Question

How would you find the appropriate buffer with given $pKa$ and a given pH?

Answer 1

The $pH$ of a sample can be tested physically through many ways like the Litmus paper and the $pH$ paper. The $pH$ paper gives different colours based on the different $pH$ of different samples while the litmus paper only allows us to know if the sample is either basic or acidic. It changes the colour to blue if the sample is basic while it changes to red in case of an acidic sample

Complete step by step answer:
The buffer of the solution given with the $pKa's$ and the pH can be determined if the pH of the solution lies in the range of the particular solution. This range is called the buffering range.
The buffering range can be simply defined as the pH range where the solution in the examination can resist any drastic change in the pH upon the dilution of the small amount of acid and base.
Ideally the range of the buffer that is the buffering range is in the range of $pKa \pm 1$.
Firstly the components of the buffer need to be determined. We need to know how to use the specific reagent to form the required buffer. After this we need to determine the buffering range of the buffer.
The examination of the $pKa$ of the acidic buffer is governed by the dissociation of the acidic part, that is we need to look at its dissociation constant.
The $pH$ of a buffer solution is calculated by the formula as stated below
$pH = p{K_a} + \log \dfrac{{[conjugate\; base]}}{{[acid]}}$ , where $[conjugate\; base]$ represent the concentration of the conjugate base in the solution and $[acid]$ represent the concentration of Lewis acid in the final solution.

Note: The dissociation of the base is represented by ${K_b}$ which is called the base dissociation constant. It is a measure of how completely the base dissociates into its constituent ions.
${K_W} = {K_a} \times {K_b}$ , here the dissociation constant of water in a solution is the same as the product of the dissociation constant of the base and the acid that is present in the solution.
The base is usually above 7, since 7 is the $pH$ of neutral compounds. For bases it ranges from 7 to 14 which is the end of the scale, while for the acids it is lower than 7.
The dissociation constant of water is fixed so if the concentration of any one of the bases or acid is known the concentration of the counterpart can be figured of easily through this constant.