To determine the normality of a solution containing 3.16 g of [tex]\( KMnO_4 \)[/tex] per liter, follow these steps:
1. Determine the Molar Mass:
First, you need to know the molar mass of [tex]\( KMnO_4 \)[/tex]. The molecular mass of [tex]\( KMnO_4 \)[/tex] is given to be 158 g/mol.
2. Calculate the Molarity:
Molarity (M) is defined as the number of moles of solute per liter of solution. To calculate the molarity:
[tex]\[
\text{molarity} = \frac{\text{mass of solute (g)}}{\text{molar mass of solute (g/mol)}}
\][/tex]
Hence,
[tex]\[
\text{molarity} = \frac{3.16 \text{ g}}{158 \text{ g/mol}} = 0.02 \text{ M}
\][/tex]
3. Determine the Valence Factor:
The valence factor for [tex]\( KMnO_4 \)[/tex] in acid medium is given to be 5. This comes from the fact that one mole of [tex]\( KMnO_4 \)[/tex] can accept 5 moles of electrons in its redox reaction in an acidic medium.
4. Calculate the Normality:
Normality (N) is defined as the molarity multiplied by the valence factor.
[tex]\[
\text{Normality} = \text{Molarity} \times \text{Valence Factor}
\][/tex]
Hence,
[tex]\[
\text{Normality} = 0.02 \text{ M} \times 5 = 0.1 \text{ N}
\][/tex]
Therefore, the normality of the solution is 0.1 N.
