that are prevailing at that time. He also introduced the pH scale which is a breakthrough of certain theories present at that time. The negative logarithm of Hydrogen ion concentration is responsible for the acidity of some compounds.

What exactly is pH?

The term pH is the potential of Hydrogen. In which it measures the acidity and basicity of chemical species. For measuring how acidic or basic the value of pH is used. From the value of pH, we can easily distinguish chemical compounds into two categories. The range value of pH represents chemical compounds. When the pH of a chemical compound is in the range of 7-14, the chemical compound will be a base. While the pH value is in a range of 0- 7, it will be acidic.

Depending on the value of pH acids and bases are also classified into two strong acids or bases and weak acids or bases. The one which has less acidity is a weak acid with a value in the range nearer to 7. And the one which has a pH in the range of 1-4 is a strong acid. And also the base within the range nearer to 7 is a weak base and one nearer to 14 is a strong base.

Calculation of PH of a Weak Acid

Calculation of pH of a weak acid is a bit complex compared to strong acid. As we know strong acids have a complete dissociation into the respective hydrogen ions but weak acids do not have this complete dissociation. The calculation of pH can be done with the help of the equation,

$$\mathrm{pH\:=\:-\log\:[h^{+}]}$$

And also the value of Ka is determined by the equation,

$$\mathrm{Ka\:=\:[H^{+}]\times\:[B^{-}]\:/\:[HB]}$$

Where,

$\mathrm{[H^{+}]\:=\:concentration\:of\:Hydrogen\:ion}$

$$\mathrm{[B^{-}]\:=\:concentration\:of\:conjugate\:base}$$

$$\mathrm{[HB]\:=\:concentration\:of\:the\:undissociated\:molecule.}$$

Calculating the pH of weak acid considers an example of dissociation of a weak acid, Benzoic acid

It when dissolved in water dissociates as,

$$\mathrm{C_{6}H_{5}COOH\:\rightarrow\:H^{+}\:+\:C_{6}H_{h}COO^{-}}$$

By substituting the corresponding concentrations of each term we can calculate the value of Ka. We know that,

$\mathrm{[H^{+}]\:=\:[C_{6}H_{5}COO^{-}]}$ ,and is because the reason that Hydrogen ions dissociated will result in the formation of $\mathrm{C_{6}H_{5}COO^{-}}$

Now replacing the concentration of Hydrogen ions, [𝐻+] as x

And the concentration before dissociation is C. Substituting all these values in the equation used for the calculation of Ka.

$\mathrm{Ka\:=\:x^{2}\:/\:(C\:-\:x)}$ ince the [𝐻𝐵] has become $\mathrm{C\:-\:x}$

That is,

$$\mathrm{[HB]\:=\:C\:-\:x}$$

Now,

$$\mathrm{(C\:-\:x)\:\times\:Ka\:=\:x^{2}}$$

$$\mathrm{X^{2}\:=\:(C\:-\:x)\times\:Ka}$$

$\mathrm{x^{2}\:=\:(C\times\:Ka\:-\:x\times\:Ka)}$

On rearrangement of the above equation leads to the formation of the quadratic equation

$$\mathrm{x^{2}\:+\:Kax\:-\:CKa\:=\:0}$$

Which can be solved by using the equation,

$$\mathrm{x\:=\:[-\:b\pm\:(b^{2}\:-\:4ac)]\:/\:4a}$$

That is,

$$\mathrm{x\:=\:[-Ka\:+\:(K^a{2}\:+\:4CKa)]\:/\:4}$$

So two equations will then be obtained from which the concentration of Hydrogen ions can be easily calculated. Which then substitute in the general equation for the calculation of pH will lead to the calculation of pH of weak acids,

$$\mathrm{pH\:=\:-\log\:[H^{+}]}$$

$\mathrm{pH\:=\:-\log\:x}$

Thus pH is obtained.

Acids and Related Components

Acids are compounds that contain protons. So the component of acid is hydrogen ion, 𝐻+. So acids are 𝐻+ ion donors. The chemical compounds that contain 𝐻+ ions are all acids. This is according to the Bronsted Lowry theory. And according to Lewis's acid- base theory acids are chemical compounds that accept electron pairs from other chemical compounds. Carboxylic acids and phenols are examples of organic acids since they contain hydrocarbons.

The acid present in milk, Lactic acid is an example of organic acid. Fatty acids are the building unit of fat present in our body a type of carboxylic acid. All the substances in the acid form taste sour. Mineral acids are inorganic acids, an example is Sulfuric acid and Nitric acid. In addition to this, there are some non-aqueous acids too. Sulfur trioxide and Boron trifluorides are in this category. Many components are made up of acids.

How to Calculate pH of a Weak Acid?

For weak acids, it is necessary to calculate the dissociation constant. This can be obtained by the equation,

$$\mathrm{Ka\:=\:x^{2}\:/\:C}$$

From which x can be easily obtained if the values of C and Ka are known.

$$\mathrm{x^{2}\:=\:Ka\times\:C}$$

Which then substitute in the pH equation,

$$\mathrm{pH\:=\:-\log\:x}$$

Leads to the calculation of the pH of weak acids.

Conclusion

Chemical compounds are classified into acids and bases. Acids and bases have a particular pH value for distinguishing them. For acids, the pH range is 1-7 and for bases, it is 7-14. Based on the value of pH, acids and bases are classified into two according to their strength.

The calculation of pH of strong acids is easy since they undergo a complete dissociation to corresponding ions while weak acid pH determination is a bit difficult to achieve. It can be done by proper methods. A new term called dissociation constant is needed for the determination of the pH of weak acids. By using the equations, $\mathrm{Ka\:=\:x^{2}\:/\:C\:and\:pH\:=\:-\log\:x}$, pH of weak acids can be easily obtained.

FAQs

1. For water what is the pH?

Water is a neutral compound which means that it is not an acid nor a base. The pH value of a neutral compound is also different and is 7. So the pH of water is 7 and the pH calculation is mainly used for checking the purity of water.

2. Give some examples of weak acids?

Some examples of weak acids are Acetic acid $\mathrm{(CH_{3}COOH)}$, Formic acid $\mathrm{(HCOOH)}$, Oxalic acid $\mathrm{(C_{2}H_{2}O_{4})}$, etc.

3. Is 𝑯𝑪𝒍 a weak acid?

No, HCl, Hydrogen chloride is an example of strong acid.

4. What is the pH of 1M benzoic acid?

The pH of 1M benzoic acid is 4.5. Benzoic acid $\mathrm{(C_{6}H_{5}COOH)}$ is an example of a weak acid.

5. Give examples of weak bases?

Weak bases are compounds that don't dissociate completely into their ions. Ammonia $\mathrm{(NH_{3})}$, Zinc hydroxide $\mathrm{(Zn(OH)_{2})}$, Methylamine $\mathrm{(CH_{3}NH_{2})}$, etc. are examples of weak bases.