Question

The aqueous solution having \[pH{\text{ 11}}\] is how many times less basic the aqueous solution having \[pH{\text{ }}8\]?
A.\[8\]
B.\[30\]
C.\[300\]
D.\[1000\]

Answer 1

Hint: The pH of a solution is a measure of hydrogen ion concentration, which in turn is a measure of its acidity. pH is calculated using the formula given below:
\[pH = - {\log _{10}}[{H^ + }]\]
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 the hydroxide-ion concentration.
\[pOH = - {\log _{10}}[O{H^ - }]\]

Complete answer:
\[{H_2}O \rightleftarrows {H^ + } + O{H^ - }\]
The equilibrium constant for this reaction, \[{K_w}\] is the product of \[{H^ + }\] and \[O{H^ - }\] concentrations. This relationship may be expressed as:
\[ \Rightarrow {K_w} = [{H^ + }][O{H^ - }]\]
At \[{25^ \circ }C\],
\[{K_w} = [{H^ + }][O{H^ - }] = {10^{ - 14}}\]
Using this information, we can now solve the problem
For aqueous solution having \[pH{\text{ 11}}\]
\[ \Rightarrow pH = 11\]
\[ - \log [{H^ + }] = 11\]
\[\log [{H^ + }] = - 11\]
\[[{H^ + }] = anti\log ( - 11)\]
\[ \Rightarrow [{H^ + }] = {10^{ - 11}}\]
We know that, \[[{H^ + }][O{H^ - }] = {10^{ - 14}}\]
 \[[O{H^ - }] = \dfrac{{{{10}^{ - 14}}}}{{[{H^ + }]}} = \dfrac{{{{10}^{ - 14}}}}{{{{10}^{ - 11}}}}\]
\[ \Rightarrow [O{H^ - }] = {10^{ - 3}}\]
Therefore, \[{[O{H^ - }]_1} = {10^{ - 3}}\]
For aqueous solution having \[pH{\text{ }}8\]
\[pH = 8\]
\[ - \log [{H^ + }] = 8\]
\[\log [{H^ + }] = - 8\]
\[[{H^ + }] = anti\log ( - 8)\]
\[ \Rightarrow [{H^ + }] = {10^{ - 8}}\]
\[[O{H^ - }] = \dfrac{{{{10}^{ - 14}}}}{{[{H^ + }]}} = \dfrac{{{{10}^{ - 14}}}}{{{{10}^{ - 8}}}}\]
\[ \Rightarrow [O{H^ - }] = {10^{ - 6}}\]
Therefore, \[{[O{H^ - }]_2} = {10^{ - 6}}\]
On taking ratio of concentration of hydroxyl ion,
\[ \Rightarrow \dfrac{{{{[O{H^ - }]}_1}}}{{{{[O{H^ - }]}_2}}} = \dfrac{{{{10}^{ - 3}}}}{{{{10}^{ - 6}}}} = {10^3}\]
Hence, aqueous solution having \[pH{\text{ 11}}\]is \[{10^3}\]i.e. \[1000\]times more basic than solution having \[pH{\text{ }}8\].

Option(D) is correct.

Note:
Acidic solutions (solutions with higher concentrations of \[{H^ + }\] ions) are measured to have lower pH values than basic or alkaline solutions. At \[{25^ \circ }C\], solutions with a pH less than 7 are acidic, and solutions with a pH greater than 7 are basic. Solutions with a pH of 7 at this temperature are neutral (e.g. pure water). The neutral value of the pH depends on the temperature, being lower than 7 if the temperature increases. The pH value can be less than 0 for very strong acids or greater than 14 for very strong bases.