Question

A dilute solution of \[{H_2}S{O_4}\] is made by adding \[{\text{5}}\,{\text{mL}}\]of 3N \[{H_2}S{O_4}\]to \[{\text{245}}\,{\text{mL}}\] of water. Find the normality and molarity of the diluted solution.

Answer 1

Hint: Molality or molal concentration, is defined as the amount of the substance which is dissolved in a certain mass of the solvent. It is also defined as the moles of a solute per kilogram of a solvent. Normality is defined as the number of the mole or gram equivalents of solute present in one litre of a solution.

Complete step by step answer:
We know from normality that,
\[{{\text{N}}_{\text{1}}}{{\text{V}}_{\text{1}}} = {{\text{N}}_{\text{2}}}{{\text{V}}_{\text{2}}}\]
Here,
\[{{\text{N}}_{\text{1}}}\]= normality of \[{H_2}S{O_4}\]
\[{{\text{N}}_{\text{2}}}\]= normality of water
\[{{\text{V}}_{\text{1}}}\]= volume of \[{H_2}S{O_4}\]
\[{{\text{V}}_{\text{2}}}\]= volume of water
We are given that,
\[{{\text{N}}_{\text{1}}}\]= 3N
\[{{\text{N}}_{\text{2}}}\]= x
\[{{\text{V}}_{\text{1}}}\]= \[{\text{5}}\,{\text{mL}}\]
\[{{\text{V}}_{\text{2}}}\]=\[{\text{245}}\,{\text{mL}}\]
Using these values in the above equation we will calculate the value of \[{{\text{N}}_{\text{2}}}\].
\[
  {{\text{N}}_{\text{1}}}{{\text{V}}_{\text{1}}} = {{\text{N}}_{\text{2}}}{{\text{V}}_{\text{2}}} \\
   \Rightarrow 3 \times 5\, = \,{\text{x}} \times \,{\text{245}} \\
   \Rightarrow \,{\text{x = }}\,{\text{0}}{\text{.0612}}\,{\text{N}} \\
 \]
Therefore, the value of normality is \[{\text{0}}{\text{.0612}}\,{\text{N}}\].
Now, we will calculate the value of molarity.
We know that the basicity of sulphuric acid is = 2.
The relation between normality, molarity and basicity is given as,
\[
  \dfrac{{{\text{Normality}}}}{{{\text{Molarity}}}} = {\text{Basicity}} \\
   \Rightarrow \dfrac{{{\text{0}}{\text{.0612}}}}{{{\text{Molarity}}}} = {\text{2}} \\
   \Rightarrow {\text{Molarity}} = {\text{0}}{\text{.0306}}\,{\text{M}} \\
 \]
$\therefore $, the value of molarity of the diluted solution is \[{\text{0}}{\text{.0306}}\,{\text{M}}\].

Note:
The number of the atoms in 1 mole is equal to the Avogadro’s number denoted as \[\left( {{{\text{N}}_{\text{A}}}} \right)\]. The value of the Avogadro’s number is \[6.022 \times {10^{23}}\]. The molar mass is given as mass divided by mole that is,
Molar mass $mass/moles=g/moles$.
The mole concept also concludes that the atomic mass of the Carbon-12 is equivalent to the 12 atomic mass units. Also, the mass of Carbon-12 is exactly \[{\text{12}}\,{\text{grams}}\] per mole.