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Question: The \(pH\)of \({10^{ - 3}}M\) monoacidic base, if it is \(1\% \) ionized is: A. \(5\) B. \(8\) ...

The pHpHof 10−3M{10^{ - 3}}M monoacidic base, if it is 1%1\% ionized is:
A. 55
B. 88
C. 33
D. 99

Explanation

Solution

We know that a monoacidic base is a base which furnishes only one hydroxyl group in water. Similarly diacidic bases will furnish two hydroxyl groups in water. The concept of pHpH gives us an idea about the acidity and basicity of a given solution.

Complete step by step solution:
As we know that monoacidic base furnishes only one hydroxyl group in water. Let the monoacidic base be BOHBOH. It is given that in the solution it is 1%1\% ionized. Let the degree of ionization be α\alpha . Then α=1%=10−2\alpha = 1\% = {10^{ - 2}}. We have given the value of concentration (C)(C) of the BOHBOH solution, that is C=10−3MC = {10^{ - 3}}M. So ,
BOH⇄B+1+OH−1BOH \rightleftarrows {B^{ + 1}} + O{H^{ - 1}}
In the above reaction , the concentration of OH−1O{H^{ - 1}} will be [OH−1]=Cα=10−3×10−2=10−5[O{H^{ - 1}}] = C\alpha = {10^{ - 3}} \times {10^{ - 2}} = {10^{ - 5}}.
We know that,
Kw=[H+][OH−]=10−14 ⇒[H+]=10−1410−5=10−9  {K_w} = [{H^ + }][O{H^ - }] = {10^{ - 14}} \\\ \Rightarrow [{H^ + }] = \dfrac{{{{10}^{ - 14}}}}{{{{10}^{ - 5}}}} = {10^{ - 9}} \\\
Here , Kw={K_w} = ionic product of water.
So now as we have got the value of the concentration of hydrogen ion, that is [H+]=10−9[{H^ + }] = {10^{ - 9}}.
Now we can directly apply the formula of pHpH, to get the value of pHpHof the given solution.
pH=−log⁡[H+] ⇒pH=−log⁡[10−9] ⇒pH=9  pH = - \log [{H^ + }] \\\ \Rightarrow pH = - \log [{10^{ - 9}}] \\\ \Rightarrow pH = 9 \\\
So from the above explanation and calculation it is clear to us that the correct answer of the given question is option : 99

Hence, the correct answer is option D.

Additional information:
The range of pHpH of an acidic solution is less than 77 and the pHpHof a basic solution is greater than 77 and less than 1414. Some of the examples of strong acids are HCl,H2SO4,HNO3HCl,{H_2}S{O_4},HN{O_3} and some examples of strong bases are NaOH,KOH,LiOHNaOH,KOH,LiOH. Strong bases and acids dissociate completely in water . They are also known as strong electrolytes.

Note: Always remember that pHpH of a solution is given by pH=−log⁡[H+]pH = - \log [{H^ + }]. The ionic product of water is given by Kw=[H+][OH−]=10−14{K_w} = [{H^ + }][O{H^ - }] = {10^{ - 14}}. Monoacidic bases furnish only one hydroxyl group and diacidic bases furnish two hydroxyl groups. Always try to avoid silly mistakes and calculation errors while solving the question.