What would be the molality of 20% (mass/mass) aqueous solution of Kl? (molar mass of Kl = `166 g mol^(-1)`)

Options

A. 1.51
B. 1.35
C. 1.08
D. 1.48

Answer

To find the molality of a 20% (mass/mass) aqueous solution of KI, follow these steps:

### Step 1: Understand the 20% (mass/mass) solution
A 20% (mass/mass) solution means that there are 20 grams of KI in 100 grams of the solution.

### Step 2: Identify the mass of the solute and solvent
- Mass of solute (KI) = 20 grams
- Total mass of solution = 100 grams
- Therefore, mass of solvent (water) = Total mass of solution - Mass of solute = 100 grams - 20 grams = 80 grams

### Step 3: Convert the mass of the solvent to kilograms
Since molality is defined as moles of solute per kilogram of solvent, we need to convert the mass of the solvent from grams to kilograms:
- Mass of solvent = 80 grams = 80/1000 kg = 0.08 kg

### Step 4: Calculate the number of moles of solute (KI)
To calculate the number of moles of KI, use the formula:
\[ \text{Number of moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]
Given:
- Mass of KI = 20 grams
- Molar mass of KI = 166 g/mol

Calculating the moles of KI:
\[ \text{Number of moles of KI} = \frac{20 \text{ g}}{166 \text{ g/mol}} \approx 0.1204 \text{ moles} \]

### Step 5: Calculate the molality
Now, use the formula for molality:
\[ \text{Molality (m)} = \frac{\text{Number of moles of solute}}{\text{Mass of solvent (kg)}} \]
Substituting the values:
\[ \text{Molality} = \frac{0.1204 \text{ moles}}{0.08 \text{ kg}} \approx 1.505 \text{ mol/kg} \]

### Conclusion
The molality of the 20% (mass/mass) aqueous solution of KI is approximately **1.51 mol/kg**.

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