Question

Find the pH value of a decinormal solution of \[N{H_4}OH\], which is \[20\% \] ionized.
A.\[13.30\]
B.\[14.70\]
C.\[12.30\]
D.\[12.95\]

Answer 1

Hint:
The pH value of a solution may be defined as the negative logarithm of base 10 of the \[[{H_3}{O^ + }]\] concentration which is expressed in moles per liter. The pOH value of a solution may be defined as the negative logarithm of base 10 of the \[[O{H^ - }]\] present in the solution. The pH and the pOH are related to each other as follows: \[pH + pOH = 14\]

Step-by-step explanation:
Step 1:
\[N{H_4}OH\] is a mono-acidic base, so the concentration terms in molarity will be equal to its normality.
It is a decinormal solution which means its normality is \[0.1N = 0.1M\]
Step 2:
As \[N{H_4}OH\] is a weak base its degree of ionization is given \[20\% \] \[ = 0.2\]. As the concentration of \[[O{H^ - }]\] ions depends upon the number of \[[O{H^ - }]\] ions present in the solution, the concentration of the \[[O{H^ - }]\] ions will be the product of its molar concentration and the degree of ionization.
Step 3
\[[O{H^ - }] = 0.1 \times 0.2 = 0.02M\]
As we know pOH is the negative logarithm of base 10 of the \[[O{H^ - }]\] present in the solution,
So, \[pOH = - \log 0.02\]
      \[pOH = - \log ({10^{ - 2}} \times 2)\]
      \[pOH = 2\log 10 - \log 2\]
      \[pOH = 2 - \log 2\] \[[\log 10 = 1]\]
       \[pOH = 2 - 0.301\] \[[\log 2 = 0.301]\]
        \[pOH = 1.699\]
Step 4
As we know, \[pH + pOH = 14\]
 So, \[pH = 14 - 1.699\]
        \[pH = 12.301\]
From the given options \[12.30\] is closest to the derived answer,

Hence, the correct answer i.e. the pH value for a decinormal solution of \[20\% \] ionized \[N{H_4}OH\]is option (c) \[12.30\].

Note: The pH of a neutral solution is 7. The pH value decreases as the solution becomes increasingly acidic. The solutions with pH range 0 – 2 are strongly acidic, those with pH range 2 – 4 are moderately acidic while the solutions with pH values between 4 – 7 are weakly acidic. As the pH value increases the solution gradually becomes more basic. The solutions having a pH range of 7 – 10 are weakly basic, those having the pH range between 10 – 12 are moderately basic whereas the solution having the pH range of 13 – 14 is highly basic.