Question

For \[BrO_{3}^{-}\to B{{r}^{-}}\], the relation between normality and molarity is given as \[N=M\times x\]. The value of x is:

Answer 1

Hint: The relationship between normality and molarity can be calculated by knowing the n-factor / valence factor. n-factor defined as the number of \[{{H}^{+}}\]replaced by one mole of an acid. As the above given reaction is a redox reaction, we can simply calculate it by determining the oxidation number.

Complete step by step solution:
Normality and molarity are related to each other by the following equation.
\[\text{normality=molarity }\!\!\times\!\!\text{ }\dfrac{\text{Molar mass}}{\text{equivalent mass}}\]
The normality of the acids is calculated using the formula
\[\text{normality=molarity }\!\!\times\!\!\text{ basicity}\]
The normality of bases is determined by this formula.
\[\text{normality=molarity }\!\!\times\!\!\text{ acidity}\]
But since \[BrO_{3}^{-}\to B{{r}^{-}}\] is redox reaction we are calculating the relationship using the oxidation states of react and product, and further finding the n-factor or valence factor.
In the given reaction \[BrO_{3}^{-}\to B{{r}^{-}}\] undergoes a redox reaction. In the redox reaction, the n-factors are calculated using oxidation number.
The oxidation number of \[BrO_{3}^{-}\]:
Take the oxidation number of \[Br\] as x. The oxidation number of oxygen is -2. Since there are 3 moles of oxygen, the oxidation number of oxygen is -6. The overall oxidation number of \[BrO_{3}^{-}\]is -1.
\[x-6=-1\]
$\therefore$ \[x=5\]
Therefore, the oxidation number of \[BrO_{3}^{-}\] is 5.
Now calculate the oxidation number of \[B{{r}^{-}}\] is \[x=-1\]
Therefore, the oxidation number of \[B{{r}^{-}}\] is 1.
When \[BrO_{3}^{-}\] reacts to give \[B{{r}^{-}}\], the oxidation number changes from +5 to -1. Therefore, the valence factor for this reaction is x=6.

Therefore, the relation between normality and molarity in \[BrO_{3}^{-}\to B{{r}^{-}}\]is given as\[N=M\times 6=6M\].

Additional information:
- Molarity is defined as the number of moles of solute dissolved in one liter of solution. It is represented by M.
\[\text{molarity=}\dfrac{\text{number of moles of solute}}{\text{volume of solution in one litre}}\]
- Normality is defined as the number of gram-equivalent of solute dissolved in one litre of solution. It is represented by N.
\[\text{normality=}\dfrac{\text{molecular mass}}{\text{equivalent mass of solute}}\]

Note: - In order to determine the basicity of the molecule, we can count number of\[{{H}^{+}}\]ions in an acid molecule.
- Similarly, to determine the acidity of the molecule, count the number of hydroxide ions present in the base molecule.