Understanding Molality Calculation for KI Solution

The question asks us to calculate the molality of a Potassium Iodide (KI) solution, given its concentration in mass percentage and its density. Molality is a key concept in chemistry that describes the concentration of a solute in a solution.

Defining Molality

Molality (denoted by m) is defined as the number of moles of solute dissolved per kilogram of solvent.

The formula for molality is:

$$ m = \frac{\text{Moles of solute}}{\text{Mass of solvent (in kg)}} $$

Given Information

We are provided with the following details:

• Concentration of KI solution = 20% (mass/mass)
• Density of the solution = 1.202 g $mL^{-1}$
• Molar mass of KI = 166 g $mol^{-1}$

Step-by-Step Calculation

1. Assume a basis for calculation: Let's assume we have 100 grams of the KI solution. This is a common practice when dealing with mass percentages.

2. Calculate the mass of the solute (KI): Since the solution is 20% KI by mass, the mass of KI in 100 g of solution is:

   $$ \text{Mass of KI} = 20\% \times 100 \text{ g} = 0.20 \times 100 \text{ g} = 20 \text{ g} $$

3. Calculate the mass of the solvent (water): The solvent in this case is water. The mass of the solvent is the total mass of the solution minus the mass of the solute:

   $$ \text{Mass of solvent} = \text{Total mass of solution} - \text{Mass of solute} $$

   $$ \text{Mass of solvent} = 100 \text{ g} - 20 \text{ g} = 80 \text{ g} $$

4. Convert the mass of the solvent to kilograms: Molality requires the solvent mass in kilograms.

   $$ \text{Mass of solvent (kg)} = \frac{80 \text{ g}}{1000 \text{ g/kg}} = 0.080 \text{ kg} $$

5. Calculate the moles of solute (KI): Using the molar mass of KI, we find the number of moles:

   $$ \text{Moles of KI} = \frac{\text{Mass of KI}}{\text{Molar mass of KI}} $$

   $$ \text{Moles of KI} = \frac{20 \text{ g}}{166 \text{ g/mol}} \approx 0.12048 \text{ mol} $$

6. Calculate the molality: Now, plug the moles of solute and mass of solvent (in kg) into the molality formula:

   $$ m = \frac{\text{Moles of KI}}{\text{Mass of solvent (kg)}} $$

   $$ m = \frac{0.12048 \text{ mol}}{0.080 \text{ kg}} \approx 1.506 \text{ mol kg}^{-1} $$

7. Final Answer: Rounding the result to an appropriate number of significant figures (or matching the options provided), the molality is approximately 1.5 mol $kg^{-1}$. The density information was not needed for this calculation method, which relies on the mass/mass percentage.

Result Summary

The calculated molality of the 20% KI solution is approximately 1.5 mol $kg^{-1}$.