Calculate the number of millimoles of `SO_(2)` if in the reaction,10mL of 0.1M `KMnO_(4)` solution are required for complete titration.
`SO_(2)+MnO_(4)^(-)toSO_(4)^(-)+Mn^(+2)`

Options

A. 2.5
B. 0.5
C. 1.25
D. None of these

Answer

To calculate the number of millimoles of \( SO_2 \) in the given reaction, we can follow these steps:

### Step 1: Determine the moles of \( KMnO_4 \) used
We know the volume and molarity of the \( KMnO_4 \) solution used in the titration.

\[ \text{Molarity (M)} = \frac{\text{moles of solute}}{\text{liters of solution}} \]

Given:
- Volume of \( KMnO_4 \) = 10 mL = 0.01 L
- Molarity of \( KMnO_4 \) = 0.1 M

Now, we can calculate the moles of \( KMnO_4 \):

\[ \text{Moles of } KMnO_4 = \text{Molarity} \times \text{Volume in L} \]
\[ \text{Moles of } KMnO_4 = 0.1 \, \text{mol/L} \times 0.01 \, \text{L} = 0.001 \, \text{mol} \]

### Step 2: Convert moles of \( KMnO_4 \) to millimoles
To convert moles to millimoles, we multiply by 1000:

\[ \text{Millimoles of } KMnO_4 = 0.001 \, \text{mol} \times 1000 = 1 \, \text{mmol} \]

### Step 3: Determine the stoichiometry of the reaction
From the balanced reaction:
\[ SO_2 + MnO_4^- \rightarrow SO_4^{2-} + Mn^{2+} \]
The stoichiometry shows that 1 mole of \( SO_2 \) reacts with 1 mole of \( KMnO_4 \).

### Step 4: Calculate the number of millimoles of \( SO_2 \)
Since the stoichiometry is 1:1, the millimoles of \( SO_2 \) will be equal to the millimoles of \( KMnO_4 \):

\[ \text{Millimoles of } SO_2 = \text{Millimoles of } KMnO_4 = 1 \, \text{mmol} \]

### Final Answer
The number of millimoles of \( SO_2 \) is **1 mmol**.

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