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Step 1: Write the Balanced Chemical Equation
The reaction between hydrogen peroxide ( H_{2}O_{2} ) and permanganate ion ( \mathrm{MnO_{4}^{-}} ) in acidic medium is given by:
5\,H_{2}O_{2} + 2\,MnO_{4}^{-} + 6\,H^{+} \to 2\,Mn^{2+} + 5\,O_{2} + 8\,H_{2}O
Step 2: Calculate the Moles of KMnO4
Given mass of KMnO4 = 0.316 g
Molecular mass of KMnO4 = 158 g/mol
Moles of KMnO4 = \frac{0.316}{158} = 2 \times 10^{-3} moles
Step 3: Relate the Moles of KMnO4 to Moles of H2O2
From the balanced equation, 2 moles of \mathrm{MnO_{4}^{-}} react with 5 moles of H_{2}O_{2} .
Thus, the molar ratio between H_{2}O_{2} and KMnO4 is 5:2.
Hence, moles of H_{2}O_{2} = \left(\frac{5}{2}\right) \times (moles of KMnO4)
Step 4: Calculate the Actual Moles of H2O2
Moles of H_{2}O_{2} = \frac{5}{2} \times 2 \times 10^{-3} = 0.005
Step 5: Find the Mass of Pure H2O2
Molecular mass of H_{2}O_{2} = 34 g/mol
Mass of pure H_{2}O_{2} = (moles of H_{2}O_{2} ) \times (molecular mass)
= 0.005 \times 34 = 0.170 g
Step 6: Determine the Percentage Purity
Given mass of impure sample = 0.2 g
Percentage purity = \frac{\text{Mass of pure } H_{2}O_{2}}{\text{Mass of impure sample}} \times 100
= \frac{0.170}{0.2} \times 100 = 85\%
