Question

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

Answer 1

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

Complete answer:
Firstly, we have to understand some chemical terms like ${pH}$ and ${k_w}$ .
${pH}$ stand for potential of hydrogen , since ${pH}$ is effectively a measure of the concentration of hydrogen ions in a substance and is given as-
${pH} = - \log \left( {{H^ + }} \right)$
And ${k_w}$ 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 ${25^0}C$ its value is $1*{10^{ - 14}}$ .
For a given reaction ,
$H_2O \rightleftharpoons {H^ + } + O{H^ - }$
Then equilibrium constant may be given as
$k = \left[ {{H^ + }} \right]\left[ {O{H^ - }} \right]/H_2O$
$k\left[ {H_2O} \right] = \left[ {{H^ + }} \right]\left[ {O{H^ - }} \right]$
$ \Rightarrow {k_w} = \left[ {{H^ + }} \right]\left[ {O{H^ - }} \right]$
Now, at ${100^0}C$
${k_w} = 55*{10^{ - 14}}$
${H^ + } = \sqrt {55*{{10}^{ - 14}}} $ =$7.41*{10^{ - 7}}$
$pH = - \log \left[ {{H^ + }} \right]$
And hence on substituting the values,we have
$ = - \log \left[ {7.41*{{10}^{ - 7}}} \right]$
$ = - \left[ {\log 7.41 + \log {{10}^{ - 7}}} \right]$
And hence on doing the simplification,we have
$ = - \left[ {0.86 - 7} \right] = - \left[ { - 6.13} \right]$
$ = 6.13$
Hence, the required answer for the given question is $6.13$ .

Additional information :
Ionic equilibrium is the equilibrium established between the unionized molecule and the ions in solution of weak electrolytes. ${pH}$ 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:
${pH}$ is a measure of how acidic or basic an aqueous solution is. The ${pH}$ scale is a logarithmic scale that usually runs from $1$ to $14$ .${pH}$ value lower than $7$ are termed as acidic and those higher than $7$ are termed as basic.
${pH}$ and ${k_w}$ are directly related to each other as the value of ${k_w}$ of changes with temperature ${pH}$ value also differ.