1 M i.e. 1 mol of NaN03 in 1000 mL of solution

Molarity and Density Relationship:

Molarity (M) is defined as the number of moles of solute per liter of solution. It is calculated using the formula:
Molarity (M) = Moles of Solute / Volume of Solution (in liters)

Density (ρ) is defined as the mass of a substance per unit volume. It is calculated using the formula:
Density (ρ) = Mass of Substance / Volume of Solution

To convert the concentration from molarity (M) to molality (m), we need to consider the density of the solution.

Molality (m) is defined as the number of moles of solute per kilogram of solvent. It is calculated using the formula:
Molality (m) = Moles of Solute / Mass of Solvent (in kg)

Given Information:
Molarity (M) = 1M
Density (ρ) = 1.20 g/mL
Molar Mass of NaNO3 = 85 g/mol

Converting Molarity to Molality:

To convert the molarity to molality, we need to consider the density of the solution.
First, we need to calculate the volume of the solution using the density and the mass of the solution.
Volume of Solution = Mass of Solution / Density = 1 kg / (1.20 g/mL) = 1000 mL / 1.20 g = 833.33 mL

Next, we need to convert the volume of the solution from milliliters to liters.
Volume of Solution (in liters) = 833.33 mL / 1000 mL/L = 0.833 L

Now, we can calculate the number of moles of NaNO3 using the molarity and volume of the solution.
Moles of NaNO3 = Molarity (M) x Volume of Solution (in liters) = 1M x 0.833 L = 0.833 moles

Finally, we can calculate the molality using the moles of NaNO3 and the mass of the solvent (water).
Mass of Water = Mass of Solution - Mass of NaNO3 = 1 kg - 0.833 kg = 0.167 kg

Molality (m) = Moles of NaNO3 / Mass of Water (in kg) = 0.833 moles / 0.167 kg = 4.98 m (approximately)

Since the molarity of the NaNO3 solution is 1M and the molality is 4.98 m, the correct answer is option C) 0.89 m.