Question

The hydrogen, ion concentration of a solution is 0.001 M. What is the \[pH\] of the solution?

Answer 1

Hint: In chemistry pH is a scale to measure the acidity or basicity of a solution. It is can be calculated by the formula \[{\text{pH = - log}}{\left[ {\text{H}} \right]^{\text{ + }}}\], where \[{\left[ {\text{H}} \right]^{\text{ + }}}\] is the molar concentration of hydrogen ion present in the solution. Molar concentration is also called molarity means the number of moles of a particular solute in a solvent per liter volume of solution.
Formula used:
\[{\text{pH = - log}}{\left[ {\text{H}} \right]^{\text{ + }}}\]

Complete step by step answer:
Calculation of \[pH\] of strong acid can be done using the given molar concentration of hydrogen ion present in the solution. Because, strong acids dissociate fully in the solutions. But in case of weak acids dissociation tendency is very low, as a result molar concentration of hydrogen ion cannot be equal with the concentration of the acid. In this case a new term is introduced which is dissociation constant \[\left( {{K_a}} \right).\]
\[HA \to {H^ + } + {A^ - }\]
\[{K_a} = \dfrac{{\left[ {{H^ + }} \right]\left[ {{A^ - }} \right]}}{{\left[ {HA} \right]}}\]
The pH of the weak acid is
\[\sqrt {{{\text{K}}_{\text{a}}}\left[ {{\text{HA}}} \right]} \]\[
  {{\text{K}}_{\text{a}}}{\text{ = }}\dfrac{{\left[ {{{\text{H}}^{\text{ + }}}} \right]\left[ {{{\text{A}}^{\text{ - }}}} \right]}}{{\left[ {{\text{HA}}} \right]}}{\text{,for weak acids}}\left[ {{{\text{H}}^{\text{ + }}}} \right]{\text{ = }}\left[ {{{\text{A}}^{\text{ - }}}} \right] \\
  {\text{or,}}{{\text{K}}_{\text{a}}}\left[ {{\text{HA}}} \right]{\text{ = }}{\left[ {{{\text{H}}^{\text{ + }}}} \right]^{\text{2}}} \\
  {\text{or,}}\sqrt {{{\text{K}}_{\text{a}}}\left[ {{\text{HA}}} \right]} {\text{ = }}\left[ {{{\text{H}}^{\text{ + }}}} \right] \\
  {\text{pH = log}}\left[ {{{\text{H}}^{\text{ + }}}} \right] \\
  {\text{or,pH = log}}\sqrt {{{\text{K}}_{\text{a}}}\left[ {{\text{HA}}} \right]} \\
  \]
Now according to the formula \[{\text{pH = - log}}{\left[ {\text{H}} \right]^{\text{ + }}}\], the pH of the solution with concentration of hydrogen ion 0.001M is
\[
  {\text{pH = - log}}{\left[ {\text{H}} \right]^{\text{ + }}} \\
  {\text{or,pH = - log0}}{\text{.001}} \\
  {\text{or, pH = 3}} \\
  \]

Note:
 For weak acids \[pH\] value depends upon the dissociation constant of acids higher the dissociation constant of acids higher will be the acidity of the solution.According to the pH scale if any solution is with lower pH value( less than 7) is acidic in nature, and if the pH of the solution is higher(greater than 7) than the solution is basic. For pure water the pH of the solution is 7.