Answer:
3.39 mol/kg
Step-by-step explanation:
To find the molality of the solution, you need to know the mass of the solute (potassium chloride, KCl) and the mass of the solvent (water), and then use the following formula:
Molality (m) = (moles of solute) / (mass of solvent in kilograms)
First, you need to find the moles of KCl. To do this, use the molar mass of KCl, which is the sum of the atomic masses of potassium (K) and chlorine (Cl):
Molar mass of KCl = (39.10 g/mol for K) + (35.45 g/mol for Cl) = 74.55 g/mol
Now, calculate the moles of KCl:
Moles of KCl = (9.68 g) / (74.55 g/mol) ≈ 0.1297 moles
Next, you need to find the mass of the solvent in kilograms. Since the solvent is water, we can assume that the density of water is approximately 1 g/mL, which is the same as 1 kg/L. Therefore, 9.68 g of KCl dissolved in water will still have almost the same mass, so the mass of the solvent is also 9.68 g.
Now, convert the mass of the solvent to kilograms:
Mass of solvent = 9.68 g = 0.00968 kg
Finally, use the formula for molality:
Molality (m) = (moles of solute) / (mass of solvent in kilograms)
Molality = 0.1297 moles / 0.00968 kg ≈ 13.39 mol/kg
So, the molality of the solution is approximately 13.39 mol/kg.