Question

What is the $pOH$ of an aqueous solution with hydrogen ion concentration equal to
$3 \times {10^{ - 5}}mol/l$
A. $9.47$
B. $4.52$
C. $12.69$
D. $11.69$

Answer 1

Hint: We all know that $pH$ is a scale used to specify the acidity or basicity of an aqueous solution. In order to calculate we need to use this equation $pH + pOH$ = $14$.

Complete answer:
The $pH$ and $pOH$ of a solution come from the hydrogen ions and the hydroxide ions that form at equilibrium. They serve as an indicator of the strength of the solution whether it be acidic or basic. $pH$ is a measure of hydronium ion concentration.
As in the question the concentration of hydrogen ions is given as $3 \times {10^{ - 5}}mol/l$
$[{H^ + }] = $$3 \times {10^{ - 5}}mol/l$
We know the $pH$ can be found out using the formula $pH = - \log [{H^ + }]$ where $\log $ is to the base $10$.
Therefore
$pH$ $ = - \log (3 \times {10^{ - 5}})$
Using the property of log that is $\log (ab) = \log a + \log b$ we can write
      $pH = - (\log 3 + \log {10^{ - 5}})$
Now again we can use the property of log as $\log {a^b} = b\log a$
So using this property we can expand this equation as follow
$pH = - (\log 3 - 5\log 10)$
Now we know that $\log 10 = 1$, and value of $\log 3 = 0.4771$ using this we can write
$
  pH = - (\log 3 - 5) \\
  pH = 5 - \log 3 \\
  pH = 5 - 0.4771 \\
  pH = 4.5229 \\
 $
 From the value of $pH$we can easily calculate the $pOH$using the equation $pH + pOH = 14$.
As we know that $pOH$$ = $ $14 - $$pH$
$pOH$
$
   = 14 - 4.5229 \\
   = 9.47 \\
 $

So the answer is A.

Note:
$pH$ is a scale used to specify the acidity or basicity of an aqueous solution. Acidic solutions have lower $pH$ values and basic solutions have higher $pH$ values. The range of $pH$ is $14$. If the value of $pH$ is $7$then it is neutral. Learn thoroughly about the exception cases.