Question

A buffer solution is made up of acetic acid [$p{{K}_{a}}=5$] having conc. 1.5M and sodium acetate having conc. = 0.15M. What is the number of $O{{H}^{-}}$ ions present in 1litre solution?
(A) ${{10}^{-10}}M$
(B) ${{10}^{-4}}M$
(C) ${{10}^{-3}}M$
(D) ${{10}^{-6}}M$

Answer 1

Hint: Recollect the pH and buffer concept. In the question, an acidic buffer solution is given. We need to find the concentration of hydroxyl ions. In case of acids, we need to first find pH and then use the relation, pH+pOH=14 to find pOH. pH can be calculated using Henderson equation for buffer solution.

Complete step by step answer:
- Let’s look at the question and write down the given data.
- $p{{K}_{a}}=5$
- Conc. of acetic acid = 1.5M
- Conc. of sodium acetate = 0.15M
- According to Henderson equation for acidic buffer solution,
\[pH=p{{K}_{a}}+\log \dfrac{\left[ salt \right]}{\left[ acid \right]}\]
\[pH=5+\log \dfrac{0.15}{0.5}=5-0.523=4.477\]
- Therefore, pH of the buffer solution is 4.477.
- We know that, pH + pOH = 14
- Therefore, pOH = 14 – pH = 14 – 4.477 = 9.523.

- So, now we have calculated the pOH of the buffer solution as 9.523.
- We have to calculate the concentration of hydroxyl ions present in the buffer solution.
- From the equation, $pOH=-\log [O{{H}^{-}}]$, concentration of hydroxyl ions can be found out.
- Therefore, $[O{{H}^{-}}]={{10}^{\left( -pOH \right)}}={{10}^{-9.523}}=2.999\times {{10}^{-10}}M$
- Therefore, concentration of hydroxyl ions present in the acidic buffer solution is $2.999\times {{10}^{-10}}M$.
- Molarity is the number of moles of a species dissolved in one litre of solution. Therefore, the number of $O{{H}^{-}}$ ions present in 1litre solution is $2.999\times {{10}^{-10}}$.
So, the correct answer is “Option A”.

Note: Remember pH is given as negative logarithm of the concentration of hydrogen ions or protons present in the solution and pOH is given as negative logarithm of the concentration of hydroxyl ions present in the solution. For buffer solutions, the Henderson equation is used for calculating pH.