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Question: The \(p{K_a}\) of a weak acid (HA) is 4.5. The \({\rm{pOH}}\) of an aqueous buffer solution of HA in...

The pKap{K_a} of a weak acid (HA) is 4.5. The pOH{\rm{pOH}} of an aqueous buffer solution of HA in which 50% of the acid is ionized is:

A.7.0
B.4.5
C.2.5
D.9.5

Explanation

Solution

We know that, a solution that prohibits the change of pH of a solution on adding a small quantity of acid or base to it is termed as a buffer solution. Here, we have to use Henderson's equation to calculate the pOH{\rm{pOH}} of the solution.

Complete step by step answer: We know that, Henderson equation for acidic buff is,

pH=pKa+log⁡[Salt][Acid]p{\rm{H}} = p{K_a} + \log \dfrac{{\left[ {{\rm{Salt}}} \right]}}{{\left[ {{\rm{Acid}}} \right]}}
…… (1)
Given that, acid is 50% ionized, that means, concentration of salt is equal to the concentration of acid. Let’s take concentration as x. Now, we put the value of pKap{K_a} of a weak acid (HA) 4.5 and x in equation (1).
pH=pKa+log⁡[Salt][Acid]p{\rm{H}} = p{K_a} + \log \dfrac{{\left[ {{\rm{Salt}}} \right]}}{{\left[ {{\rm{Acid}}} \right]}}

⇒pH=4.5+log⁡xx \Rightarrow p{\rm{H}} = 4.5 + \log \dfrac{x}{x}

⇒pH=4.5+log⁡1 \Rightarrow pH = 4.5 + \log 1

⇒pH=4.5 \Rightarrow p{\rm{H}} = 4.5 (log 1=0)

So, the pH of the solution is 4.5.

Now, we have to calculate the pOH. We know summation of pH and pOH is equal to 14. So, pOH can be calculated by subtracting pH value from 14.

pH+pOH=14p{\rm{H}} + p{\rm{OH}} = {\rm{14}}

⇒pOH=14−pH \Rightarrow p{\rm{OH}} = 14 - p{\rm{H}}

⇒pOH=14−4.5 \Rightarrow pOH = 14 - 4.5

⇒pOH=9.5 \Rightarrow p{\rm{OH}} = 9.5

Therefore, pOH value is 9.5.Hence, correct option is option D.

Additional Information:

A buffer has reverse acidity which it uses against a base and a reverse basicity which it employs against an acid. This is the reason for the resistance of pH change by buffer solution.

Note: Both basic and acidic buffers are regarded as weak buffers. Since the bases and acids involved in them are weak, the pH of acidic buffers is always between 4 and 7 while that of basic buffers ranges from 7 to 10. It is to be noted that aqueous solutions of strong acids namely, hydrochloric acid, nitric acid and that of strong bases like sodium hydroxide and potassium hydroxide can also form buffers.