To find the percentage of oxalate ion in the given sample of oxalate salt, we can follow these steps:
### Step 1: Determine the number of equivalents of KMnO4 used
We know that the volume of KMnO4 solution used is 90 mL, and its normality is \( \frac{1}{20} \, N \).
To calculate the number of equivalents of KMnO4:
\[
\text{Number of equivalents} = \text{Volume (L)} \times \text{Normality}
\]
Convert 90 mL to liters:
\[
90 \, \text{mL} = 0.090 \, \text{L}
\]
Now, calculate the number of equivalents:
\[
\text{Number of equivalents of KMnO4} = 0.090 \, \text{L} \times \frac{1}{20} \, N = 0.090 \times 0.05 = 0.0045 \, \text{equivalents}
\]
### Step 2: Relate the equivalents of oxalate ion to KMnO4
Since the reaction is a complete oxidation, the number of equivalents of oxalate ion will be equal to the number of equivalents of KMnO4 used:
\[
\text{Number of equivalents of oxalate ion} = 0.0045 \, \text{equivalents}
\]
### Step 3: Calculate the number of moles of oxalate ion
The n-factor for oxalate ion (C2O4^2-) is 2 because it can donate 2 electrons during oxidation. Thus, the number of moles of oxalate ion can be calculated as:
\[
\text{Number of moles of oxalate ion} = \frac{\text{Number of equivalents}}{\text{n-factor}} = \frac{0.0045}{2} = 0.00225 \, \text{moles}
\]
### Step 4: Calculate the mass of oxalate ion
The molar mass of oxalate ion (C2O4^2-) is 88 g/mol. Therefore, the mass of oxalate ion can be calculated as:
\[
\text{Mass of oxalate ion} = \text{Number of moles} \times \text{Molar mass} = 0.00225 \, \text{moles} \times 88 \, \text{g/mol} = 0.198 \, \text{g}
\]
### Step 5: Calculate the percentage of oxalate ion in the sample
The total mass of the oxalate salt sample is 0.3 g. The percentage of oxalate ion in the sample can be calculated as:
\[
\text{Percentage of oxalate ion} = \left( \frac{\text{Mass of oxalate ion}}{\text{Mass of oxalate salt}} \right) \times 100 = \left( \frac{0.198 \, \text{g}}{0.3 \, \text{g}} \right) \times 100 \approx 66\%
\]
### Final Answer:
The percentage of oxalate ion in the given sample of oxalate salt is approximately **66%**.
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