Question

The degree of ionization of a $0.1M$ bromoacetic acid solution is 0.132. Calculate the $pH$ of the solution and the $p{K_a}$ , of a bromoacetic acid.
$pH$ of solution is = $1.88$
$p{K_a}$ of bromo acetic acid = $2.69$

Answer 1

Hint: $pH$ is a measure of hydrogen ion concentration, $[{H^ + }]$ ,in an aqueous (water) solution. The $pH$ scale ranges from $0 - 14$ . A low $pH$ value indicates acidity, a $pH$ of $7$ is neutral, and a high $pH$ value indicates alkalinity.
The formulas to calculate $pH$ is:
$pH = - \log [{H^ + }]$
At ${25^0}C$ :
$pH + pOH = 14$

${K_a}$	$p{K_a}$
It is the acid dissociation constant.	It is the $ - \log $ of this constant.
Describes the degree of ionization.	Also describes the degree of ionisation.
True indicator of acid strength.Reason: Addition of water does not change the equilibrium.	True indicator of acid strength.Reason: Addition of water does not change the equilibrium.

The acid dissociation constants are usually expressed in terms of ${l^{ - 1}}mol$ .
Acids and bases dissociate according to general equations:
$HA + {H_2}O \to {A^ - } + {H_3}{O^ + }$
${K_a} = \dfrac{{[{H^ + }][{A^ - }]}}{{[HA]}}$
$p{K_a} = - \log {K_a}$

At half the equivalence point, 
$pH = p{K_a}$$pH = p{K_a} = - \log K$

Complete step by step answer:
$C{H_2}BrCOOH \to C{H_2}BrCO{O^ - } + {H^ + }$

Initial concentration	$C$	$0$	$0$
Concentration at equilibrium	$C - C\alpha $	$C\alpha $	$C\alpha $

So, the acid dissociation constant will be:
${K_a} = \dfrac{{C\alpha \times C\alpha }}{{C(1 - \alpha )}} \Rightarrow \dfrac{{C{\alpha ^2}}}{{1 - \alpha }} \simeq C{\alpha ^2}$
$\
   \Rightarrow 0.1 \times 0.132 \\
   \Rightarrow 1.74 \times {10^{ - 3}} \\
  p{K_a} = - \log (1.74 \times {10^{ - 3}}) \\
   \Rightarrow 2.76 \\
\ $
From the above values, we can find the concentration of hydrogen ion as:
$\
  [{H^ + }] = C\alpha \Rightarrow 0.1 \times 0.132 \\
   \Rightarrow 1.32 \times {10^{ - 2}}M \\
\ $
So, the final calculation of $pH$ will be:
$\
  pH = - \log (1.32 \times {10^{ - 2}}) \\
   \Rightarrow 1.88 \\
\ $

Note:
A large ${K_a}$ value indicates a strong acid because it means the acid is largely dissociated into its ions. A large ${K_a}$ value also means the formation of products in the reaction is favored. A small ${K_a}$ value means little of the acid dissociates, so you have a weak acid. The ${K_a}$ value for most weak acids ranges from ${10^{ - 2}} - {10^{ - 14}}$ .
The $p{K_a}$ gives the same information, just in a different way. The smaller the value of $p{K_a}$ , the stronger the acid. Weak acids have a $p{K_a}$ ranging from $2 - 14$
Another important point is $pI$ .This is the isoelectric point. It is at which protein molecule is electrically neutral that is having no net electric.