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Question: For preparing a buffer solution of pH 6 by mixing sodium acetate and acetic acid, the ratio of the c...

For preparing a buffer solution of pH 6 by mixing sodium acetate and acetic acid, the ratio of the concentration of salt and acid should be (Ka=10−5)\left( {{{\text{K}}_{\text{a}}} = {{10}^{ - 5}}} \right)
A.1:101:10
B.10:110:1
C.100:1100:1
D.1:1001:100

Explanation

Solution

To answer this question, you must recall the concept of acidic buffer. An acidic buffer is formed when a solution contains a weak acid and its salt formed as a result of the reaction with a strong base.
Formula used: Henderson- Hasselbalch Equation: pH=pKa+log[salt][acid]{\text{pH}} = {\text{p}}{{\text{K}}_{\text{a}}} + {\text{log}}\dfrac{{\left[ {{\text{salt}}} \right]}}{{\left[ {{\text{acid}}} \right]}}

Complete step by step answer:
We are given acetic acid and sodium acetate which is the salt of weak acid, acetic acid and strong base sodium hydroxide. We are given in the question, the dissociation constant for the acid.
So the reaction for the dissociation of acetic acid can be written as
CH3COOH→CH3COO−+H+C{H_3}COOH \to C{H_3}CO{O^ - } + {H^ + }
The required solution must have a pH of 6.
First we find pKa=−log⁡Kap{K_a} = - \log {K_a}
⇒pKa=−log⁡10−5=5\Rightarrow p{K_a} = - \log {10^{ - 5}} = 5
Using the Henderson- Hasselbalch Equation, pH=pKa+log[salt][acid]{\text{pH}} = {\text{p}}{{\text{K}}_{\text{a}}} + {\text{log}}\dfrac{{\left[ {{\text{salt}}} \right]}}{{\left[ {{\text{acid}}} \right]}}, we find the ratio of the concentration of the salt to that of the acid.
Substituting the known values into the equation, we get,
6=5+log⁡[salt][acid]6 = 5 + \log \dfrac{{\left[ {salt} \right]}}{{\left[ {acid} \right]}}
Simplifying:
⇒1=log⁡[salt][acid]\Rightarrow 1 = \log \dfrac{{\left[ {salt} \right]}}{{\left[ {acid} \right]}}
Rearranging:
⇒[salt][acid]=antilog⁡(1)=10\Rightarrow \dfrac{{\left[ {salt} \right]}}{{\left[ {acid} \right]}} = anti\log \left( 1 \right) = 10

Thus, the correct answer is B.
Additional information: A buffer solution maintains the pH of the solution by consuming any small amount of hydrogen ion or hydroxide ion entering the solution. In an acidic buffer, for instance, if we add a base, the weak acid will release protons and neutralize the base. If acid is added, the dissociation of the weak acid decreases. Thus, the pH is maintained.

Note:
A buffer is a solution that can maintain its pH or the hydrogen on concentration with addition of small amounts of acid or base or on dilution. Since the pH of the solution does not change with minor changes, thus it can be used in various applications namely, fermentation, drug delivery, electroplating, activity of enzymes, etc.