calculate the molality of one molarity solution of sodium nitrare. the density of solution is 1.25g cm cube.

molality = moles/kg solvent

M = moles/L = 1 mole NaNO3/L soln.

The mass of 1000 mL =
1000 x 1.25 g/mL = 1250 grams.
1 mole NaNO3 = 85 grams (approximately--you need to do it more accurately).
1250 = mass soln
85 = mass NaNO3
----
1,165 grams H2O or 1.165 kg solvent.
m = 1 mole/1.165 kg = 0.858m
Check my work.

To calculate the molality of a sodium nitrate solution, we need to know the moles of sodium nitrate dissolved in 1 kilogram of solvent (usually water).

First, we need to convert the given density from grams per cubic centimeter to grams per milliliter. Since 1 cm^3 = 1 mL, the density is already in grams per milliliter.

Next, we need to convert the given molarity (moles of solute per liter of solution) to moles of solute per kilogram of solvent.

The molecular weight of sodium nitrate (NaNO3) is:
Sodium (Na) - 22.99 g/mol
Nitrogen (N) - 14.01 g/mol
Oxygen (O) - 16.00 g/mol (3 oxygen atoms)
Adding these up, we get (22.99 + 14.01 + 16.00*3) = 85.00 g/mol.

To convert from molarity (moles of solute per liter of solution) to molality (moles of solute per kilogram of solvent), we use the following equation:
Molality (m) = Molarity (M) / (1000 * Density (g/mL) / Molecular weight (g/mol))

Plugging in the values, we get:
Molality (m) = 1 M / (1000 * 1.25 g/mL / 85.00 g/mol)
= 0.008 M / (1.25 g/mL / 85.00 g/mol)
= 0.008 M / (0.0147 mol/mL)
= 0.544 mol/kg

Therefore, the molality of a 1.00 M sodium nitrate solution is approximately 0.544 mol/kg.

To calculate the molality of a solution, you need to know the molarity of the solute and the mass of the solvent. In this case, sodium nitrate (NaNO3) is the solute and the solution's density is provided to find the mass.

Here are the steps to calculate the molality:

Step 1: Convert the given density into grams per milliliter (g/mL).

Given density = 1.25 g/cm^3

To convert from g/cm^3 to g/mL, divide by 1, since 1 cm^3 = 1 mL.

Density in g/mL = 1.25 g/cm^3

Step 2: Determine the mass of the solvent using the given density and its volume.

Since we know that 1 mL of a solution has a mass of 1.25 g, we can assume that the density represents the solvent density as well. Let's assume we have 1 L (1000 mL) of the solution.

Mass of solvent = density x volume
= 1.25 g/mL x 1000 mL
= 1250 g

Step 3: Find the number of moles of solute, NaNO3, by using its molarity.

Molarity is defined as the number of moles of solute per liter of solution. However, we need to make sure the units are consistent, so we convert 1 molarity (1 M) to moles per kilogram (mol/kg).

To convert from moles per liter to moles per kilogram, divide by the density of the solvent (in kg/L). We can use the density to calculate the mass of the solvent in kilograms.

Let's assume the molarity is 1 M.

Number of moles of solute (NaNO3) = (molarity x mass of solvent) / molar mass of NaNO3

The molar mass of NaNO3 = 22.99 g/mol (Na) + 14.01 g/mol (N) + (3 x 16.00 g/mol) (O)
= 85.00 g/mol

Number of moles of NaNO3 = (1 M x 1250 g) / 85.00 g/mol
= 14.71 mol

Step 4: Calculate the molality using the number of moles of solute and the mass of the solvent (in kg).

Molality = number of moles of solute / mass of solvent (in kg)

Dividing the number of moles of solute (14.71 mol) by the mass of the solvent (1250 g / 1000 = 1.25 kg):

Molality = 14.71 mol / 1.25 kg
= 11.77 mol/kg

Therefore, the molality of the sodium nitrate solution is approximately 11.77 mol/kg.