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Question: At \({100^0}C\) the \({k_w}\) of water is \(55\) times its value at \({25^0}C\) . What will be the \...

At 1000C{100^0}C the kw{k_w} of water is 5555 times its value at 250C{25^0}C . What will be the pH{pH} of neutral solution?
(log⁡55=1.74)\left( {\log 55 = 1.74} \right)

Explanation

Solution

To get the solution of above question we have to first understand that kw{k_w} is the ionic product of water and given as kw=[H+][OH−]{k_w} = \left[ {{H^ + }} \right]\left[ {O{H^ - }} \right] .

Complete answer:
Firstly, we have to understand some chemical terms like pH{pH} and kw{k_w} .
pH{pH} stand for potential of hydrogen , since pH{pH} is effectively a measure of the concentration of hydrogen ions in a substance and is given as-
pH=−log⁡(H+){pH} = - \log \left( {{H^ + }} \right)
And kw{k_w} stands for ionic product of water and it is given as the product of positively charged hydronium ion and a negatively charged hydroxide ion. Its value is fixed for fixed temperature . at 250C{25^0}C its value is 1∗10−141*{10^{ - 14}} .
For a given reaction ,
H2O⇌H++OH−H_2O \rightleftharpoons {H^ + } + O{H^ - }
Then equilibrium constant may be given as
k=[H+][OH−]/H2Ok = \left[ {{H^ + }} \right]\left[ {O{H^ - }} \right]/H_2O
k[H2O]=[H+][OH−]k\left[ {H_2O} \right] = \left[ {{H^ + }} \right]\left[ {O{H^ - }} \right]
⇒kw=[H+][OH−]\Rightarrow {k_w} = \left[ {{H^ + }} \right]\left[ {O{H^ - }} \right]
Now, at 1000C{100^0}C
kw=55∗10−14{k_w} = 55*{10^{ - 14}}
H+=55∗10−14{H^ + } = \sqrt {55*{{10}^{ - 14}}} =7.41∗10−77.41*{10^{ - 7}}
pH=−log⁡[H+]pH = - \log \left[ {{H^ + }} \right]
And hence on substituting the values,we have
=−log⁡[7.41∗10−7]= - \log \left[ {7.41*{{10}^{ - 7}}} \right]
=−[log⁡7.41+log⁡10−7]= - \left[ {\log 7.41 + \log {{10}^{ - 7}}} \right]
And hence on doing the simplification,we have
=−[0.86−7]=−[−6.13]= - \left[ {0.86 - 7} \right] = - \left[ { - 6.13} \right]
=6.13= 6.13
Hence, the required answer for the given question is 6.136.13 .

Additional information :
Ionic equilibrium is the equilibrium established between the unionized molecule and the ions in solution of weak electrolytes. pH{pH} is a measure of acidity or alkalinity of a solution .Acid produces hydrogen ions in solution .While a sparingly soluble salt is dissolved in water , a dynamic equilibrium is established.

Note:
pH{pH} is a measure of how acidic or basic an aqueous solution is. The pH{pH} scale is a logarithmic scale that usually runs from 11 to 1414 .pH{pH} value lower than 77 are termed as acidic and those higher than 77 are termed as basic.
pH{pH} and kw{k_w} are directly related to each other as the value of kw{k_w} of changes with temperature pH{pH} value also differ.