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Question: Calculate pH of a solution containing 0.1M \(C{{H}_{3}}COOH\) and 0.1M benzoic acid. \({{K}_{a}}\) f...

Calculate pH of a solution containing 0.1M CH3COOHC{{H}_{3}}COOH and 0.1M benzoic acid. Ka{{K}_{a}} for CH3COOHC{{H}_{3}}COOH and benzoic acid are 1.8×10−51.8\times {{10}^{-5}}and 6.5×10−56.5\times {{10}^{-5}} respectively.

Explanation

Solution

pH is used to measure hydrogen ion concentration in an aqueous solution. The pH scale ranges from 0 to 14. Whereas if a compound having pH value less than 7 they are acidic in nature and higher than 7 indicates basic compounds whereas pH exactly 7 is neutral in nature.

Complete Solution :
The pH value helps us to determine whether it is an acid or a base. Whereas Ka{{K}_{a}} and Kb{{K}_{b}} values helps us to determine whether the given species will donate or accept protons at a specific pH value. Ka{{K}_{a}} is acid dissociation constant while Kb{{K}_{b}} is base dissociation constant.
- Both the compounds given in the question are acidic in nature. Acetic acid dissociates into:
CH3COOH⇄CH3COO−+H+C{{H}_{3}}COOH\rightleftarrows C{{H}_{3}}CO{{O}^{-}}+{{H}^{+}}

- In the similar manner benzoic acid dissociates into:
C6H5COOH⇄C6H5COO−+H+{{C}_{6}}{{H}_{5}}COOH\rightleftarrows {{C}_{6}}{{H}_{5}}CO{{O}^{-}}+{{H}^{+}}

Now we know the formula of calculating H+{{H}^{+}}which is as shown below:
[H+]=K1C1+K2C2[{{H}^{+}}]=\sqrt{{{K}_{1}}{{C}_{1}}+{{K}_{2}}{{C}_{2}}}
Here value of C1=0.1,C2=0.1,K1=1.8×10−5,K2=6.5×10−5{{C}_{1}}=0.1,{{C}_{2}}=0.1,{{K}_{1}}=1.8\times {{10}^{-5}},{{K}_{2}}=6.5\times {{10}^{-5}}

- By putting all the values in the formula
[H+]=1.8×10−5×0.1+6.5×10−5×0.1[{{H}^{+}}]=\sqrt{1.8\times {{10}^{-5}}\times 0.1+6.5\times {{10}^{-5}}\times 0.1}
[H+]=1.8×10−6+6.5×10−6[{{H}^{+}}]=\sqrt{1.8\times {{10}^{-6}}+6.5\times {{10}^{-6}}}
[H+]=8.3×10−6[{{H}^{+}}]=\sqrt{8.3\times {{10}^{-6}}}
[H+]=2.88×10−3[{{H}^{+}}]=2.88\times {{10}^{-3}}
pH=−log⁡[H+]=−log⁡(2.88×10−3)pH=-\log [H+]=-\log (2.88\times {{10}^{-3}})
=3−log⁡2.88=2.540=3-\log 2.88=2.540
Hence the pH of a solution containing 0.1M CH3COOHC{{H}_{3}}COOH and 0.1M benzoic acid. Ka{{K}_{a}} for CH3COOHC{{H}_{3}}COOH and benzoic acid are 1.8×10−51.8\times {{10}^{-5}} and 6.5×10−56.5\times {{10}^{-5}} respectively is 2.540.

Note: Ka{{K}_{a}} and Kb{{K}_{b}} describe the degree of ionization of an acid or base and are true indicators of acid or base strength because adding water to a solution will not change the equilibrium constant. Ka{{K}_{a}} is related to acids while Kb{{K}_{b}} represents the base.