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

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.