Question

The amount of \[{\left( {N{H_4}} \right)_2}S{O_4}\] ​ to be added to \[500mL\] of \[0.01m\] \[N{H_4}OH\] solution (\[p{K_a}\] ​ for \[N{H_4}^ + \]​ is \[9.26\]) prepare a buffer of \[pH = 8.26\] is?
(A) 0.05mole
(B) 0.025mole
(C) 0.1 mole
(D) 0.005 mole

Answer 1

Hint: In science and organic chemistry, the Henderson–Hassel Balch condition/ equation:
\[pH = p{K_a} + {\log _{10}}(\dfrac{{[Base]}}{{[Acid]}})\]
It tends to be utilized to gauge the \[pH\] of a buffer solution. The mathematical estimation of the acid separation consistent, \[{K_a}\], of the acid is known or accepted. The \[pH\] is determined for given estimations of the concentration of the acid, \[HA\] and of a salt, \[MA\], of its form base, \[{A^ - }\]; for instance, the arrangement may contain acidic acid and sodium acetic acid derivation.

Complete step by step answer:
A basic buffer solution comprises an answer of an acid and a salt of the form base of the acid. For instance, the acid might be acidic acid and the salt might be sodium acetic acid derivation. The Henderson–Hassel Balch condition relates the \[pH\] of an answer containing a combination of the two segments to the acid separation steady, \[{K_a}\], and the convergences of the species in solution. To determine the condition various disentangling suppositions must be made. The combination can oppose changes in \[pH\] when a limited quantity of acid or base is added, which is the characterizing property of a support arrangement.
We are given, \[pH = 8.26\]
\[pOH = 14 - pH\]
\[ = 14 - 8.26\]
\[ = 5.74\]
Additionally, \[p{K_a}{\text{ }} = 9.26\]
\[p{K_b}{\text{ }} = 14 - p{K_a}\]
\[ = 14 - 9.26\]
\[ = 4.74\]
Utilizing Henderson Hassel Balch condition,
\[pOH = p{K_b} + log{\text{ }}\dfrac{{\left[ {N{H_4}^ + } \right]}}{{\left[ {N{H_4}OH} \right]}}\]
\[5.74 = 4.74 + log\dfrac{{\left[ {N{H_4}^ + } \right]}}{{0.01}}\]
\[1 = log\left[ {N{H_4}^ + } \right] - log\left( {0.01} \right)\]
\[1 = log\left[ {N{H_4}^ + } \right] + 2\]
\[log\left[ {N{H_4}^ + } \right] = - 1\]
Taking antilog
\[\left[ {N{H_4}^ + } \right] = 0.1\]

So, the correct answer is Option C.

Note: The Henderson–Hassel Balch condition can be utilized to ascertain the pH of an answer containing the acid and one of its salts, that is, of a buffer solution. With bases, if the estimation of a balance steady is known as a base affiliation consistent, \[{K_b}\] the separation consistent of the form acid might be determined from
\[p{K_a} + {\text{ }}p{K_b} = p{K_w}\] where \[{K_w}\] is the self-separation steady of water. \[p{K_w}\] has an estimation of around \[14\] at\[25^\circ C\].