Question

The value of ${{k}_{w}}$in a neutral solution is $5.474\times {{10}^{-14}}\,$at 50 degrees. Calculate the pH of the solution at this temperature.

Answer 1

Hint: Before solving this question, we should first know about the formula to calculate pH.
pH = $-\log \,({{H}^{+}})$ and ${{k}_{w}}$= $({{H}^{+}})\,(O{{H}^{-}})$and as the solution is neutral, therefore $({{H}^{+}})=\,(O{{H}^{-}})$. Now, we can apply this formula and solve the numerical easily.

Complete answer:
To find the pH of this solution, we have to use two formulas-
First of equilibrium constant :
${{k}_{w}}=\,({{H}^{+}})(O{{H}^{-}})$
The second is of pH :
$pH=-\log ({{H}^{+}})$
The first thing to do is to calculate the concentration of $({{H}^{+}})$ ions that is present in the water at a particular temperature.
As It is mentioned: The solution is neutral .
Therefore,the concentration of $({{H}^{+}})$ ions = The concentration of $(O{{H}^{-}})$ions
${{k}_{w}}=\,({{H}^{+}})(O{{H}^{-}})$
${{k}_{w}}=\,({{H}^{+}})({{H}^{+}})$
Now, there will be a square of $({{H}^{+}})$ ions
${{k}_{w}}=\,{{({{H}^{+}})}^{2}}$
For the concentration of $({{H}^{+}})$ ions, we have to square root ${{k}_{w}}$ .
In This question ${{k}_{w}}$is given as $5.474\times {{10}^{-14}}\,$
So, $5.474\times {{10}^{-14}}\,$$=\,({{H}^{+}})({{H}^{+}})$
${{H}^{+}}=\,\sqrt{5.474\times {{10}^{-14}}}$
              = $2.339\times {{10}^{-7}}$M
Now, we have to apply the formula of pH:
$pH=-\log ({{H}^{+}})$
     $=\,-\,\log (2.339\,\times {{10}^{-7}})$
       = 6.630
So, the pH of the solution at temperature is 6.630.

Additional Information:
pH has various uses like
Hydrochloric acid in our stomach helps to digest the food without damaging our stomach. But if the concentration of acid exceeds a certain limit, then we face problems like pain and indigestion. SO, to neutralize it Antacids are taken to balance the pH.
Soils need a certain amount of pH to be fertile. The soil should not be too acidic or too alkaline. It hampers the growth of the plant.

Note:
The calculation of the Acidity or alkalinity of a solution is known as pH. The relative quantity $({{H}^{+}})$ is stated by pH. Acidity depends on the concentration of the $({{H}^{+}})$ ions. If the concentration of$({{H}^{+}})$ ions is more then more is the acidity of the solution.