Calculate the percentage of oxalate ions in a given sample of oxalate salt 3.0 of which has been dissolve per litre of the solution 10 mL of the oxalate salt solution required 8 mL of 0.01 M `KMnO_(4)` solution complete oxidation

Explanation

To calculate the percentage of oxalate ions in the given sample of oxalate salt, we will follow these steps:

### Step 1: Understand the Reaction
The reaction involves the oxidation of oxalate ions (C₂O₄²⁻) by potassium permanganate (KMnO₄) in acidic medium. The balanced reaction is:
\[ \text{C}_2\text{O}_4^{2-} + 8 \text{H}^+ + 5 \text{MnO}_4^{-} \rightarrow 2 \text{CO}_2 + 4 \text{H}_2\text{O} + 5 \text{Mn}^{2+} \]

### Step 2: Calculate the Equivalent Factor (n_f)
For oxalate ions:
- Each C atom in C₂O₄²⁻ changes from +3 to +4 oxidation state, resulting in a change of 1 for each carbon atom. Since there are 2 carbon atoms, the total change is 2.
- Therefore, the number of equivalents (n_f) for oxalate is 2.

For KMnO₄ in acidic medium:
- Mn changes from +7 to +2, which is a change of 5.
- Therefore, the number of equivalents (n_f) for KMnO₄ is 5.

### Step 3: Calculate the Moles of KMnO₄ Used
Using the molarity and volume of KMnO₄:
- Molarity (M) = 0.01 M
- Volume (V) = 8 mL = 0.008 L

The number of moles of KMnO₄ used:
\[ \text{Moles of KMnO}_4 = \text{Molarity} \times \text{Volume} = 0.01 \, \text{mol/L} \times 0.008 \, \text{L} = 0.00008 \, \text{mol} \]

### Step 4: Calculate the Equivalent of KMnO₄
Using the number of equivalents:
\[ \text{Equivalents of KMnO}_4 = \text{Moles} \times n_f = 0.00008 \, \text{mol} \times 5 = 0.0004 \, \text{equivalents} \]

### Step 5: Calculate the Moles of Oxalate Ions
Since the reaction ratio between KMnO₄ and oxalate ions is 5:1, the equivalents of oxalate ions will also be 0.0004:
\[ \text{Equivalents of C}_2\text{O}_4^{2-} = 0.0004 \]

### Step 6: Calculate the Moles of Oxalate Ions
Using the equivalent factor for oxalate:
\[ \text{Moles of C}_2\text{O}_4^{2-} = \frac{\text{Equivalents}}{n_f} = \frac{0.0004}{2} = 0.0002 \, \text{mol} \]

### Step 7: Calculate the Mass of Oxalate Ions
The molar mass of oxalate (C₂O₄²⁻) is:
\[ \text{Molar mass} = 2 \times 12 + 4 \times 16 = 88 \, \text{g/mol} \]

Mass of oxalate ions:
\[ \text{Mass} = \text{Moles} \times \text{Molar mass} = 0.0002 \, \text{mol} \times 88 \, \text{g/mol} = 0.0176 \, \text{g} \]

### Step 8: Calculate the Percentage of Oxalate Ions
Given that 3.0 g of oxalate salt was dissolved in 1 L of solution:
\[ \text{Percentage of C}_2\text{O}_4^{2-} = \left( \frac{\text{Mass of C}_2\text{O}_4^{2-}}{\text{Total mass of salt}} \right) \times 100 \]
\[ = \left( \frac{0.0176 \, \text{g}}{3.0 \, \text{g}} \right) \times 100 = 0.5867\% \]

### Final Answer
The percentage of oxalate ions in the given sample of oxalate salt is approximately **0.5867%**.