Question

If $[OH^-]= 5.0 × 10^{-5}$ M then pH will be:
A. \[5-\log 5\]
B. \[9+\log 5\]
C. \[\log 5-5\]
D. \[\log 5-9\]

Answer 1

Hint: The pH of a solution is negative-logarithm of hydrogen ion concentration. As with the hydrogen-ion concentration, the concentration of the hydroxide ion can be expressed logarithmically by the pOH. The pOH of a solution is the negative-logarithm of hydroxide-ion concentration in that solution. Regardless of what is added to the solution the sum of pH and pOH will be always 1.0 x $10^{-14}$ at $25^oC$.
      \[\Rightarrow {{p}{H}}+{{p}{OH}}=14\]

Complete step by step answer:
Given that,[OH-]= 5.0 × 10-5, hence the pOH will be,
        \[\Rightarrow {{p}{OH}}=-\log [O{{H}^{-}}]\]
                        \[=-\log (5\times {{10}^{-5}})\]
              \[{{p}{OH}}=5-\log 5\]
Now, we have known that,
       \[\Rightarrow {{p}{H}}+{{p}{OH}}=14\]
       \[\Rightarrow {{p}{H}}=14-{{p}{OH}}\]

       \[\Rightarrow {{p}{H}}=9+\log 5\]

Hence, the correct option is B.

Note:
pH is a measure of how acidic/basic water is. The range goes from 0 to 14, with 7 being neutral. When pH of less than 7 indicates acidity, whereas a pH of greater than 7 indicates a base.The pH and pOH are really a measure of the relative amount of free hydrogen and hydroxyl ions in the water.