Question

Which one is correct for ${{H}_{2}}O$ at ${{25}^{\circ }}C$?
(a) Ionic product of water, ${{K}_{w}}={{10}^{-14}}$
(b) Equilibrium constant for dissociation of water ${{K}_{c}}=1.8\times {{10}^{-16}}$
(c) Autoprotolysis constant of water, ${{K}_{AP}}=3.2\times {{10}^{-18}}$
(d) On heating ${{K}_{w}}$ increases with temperature

Answer 1

Hint: We should know that temperature plays an important role in determining the values of different constants of a liquid thus always carefully check and calculate the values according to the given temperature. Here we are provided water at ${{25}^{\circ }}C$.

Complete answer:
${{H}_{2}}O$ is one of the most important substances for the survival of living beings on earth and hence it is necessary to study and learn its properties.
We know that ionic product of water is: ${{K}_{w}}={[{H}^{+}]}{[O{H}^{-}]}$
Therefore ${{K}_{w}}$ of water is dependent on the concentration of ${H}^{+}$ and $O{H}^{-}$ ions in the solution.
Now, let us go through the options one by one:-
(a) Ionic product of water, ${{K}_{w}}={{10}^{-14}}$ :-
Since ${{H}_{2}}O$ at ${{25}^{\circ }}C$, the active mass of ${H}^{+}$ and $O{H}^{-}$ ions is approximately equal to ${{10}^{-7}}$ units. So ${{K}_{w}}$ of water will be : ${{K}_{w}}={[{H}^{+}]}{[O{H}^{-}]}$
\[\Rightarrow {{10}^{-7}}\times {{10}^{-7}}={{10}^{-14}}\]
(b) Equilibrium constant for dissociation of water ${{K}_{c}}=1.8\times {{10}^{-16}}$ :-
For a reaction ${{A}_{x}}{{B}_{y}}\to xA+yB$, Dissociation constant (${{K}_{c}}$) = \[\dfrac{{{[A]}^{x}}{{[B]}^{y}}}{[{{A}_{x}}{{B}_{y}}]}\]
So for ${{H}_{2}}O\to 2{{H}^{+}}+O{{H}^{-}}$, Dissociation constant (${{K}_{c}}$) = \[\dfrac{{{[{{H}^{+}}]}^{2}}[O{{H}^{-}}]}{[{{H}_{2}}O]}\]
Using molar properties of ${{H}_{2}}O$at${{25}^{\circ }}C$and further calculations it is observed that ${{K}_{c}}$ for water is $1.8\times {{10}^{-16}}$
(c) Autoprotolysis constant of water, ${{K}_{AP}}=3.2\times {{10}^{-18}}$:-
Through several experimental observation, scientists have observed that at ${{25}^{\circ }}C$, the ${{K}_{AP}}$ of water is $3.2\times {{10}^{-18}}$.
(d) On heating ${{K}_{w}}$ increases with temperature:-
As we increase the temperature, the amount of available energy required to cross the activation energy barrier also increases. Thus a large number of ${H}^{+}$ and $O{H}^{-}$ ions will be observed. Since we already discussed above that ${{K}_{w}}$ of water is dependent on the concentration of ${H}^{+}$ and $O{H}^{-}$ ions so on heating ${{K}_{w}}$ increases with temperature.

-Hence the correct answers are (a), (b), (c) and (d).

Note:
Water (${{25}^{\circ }}C$) is the most abundant and important substance on the planet earth, thus it is important that we learn and remember its properties.
-Certain values of important constants are calculated in scientific laboratories after various measurements. Those values are provided to us by the scientists and we must try to learn these important values in chemistry.