A \[{10^{ - 3}}\] M solution has been diluted to \[100\] times. Calculate the pH of the diluted solution?

Hint: The concentration of the solution is very important in chemistry. The strength of the solution is very important for inhaled solution and medicinal chemistry. Different ways of representation in the concentration of solutions are possible. The molality, molarity, normality, formality, mole fraction, mass percentage, volume percentage, mass by volume, and parts per million are the concentration of solutions.
Formula used:
The molarity of the solution depends on the number of moles of the solute and the volume of the solution in liters. The molarity of the solution is equal to the ratio of the number of moles of the solute to the volume of the solution in liters. The symbol of molarity is M.
\[{\text{Molarity = }}\dfrac{{{\text{number of moles of the solute}}}}{{{\text{volume of the solution litre}}}}\]
The pH value of the solution is
pH = - log (concentration of the solution)

Complete answer:
The initial molarity of the solution is \[{10^{ - 3}}\] M.
The dilution of the solution was increased by \[100\] times. So, the volume of the solution is also increased overtimes.
Hence, the molarity of the present solution is calculated,
The molarity of the present solution is equal to the initial molarity of the solution divided by the volume increased by the solution.
\[
   = \dfrac{{{{10}^{ - 3}}}}{{100}} \\
   = {10^{ - 5}} \\
 \]
The molarity of the solution after dilution is \[{10^{ - 5}}\] M.
The pH value of the solution is
\[\begin{array}{*{20}{l}} {pH{\text{ }} = {\text{ }} - lo{g_{10}}\left( {concentration{\text{ }}of{\text{ }}the{\text{ }}solution} \right)} \\ {pH = {\text{ }} - lo{g_{10}}\left( {{{10}^{ - 5}}} \right)} \\ {pH = {\text{ }} - \left( { - 5{\text{ }}} \right)lo{g_{10}}\left( {10} \right)} \\ {lo{g_{10}}\left( {10} \right) = 1} \\ {pH = {\text{ }} - \left( { - 5{\text{ }}} \right) \times 1} \\ {pH = {\text{ }}5} \end{array}\]
According to the above discussion, we conclude A \[{10^{ - 3}}\] M solution has been diluted to \[100\] times. The pH of the diluted solution is\[5\].

Note:
The gram equivalent of the acid depends on the molecular mass of the acid divided by the basicity of the acid. The basicity of the acid is nothing but the number of hydrogen ions able to donate the acid in an aqueous medium. The gram equivalent of the acid is equal to the ratio of the molecular mass of the acid to the basicity of the acid. The hydrogen ion is very important in the acid-base concept. The acids mean proton or hydrogen ion donors. The bases are hydrogen ions or proton acceptors in the reaction. The basicity of the acid and the acidity of the base depends on the hydrogen ion in the molecule. The molecular weight of the molecule means the sum of the atomic weight of the atoms in the molecule.