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

Options

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

Answer

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

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

### Step 2: Determine the mass of the solvent
Since the total mass of the solution is 100 grams and the mass of the solute (KI) is 20 grams, the mass of the solvent (water) can be calculated as:
\[ \text{Mass of solvent} = \text{Total mass of solution} - \text{Mass of solute} = 100 \, \text{g} - 20 \, \text{g} = 80 \, \text{g} \]

### Step 3: Calculate the number of moles of solute
To find the number of moles of KI, use the formula:
\[ \text{Number of moles} = \frac{\text{Mass of solute}}{\text{Molar mass of solute}} \]
Given that the molar mass of KI is 166 g/mol, we can calculate:
\[ \text{Number of moles of KI} = \frac{20 \, \text{g}}{166 \, \text{g/mol}} \approx 0.1205 \, \text{mol} \]

### Step 4: Convert the mass of solvent to kilograms
Since molality is defined as moles of solute per kilogram of solvent, convert the mass of the solvent from grams to kilograms:
\[ \text{Mass of solvent in kg} = \frac{80 \, \text{g}}{1000} = 0.080 \, \text{kg} \]

### Step 5: Calculate molality
Now, we can calculate the molality (m) using the formula:
\[ \text{Molality} (m) = \frac{\text{Number of moles of solute}}{\text{Mass of solvent in kg}} \]
Substituting the values we have:
\[ m = \frac{0.1205 \, \text{mol}}{0.080 \, \text{kg}} \approx 1.50625 \, \text{mol/kg} \]

### Step 6: Round to appropriate significant figures
Rounding to three significant figures, the molality is:
\[ m \approx 1.51 \, \text{mol/kg} \]

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

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