Question

Assertion: The value of \[{{\text{K}}_w}\]. increases with increase in temperature. Reason: Water dissociates more as temperature increases.
A.Both Assertion and Reason are true and Reason is the correct explanation of Assertion
B.Both Assertion and Reason are true but Reason is not the correct explanation of Assertion
C. Assertion is true but Reason is false
D. Assertion is false but Reason is true E Both Assertion and Reason are false

Answer 1

Hint: In case of pure water the amount of \[\left[ {{{\text{H}}^{\text{ + }}}} \right]\] and \[\left[ {{\text{O}}{{\text{H}}^{\text{ - }}}} \right]\] is same. Water is a weak electrolyte and the amount of dissociation in pure water is very low. Due to this the amount of non-dissociated water molecules remains more or less constant. The product of \[\left[ {{{\text{H}}^{\text{ + }}}} \right]\] and \[\left[ {{\text{O}}{{\text{H}}^{\text{ - }}}} \right]\] is called ionic product of water. This is denoted as \[{{\text{K}}_w}\].

Complete step by step answer:
The ionization reaction of water is,
 \[{{\text{H}}_{\text{2}}}{\text{O}} \rightleftharpoons {{\text{H}}^{\text{ + }}}{\text{ + O}}{{\text{H}}^{\text{ - }}}\]
 The expression for equilibrium constant is,
 \[{\text{K = }}\dfrac{{\left[ {{{\text{H}}^{\text{ + }}}} \right]{\text{ }}\left[ {{\text{O}}{{\text{H}}^{\text{ - }}}} \right]}}{{\left[ {{{\text{H}}_{\text{2}}}{\text{O}}} \right]}}\]
 After rearranging this formula, we get,
 \[{\text{K}} \times \left[ {{{\text{H}}_{\text{2}}}{\text{O}}} \right]{\text{ = }}\left[ {{{\text{H}}^{\text{ + }}}} \right]{\text{ }}\left[ {{\text{O}}{{\text{H}}^{\text{ - }}}} \right]\]
 Due to the large amount of \[{{\text{H}}_{\text{2}}}{\text{O}}\] is large, that is why it can be taken as constant .
 \[{{\text{K}}_w}{\text{ = }}\left[ {{{\text{H}}^{\text{ + }}}} \right]{\text{ }}\left[ {{\text{O}}{{\text{H}}^{\text{ - }}}} \right]\]
 Where,\[{{\text{K}}_w}\] is the equilibrium constant.
 As temperature increases the concentration of \[\left[ {{{\text{H}}^{\text{ + }}}} \right]\]and\[\left[ {{\text{O}}{{\text{H}}^{\text{ - }}}} \right]\]. This is because the dissociation of water increases. This increase of dissociation of water causes the increase of the value of \[{{\text{K}}_w}\].

Therefore the correct option is A.

Note:
When a partly soluble salt dissolves into water it forms a dynamic equilibrium between the hydrated ions and its solid salt molecule. Due to this equilibrium the amount of solid salt hydrolyzed remains unchanged after achieving an amount of hydration. Due to this a new term is introduced which is solubility product \[\left( {{{\text{K}}_{{\text{sp}}}}} \right)\].With increasing the temperature solubility of the salt increases as well as the concentrations of solvated ions. Therefore, with increasing temperature the value of solubility product increases and vice-versa.