Question

Three bases \[XOH\] , \[YOH\] and \[ZOH\] have \[p{K_b}\] values \[2\] ,\[3\] and \[4\] respectively; the strongest conjugate acid is:
A. \[XO{H_2}^ + \]
B. \[YO{H_2}^ + \]
C. \[ZO{H_2}^ + \]
D. All are same

Answer 1

Hint: The \[p{K_b}\] is the measure of the strength of bases. \[p{K_b}\] is related to the base dissociation constant\[{K_b}\]. Conjugate acid is the corresponding acid obtained from a base by accepting a proton.

Complete step by step answer:
At first we have to understand the concept of conjugate acid. According to the Brønsted-Lowry definition of acids and bases, a conjugate acid-base pair is composed of two substances which only differ by the presence of a proton (\[{H^ + }\] ). Alternatively a conjugate acid is referred as a substance which is obtained when a proton is added to a base, and a conjugate base is obtained when a proton is removed from an acid.
This is expressed as
\[HA \rightleftharpoons {H^ + } + {A^ - }\] . The \[{A^ - }\] obtained from acid \[HA\] is a conjugate base.
$BOH + {H^ + } \rightleftharpoons BO{H_2}^ + $. The \[BO{H_2}^ + \] obtained from base \[BOH\] is a conjugate acid.
The dissociation of the conjugate acid is represented in a reverse manner of the formation of conjugate acid \[BO{H_2}^ + \].
$BO{H_2}^ + \rightleftharpoons BOH + {H^ + }$
The rate of the reaction is expressed by the base dissociation \[{K_b}\] in terms of the concentration of the reactants and product as
$Kb = \dfrac{{[BOH][{H^ + }]}}{{[BO{H_2}^ + ]}}$
Now another term is introduced in this respect to express the dissociation of base conveniently which is \[p{K_b}\]. \[p{K_b}\] is defined as the negative base\[ - 10\] logarithm of the base dissociation constant (\[{K_b}\]) of a solution.
\[p{K_b} = - {\log _{10}}{K_b}\]
Thus higher the value of dissociation constant the stronger is the acid. Further as the \[p{K_b}\] is the negative logarithm of the \[{K_b}\], so a lower value of \[p{K_b}\] indicates that the acid is strongest.
From the given pkb values for the three bases \[XOH\], \[YOH\] and \[ZOH\] which are \[2\] ,\[3\] and \[4\] the basic strength of the bases lies in the order \[XOH > YOH > ZOH\] which follows the same order of strength of conjugate acid.
Hence the strongest acid is \[XO{H_2}^ + \], i.e. option A is the correct answer.

So, the correct answer is Option A.

Note: According to Brønsted-Lowry theory, an acid is any substance which donates an H+ ion or a proton to form its conjugate base and the base is any substance which accepts an H+ ion or a proton and generates its conjugate acid. Strong acids and bases are the ones which ionize completely in an aqueous solution while weak acids and bases remain as partially ionized in aqueous solution.