Question

If the ionic product of water is \[1.96 \times {10^{ - 14}}\]at \[35^\circ C\]. What is its value at \[10^\circ C\]?
(A) \[2.95 \times {10^{ - 14}}\]
(B) \[1.96 \times {10^{ - 7}}\]
(C) \[2.95 \times {10^{ - 15}}\]
(D) \[3.9 \times {10^{ - 12}}\]

Answer 1

Hint: The concentration of the ions in water at a specific temperature is known as the ionic product of water. When formulating the expression for ionic products, the water molecule itself is not taken into account.

Complete Step by Step Solution:
In the question, at \[{35^0}C\] the value of ionic product of water \[ = 1.96 \times {10^{ - 14}}\] is given.
Water can self-ionize, but only to a small degree. The hydronium ion, which has a positive charge, and the hydroxide ion, which has a negative charge, are the end products of the collision between the two water molecules.
\[{H_2}O(l) + {H_2}O(l) \rightleftharpoons {H_3}{O^ + }(aq) + O{H^ - }(aq)\]
Which is often simplified as \[{H_2}O(l) + \rightleftharpoons {H^ + }(aq) + O{H^ - }(aq)\]
The ionic product of water is the term for the equilibrium constant for the expression for self-ionisation of water. \[{K_W}\] is used as the symbol for ionic products of water.
\[{K_W} = \left[ {{H^ + }} \right]\left[ {O{H^ - }} \right]\]

The ionic product of water is the product of concentration of \[O{H^ - }\]and \[{H^ + }\]ions.
The temperature and the ionic product have a direct relationship; that is, the ionic product is directly proportional to temperature. The ionic product also diminishes as the temperature drops.

According to the given information, the temperature is decreasing \[\left( {{{10}^0}C} \right)\]. So, the ionic product of water also decreases.
From the given options it can be observed that \[2.95 \times {10^{ - 15}}\] is the only value less than the present value.
Therefore, the correct option is: (C) \[2.95 \times {10^{ - 15}}\].

Note: It should be noted that each aqueous solution whether it is acidic, basic or neutral possesses both hydrogen \[{H^ + }\]ion and hydroxyl \[O{H^ - }\] ion that is present in the same or different proportions. But the ionic product concentration \[{K_W}\] of the water always remains constant.