Question

For \[0.1{\text{ }}mol\;HCl\] is dissolved in distilled water of volume \[V\] then \[\mathop {\lim }\limits_{V \to \infty } {(pH)_{solution}}\] is equal to
A.Zero
B.\[1\]
C.\[7\]
D.\[14\]

Answer 1

Hint: \[pH\], denoting 'potential of hydrogen' or 'power of hydrogen' is a scale used to specify the acidity or basicity of an aqueous solution. Acidic solutions (solutions with higher concentrations of \[{H^ + }\] ions) are measured to have lower \[pH\] values than basic or alkaline solutions. \[pH\] is defined as the decimal logarithm of the reciprocal of the hydrogen ion activity, \[{a_{{H^ + }}}\], in a solution.

Complete answer:
In the above question, it is given that \[0.1{\text{ }}mol\;HCl\] is dissolved in distilled water. Hence, \[{K_W} = [{H^ + }][O{H^ - }]\]. Here, \[{K_W}\] is the self-ionization constant of water. It is also given that \[0.1{\text{ }}mol\;HCl\] is being dissolved in an infinite volume of distilled water. After a certain stage of dissolving, \[[{H^ + }] < {10^{ - 7}}M\].
On taking the logarithm of the above equation, we will get \[pOH = p{K_W} - pH\]. For \[[{H^ + }]\], the equation is modified to \[pH = p{K_W} + pOH\]. Here, \[p{K_W} = {10^{ - 7}}\] and \[pOH = {10^{ - x}}\] where \[x > 7\]
Hence, \[[{H^ + }] = {10^{ - 7}}M + {10^{ - x}}M\]
This makes the whole solution neutral and we know that the \[pH\] of a neutral solution is \[7\].
Hence, the correct option is C.

Additional information:
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 (example: 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.

Note:
The \[pH\] scale is logarithmic and inversely indicates the concentration of hydrogen ions in the solution. This is because the formula used to calculate \[pH\] approximates the negative of the base \[10\] logarithm of the molar concentration of hydrogen ions in the solution as we saw above. More precisely, \[pH\] is the negative of the base 10 logarithm of the activity of the \[{H^ + }\] ion.