If an ore sample containing `Mn`, is treated with `50 mL` of `0.2750M Na_(2)C_(2)O_(4)` and the unreacted `Na_(2)C_(2)O_(4)` required `18.28 mL` of `0.1232 M KMnO_(4)` in acidic medium,then the number of moles of `Mn` in the ore is

Options

A. `1.38xx10^(-2)`
B. `1.49xx10^(-3)`
C. `1.15xx10^(-2)`
D. `8.12xx10^(-3)`

Explanation

To find the number of moles of manganese (Mn) in the ore sample, we can follow these steps:

### Step 1: Calculate the moles of Na2C2O4 initially present
We have a solution of Na2C2O4 with a concentration of 0.2750 M and a volume of 50 mL.

\[ \text{Moles of Na2C2O4} = \text{Molarity} \times \text{Volume (L)} \]
\[ = 0.2750 \, \text{mol/L} \times 0.050 \, \text{L} = 0.01375 \, \text{mol} \]

### Step 2: Calculate the moles of KMnO4 used
Next, we need to calculate the moles of KMnO4 that reacted with the unreacted Na2C2O4. The volume of KMnO4 used is 18.28 mL at a concentration of 0.1232 M.

\[ \text{Moles of KMnO4} = \text{Molarity} \times \text{Volume (L)} \]
\[ = 0.1232 \, \text{mol/L} \times 0.01828 \, \text{L} = 0.00225 \, \text{mol} \]

### Step 3: Calculate the equivalent moles of C2O4^2- that reacted with KMnO4
In acidic medium, 1 mole of KMnO4 reacts with 5 moles of C2O4^2-. Therefore, the moles of C2O4^2- that reacted can be calculated as follows:

\[ \text{Moles of C2O4^2- reacted} = 5 \times \text{Moles of KMnO4} \]
\[ = 5 \times 0.00225 = 0.01125 \, \text{mol} \]

### Step 4: Calculate the moles of C2O4^2- that were initially present
From Step 1, we found that the initial moles of C2O4^2- were 0.01375 mol.

### Step 5: Calculate the moles of C2O4^2- that reacted with MnO2
Now, we can find the moles of C2O4^2- that reacted with MnO2:

\[ \text{Moles of C2O4^2- reacted with MnO2} = \text{Initial moles} - \text{Moles reacted with KMnO4} \]
\[ = 0.01375 - 0.01125 = 0.0025 \, \text{mol} \]

### Step 6: Relate moles of C2O4^2- to moles of MnO2
Since 1 mole of MnO2 reacts with 2 moles of C2O4^2-, we can find the moles of MnO2 that reacted:

\[ \text{Moles of MnO2} = \frac{\text{Moles of C2O4^2- reacted}}{2} \]
\[ = \frac{0.0025}{2} = 0.00125 \, \text{mol} \]

### Step 7: Conclusion
Thus, the number of moles of Mn in the ore sample is equal to the moles of MnO2 reacted, which is:

\[ \text{Moles of Mn} = 0.00125 \, \text{mol} \]

### Final Answer
The number of moles of Mn in the ore is **0.00125 mol**.

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