Question

An alcoholic drink substance pH = 4.7 then $O{{H}^{-}}$concentration of this solution is:-
(${{K}_{w}}={{10}^{-14}}mo{{l}^{2}}{{L}^{-2}}$)
(A) $3\times {{10}^{-10}}$
(B) $5\times {{10}^{-10}}$
(C) $1\times {{10}^{-10}}$
(D) $5\times {{10}^{-8}}$

Answer 1

Hint: As we know that pH is the abbreviation for power of hydrogen and it tells about the concentration of hydrogen ion (${{H}^{+}}$) in a solution whereas pOH is the abbreviation for power of hydroxide ion and it tells about the concentration of hydroxide ion ($O{{H}^{-}}$ ) in a solution. So here we have to calculate the concentration of hydroxide ion in the given substance.
Formula used:
We will use the following formulas in this solution:-
pH + pOH = 14
pOH = $-\log [O{{H}^{-}}]$

Complete answer:
Let us first discuss about pH and pOH followed by further calculations:-
-pH: It is also known as the power of hydrogen and it informs regarding the concentration of hydrogen ions (${{H}^{+}}$) in a solution. It is calculated by negative logarithm of concentration of hydrogen ions i.e., pH = $-\log [{{H}^{+}}]$ .
-pOH: It is also known as power of hydroxide ion and it informs regarding the concentration of hydroxide ion ($O{{H}^{-}}$) in a solution. It is calculated by negative logarithm of concentration of hydroxide ion i.e., pOH = $-\log [O{{H}^{-}}]$ .
The relation between pH and pOH of any substance or solution is pH + pOH = 14.
-Calculation of pOH of alcoholic drink substance using the relation between pH and pOH as follows:-
The given value of pH of alcoholic drink substance is = 4.7
On substituting this value in the formula, we get:-
$\begin{align}
  & \Rightarrow pH+pOH=14 \\
 & \Rightarrow 4.7+pOH=14 \\
 & \Rightarrow pOH=14-4.7 \\
 & \Rightarrow pOH=9.3 \\
\end{align}$
-Calculation of concentration of hydroxide ion present in the alcoholic drink substance as follows:-
As we know that pOH is negative logarithm of hydroxide ion i.e., pOH = $-\log [O{{H}^{-}}]$
So let us substitute the pOH value in this formula in order to calculate the concentration of hydroxide ion:-
$\begin{align}
  & \Rightarrow pOH=-\log [O{{H}^{-}}] \\
 & \Rightarrow -\log [O{{H}^{-}}]=9.3 \\
 & \Rightarrow \log [O{{H}^{-}}]=-9.3 \\
 & \Rightarrow [O{{H}^{-}}]={{10}^{-9.3}} \\
 & \Rightarrow [O{{H}^{-}}]=5\times {{10}^{-10}} \\
\end{align}$

-Therefore, the $O{{H}^{-}}$concentration of alcoholic drink substance is (B) $5\times {{10}^{-10}}$.

Note:
-Generally substances with pH less than 7 are acidic in nature whereas substances with pH greater than 7 are basic in nature. Since the pH of alcoholic drink substance is 4.7, therefore it is an acidic substance.
-Compounds or substances with pH = 7 are neutral in nature.