Question

The \[p{{K}_{a}}\], value of four acids are given below at \[{{25}^{0}}C\]. The strongest acid is:
A.$\text{2}\text{.0}$
B.$\text{2}\text{.5}$
C.$3.0$
D.$4.0$

Answer 1

Hint: The \[p{{K}_{a}}\] value equals the negative logarithm of \[{{K}_{a}}\] which is the ionization constant i.e. it measures the strength of the acid. So, by varying \[p{{K}_{a}}\] values accordingly given in the question we can find out \[{{K}_{a}}\] values which will give us the strongest acid.

Formula Used:
 \[p{{K}_{a}}=-\log \left( {{K}_{a}} \right)\], where\[{{K}_{a}}\] is ionization constant of an acid.

Complete step by step answer:
We have, \[p{{K}_{a}}=-\log \left( {{K}_{a}} \right)\] and \[{{K}_{a}}\] give us the strength of the acid provided the temperature remains constant.
For \[p{{K}_{a}}=2\], we have ,
$2=-\log \left( {{K}_{a}} \right)$
Taking antilog on both sides, we get, $\text{antilog 2 =}-\left( {{K}_{a}} \right)$
\[{{10}^{2}}=\left( {{K}_{a}} \right)\]
(Equality is raised to exponent of $10$ for antilog)
 Therefore, \[{{K}_{a}}=\dfrac{1}{{{10}^{2}}}=0.01\]
So, for option $\left( \text{A} \right)$ the strength of the acid is $0.01$
For, \[p{{K}_{a}}=3\] we have,
$\begin{align}
  & \Rightarrow 3=-\log \left( {{K}_{a}} \right) \\
 & \Rightarrow {{10}^{3}}=-\left( {{K}_{a}} \right) \\
 & \Rightarrow {{K}_{a}}=\dfrac{1}{{{10}^{3}}}=0.001 \\
\end{align}$
So, as we see that for \[p{{K}_{a}}=2\], \[{{K}_{a}}=0.01\] and for \[p{{K}_{a}}=3\], \[{{K}_{a}}=0.001\]. It means that the value of \[{{K}_{a}}\] reduces as the value of \[p{{K}_{a}}\] increases. It thereby means that the strength of the acid reduces as the \[p{{K}_{a}}\] value keeps on increasing.
So, from all the given options the least \[p{{K}_{a}}\] value is $2.0$. For this value, the value of \[{{K}_{a}}\] will be largest, this means that it will be the strongest acid.

So, the option-(A) is correct.

Note:
Dissociation constant of an acid: The ionization constant is a measure of acid strength. It is represented by \[{{K}_{a}}\]. The higher the \[{{K}_{a}}\] value, the greater the no. of hydrogen ions liberated per mole of acid in the solution and hence stronger is the acid. Low values of \[{{K}_{a}}\] mean that the acid does not dissociate well and that it is a weak acid.
The more easily the acid dissociates, and the stronger it is i.e. the weaker the base it is, and less strongly its bonds are held together by electron donation. Oftentimes, the \[{{K}_{a}}\] value is expressed by using the \[p{{K}_{a}}\]. The larger the value of \[p{{K}_{a}}\], the smaller the extent of dissociation. A weak acid has a \[p{{K}_{a}}\] value in the approximate range of $-2$ to $+12$ in water. Acids with \[p{{K}_{a}}\] value of less than about $-2$ are said to be strong acids.
Example of weak acid is Acetic Acid and that of strong acid is HCl.