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Question: 12 g of \(C{{H}_{3}}COOH\) and 4 g of NaOH are mixed and diluted to 1 liter solution. If \({{P}^{{{K...

12 g of CH3COOHC{{H}_{3}}COOH and 4 g of NaOH are mixed and diluted to 1 liter solution. If PKa{{P}^{{{K}_{a}}}} of CH3COOHC{{H}_{3}}COOH is 4.8 the pH of the solution is
A. 4.8
B. 5
C. 5.6990
D. 5.3010

Explanation

Solution

There is a relationship between pH and Pka of the solution and it is as follows.
pH=PKa+log⁡[saltbase]pH={{P}^{{{K}_{a}}}}+\log \left[ \dfrac{salt}{base} \right]
Here pH= pH of the solution
PKa{{P}^{{{K}_{a}}}} = Dissociation constant
Salt = concentration of the salt
Base = concentration of the base

Complete step by step solution:
- In the question it is given that 12 g of CH3COOHC{{H}_{3}}COOH and 4 g of NaOH are mixed and diluted to 1 liter solution.
- PKa{{P}^{{{K}_{a}}}} of the solution is 4.8 .
- We have to calculate the pH of the solution.
- The chemical reaction of acetic acid with sodium hydroxide is as follows.
CH3COOH+NaOH→CH3COONa+H2OC{{H}_{3}}COOH+NaOH\to C{{H}_{3}}COONa+{{H}_{2}}O
- For 12 g of acetic acid the number of moles

&\implies \dfrac{12}{60} \\\ & \implies 0.2mole \\\ \end{aligned}$$ \- For 4 g of sodium hydroxide the number of moles \- Therefore 0.2 moles of acetic acid reacts with 0.1 moles of sodium hydroxide and forms 0.1 mole of sodium acetate as the product. $$\begin{aligned} &\implies \dfrac{4}{40} \\\ &\implies0.1mol \\\ \end{aligned}$$ \- Now substitute all the known values in the below formula to get the pH of the solution. $$pH={{P}^{{{K}_{a}}}}+\log \left[ \dfrac{salt}{base} \right]$$ Here pH= pH of the solution ${{P}^{{{K}_{a}}}}$ = Dissociation constant = 4.8 Salt = concentration of the salt = 0.1 Base = concentration of the base = 0.1 $$\begin{aligned} & pH={{P}^{{{K}_{a}}}}+\log \left[ \dfrac{salt}{base} \right] \\\ & pH=4.8+\log \left[ \dfrac{0.1}{0.1} \right] \\\ & pH=4.8+0 \\\ & pH=4.8 \\\ \end{aligned}$$ \- Therefore the pH of the solution is 4.8. **\- So, the correct option is A.** **Note:** If the concentration of both salt and base are the same in a chemical reaction then the pH of the solution is equal to ${{P}^{{{K}_{a}}}}$ of the solution. Sodium acetate is a salt going to form by the reaction of sodium hydroxide with acetic acid.