The molarity (m) of `KMnO_(4)` in the acidic medium is (densityh of `KMnO_(4)` solution`=1.58gmL^(-1)Mw(KMnO_(4))=158gmol^(-1))`

Options

A. 0.025
B. 0.25
C. 0.12
D. 0.012

Explanation

To find the molality (m) of KMnO₄ in acidic medium, we can use the relationship between molarity (M), density (d), molecular weight (MW), and molality (m). Here’s a step-by-step solution:

### Step 1: Identify the given values
- Density of KMnO₄ solution (d) = 1.58 g/mL
- Molarity of KMnO₄ solution (M) = 0.02 mol/L
- Molecular weight of KMnO₄ (MW) = 158 g/mol

### Step 2: Convert density to g/L
Since the density is given in g/mL, we convert it to g/L:
\[ 1.58 \, \text{g/mL} = 1.58 \times 1000 \, \text{g/L} = 1580 \, \text{g/L} \]

### Step 3: Calculate the mass of the solution
Using the molarity, we can find the mass of the KMnO₄ in 1 L of solution:
\[ \text{Mass of KMnO₄} = \text{Molarity} \times \text{Molecular Weight} = 0.02 \, \text{mol/L} \times 158 \, \text{g/mol} = 3.16 \, \text{g} \]

### Step 4: Calculate the mass of the solvent (water)
Now, we can find the mass of the solvent (water) in 1 L of solution. The total mass of the solution is the mass of KMnO₄ plus the mass of the solvent:
\[ \text{Mass of solution} = \text{Density} \times \text{Volume} = 1580 \, \text{g/L} \times 1 \, \text{L} = 1580 \, \text{g} \]
\[ \text{Mass of solvent} = \text{Mass of solution} - \text{Mass of KMnO₄} = 1580 \, \text{g} - 3.16 \, \text{g} = 1576.84 \, \text{g} \]

### Step 5: Convert mass of solvent to kg
To calculate molality, we need the mass of the solvent in kilograms:
\[ \text{Mass of solvent in kg} = \frac{1576.84 \, \text{g}}{1000} = 1.57684 \, \text{kg} \]

### Step 6: Calculate molality (m)
Molality is defined as the number of moles of solute per kilogram of solvent:
\[ \text{Molality (m)} = \frac{\text{Moles of KMnO₄}}{\text{Mass of solvent in kg}} = \frac{0.02 \, \text{mol}}{1.57684 \, \text{kg}} \approx 0.0127 \, \text{mol/kg} \]

### Final Answer
The molality of KMnO₄ in acidic medium is approximately **0.0127 mol/kg**.

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