Question

An acid HA has dissociated in following manner
     \[HA\rightleftharpoons {{H}^{+}}+{{A}^{-}}\]
It has concentration 1M and pH=5. Find out the dissociation constant.
a.) $1 x {{10}^{-10}}$
b.) $1 x {{10}^{-6}}$
c.) $5 x {{10}^{-5}}$
d.) 5

Answer 1

Hint: The concentration of ${{H}^{+}}$ ions play a huge role in finding the dissociation constant for acids. This is because the dissociation constant gives us the ratio of products and reactants at equilibrium. Acids dissociate to give ${{H}^{+}}$ ions. Also, pH gives us the information of ${{H}^{+}}$ ions only. Knowing these facts, we can find the dissociation constant.

Complete step by step answer:
-Weak electrolytes cannot dissociate completely into their respective ions. So their ionization is less than 100%. Weak acids, weak bases and sparingly soluble salts come under this category.
Eg. Weak acids like formic acid, acetic acid, hydrogen sulfide are weak electrolytes.
       Weak bases like ammonia, pyridine and other nitrogen ring bases are weak electrolytes.
       Salts like AgCl and $BaS{{O}_{4}}$ are weak electrolytes.

-The reaction is feasible only when strong acids and strong bases react to give weak conjugate acids/bases. So, equilibrium of the reaction proceeds in that direction only where strong electrolytes are converted to weak electrolytes. This is why dissociation constant is calculated.

-Acidic strength is the tendency to give ${{H}^{+}}$ ions and basic strength is the tendency to give $O{{H}^{-}}$ ions. This is where pH scale comes into picture. It is defined as the negative logarithm of concentration of ${{H}^{+}}$ ions.
$pH=-\log \left[ {{H}^{+}} \right]\text{ or pH= -log}\left[ {{H}_{3}}{{O}^{+}} \right]$

-Dissociation constant for an acid is given from the reaction $HA+{{H}_{2}}O\rightleftharpoons {{A}^{-}}+{{H}_{3}}{{O}^{+}}$
The value of dissociation constant for above reaction is ${{K}_{a}}=\dfrac{\left[ {{H}_{3}}{{O}^{+}} \right]\left[ {{A}^{-}} \right]}{\left[ HA \right]}$

-The degree of dissociation of an electrolyte is the fraction of one mole of electrolyte which has dissociated under the given set of conditions. It depends on the nature of electrolyte, nature of solvent, dilution, pressure and temperature. It is denoted as $\alpha $ .

-In the given question, we see that 1M acid is given. Initially there will only be acid concentration. Products will not be formed. At equilibrium, if x moles of acid are dissociated, then the concentration of acid will become (1-x).
\[\begin{align}
 & \text{ }HA\rightleftharpoons {{H}^{+}}+{{A}^{-}} \\
 & At\text{ T=0 1 0 0} \\
 & \text{At T=t }\left( 1-x \right)\text{ x x} \\
\end{align}\]
Given, pH=5. So, $\left[ {{H}^{+}} \right]={{10}^{-5}}$
Thus, value of x=${{10}^{-5}}$

Now, ${{K}_{a}}=\dfrac{\left[ {{H}_{3}}{{O}^{+}} \right]\left[ {{A}^{-}} \right]}{\left[ HA \right]}$
So, $\begin{align}
 & {{K}_{a}}=\dfrac{\left( {{10}^{-5}} \right)\left( {{10}^{-5}} \right)}{1-{{10}^{-5}}} \\
 & \Rightarrow {{K}_{a}}={{10}^{-10}} \\
\end{align}$
So, the correct answer is “Option A”.

Note: For a given acid or base, pH+pOH=14 and is denoted as $p{{K}_{w}}$ and is called self-ionization constant of water. Also, there is no physical dimension of the dissociation constant although it may appear to have the unit of concentration.