Question: Find the pH value of a decinormal solution of \[N{H_4}OH\], which is \[20\% \] ionized. A.\[13.30\...

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

Solution

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.