When 10 mL of an aqueous solution of \(KMnO_4\) was titrated in acidic medium, equal volume of 0.1 M of an aqueous solution of ferrous sulphate was required for complete discharge of colour. The strength of \(KMnO_4\) in grams per litre is _________ \(\times 10^{-2}\). (Nearest integer)
[ Atomic mass of \(K = 39, Mn = 55, O = 16\) ]
Show Hint
Remember standard \(n\)-factors for \(KMnO_4\): 5 in acidic medium, 3 in neutral/weakly alkaline medium, and 1 in strongly alkaline medium.
Step 1: Understanding the Concept:
In a redox titration, the total equivalents of the oxidizing agent must equal the total equivalents of the reducing agent. Step 2: Detailed Explanation:
In acidic medium:
\(n\)-factor for \(KMnO_4\) (\(Mn^{+7} \to Mn^{2+}\)) is 5.
\(n\)-factor for \(FeSO_4\) (\(Fe^{2+} \to Fe^{3+}\)) is 1.
Equivalents of \(KMnO_4 = \text{Equivalents of } FeSO_4\)
\[ N_1 V_1 = N_2 V_2 \]
\[ (M_1 \times 5) \times 10 = (0.1 \times 1) \times 10 \]
\[ 5 M_1 = 0.1 \implies M_1 = \frac{0.1}{5} = 0.02 \, M \]
Molar mass of \(KMnO_4 = 39 + 55 + (4 \times 16) = 158 \, \text{g/mol}\).
Strength in g/L \(= \text{Molarity} \times \text{Molar mass}\)
\[ \text{Strength} = 0.02 \times 158 = 3.16 \, \text{g/L} \]
Given Strength \(= x \times 10^{-2}\):
\[ 3.16 = 316 \times 10^{-2} \] Step 3: Final Answer:
The value of \(x\) is 316.
