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Question: For dissociation constant (K) and ionic product \((K_w)\) of water which is correct. A) \(K > K_w\...

For dissociation constant (K) and ionic product (Kw)(K_w) of water which is correct.
A) K>KwK > K_w
B) Kw>KK_w > K
C) Kw=KK_w = K
D) None of these

Explanation

Solution

The dissociation constant (K) is a specific type of equilibrium constant that measures the property of a larger object of dissociating reversibly into smaller components.
Where Ionic product means, The product of their concentration of ions.
H2O{H_2}O gets dissociated in H3O+{H_3}{O^ + } and OH−O{H^ - } so the product of their concertation is an ionic product.

Complete step by step answer:
Water is a poor conductor of electricity.
H2O⇆H++OH−{H_2}O\underset {} \leftrightarrows {H^ + } + O{H^ - }
and,
2H2O⇆H3O+OH−2{H_2}O\overset {} \leftrightarrows {H_3}O + O{H^ - }
Ionic product of water may be defined as product of [H+]\left[ {{H^ + }} \right] and [OH−]\left[ {O{H^ - }} \right] where [  ][\;] denotes the concentration.
And also, can say that H+{H^ + } ions in water exist as H3O+{H_3}{O^ + } ions, therefore, ionic product of molar concentration of H3O+ and OH−{H_3}{O^ + }{\text{ and }}O{H^ - }
{K_w} = \left[ {{H^ + }} \right]\left[ {O{H^ - }} \right] \\\ {K_w} = \left[ {{H_3}{O^ + }} \right]\left[ {O{H^ - }} \right]..............(1) \\\
Dissociation constant of water is,
K=[H+].[OH−][H2O]K = \dfrac{{\left[ {{H^ + }} \right].\left[ {O{H^ - }} \right]}}{{\left[ {{H_2}O} \right]}}
And for dissociation of H3O+{H_3}{O^ + } and OH−O{H^ - }, we can say,
K=[H3O+][OH−][2.H2O]=Kw[2.H2O]=Kw[H2O]2K = \dfrac{{\left[ {{H_3}{O^ + }} \right]\left[ {O{H^ - }} \right]}}{{\left[ {2.{H_2}O} \right]}} = \dfrac{{{K_w}}}{{\left[ {2.{H_2}O} \right]}} = \dfrac{{{K_w}}}{{{{\left[ {{H_2}O} \right]}^2}}}
[Put the value of Kw{K_w} from (1)].
Here, we can see, that dissociation constant is smaller too Kw{K_w} because [H2O]2{\left[ {{H_2}O} \right]^2} is divided with Kw{K_w} to get, K.
∴K<Kw\therefore K < {K_w}

∴\therefore Option B is correct.

Note: We get by experiment that dissociation constant of water is 1.0×10−71.0 \times {10^{ - 7}}. Water dissociates only slightly, as water is a weak electrolyte. Ionic product is the normal product of concentrate of ions, each raised to the power specified by its stoichiometric coefficient in a solution of a salt.