Calculating Molality:

Molality is defined as the number of moles of solute per kilogram of solvent. In order to calculate the molality of a solution, we need to know the number of moles of solute and the mass of the solvent.

Step 1: Calculate the number of moles of acetic acid.

The molar mass of acetic acid (CH3COOH) is calculated by adding up the atomic masses of all the atoms in the molecule:
C = 12.01 g/mol
H = 1.01 g/mol (3 hydrogen atoms)
O = 16.00 g/mol (2 oxygen atoms)
The molar mass of acetic acid is therefore:
12.01 + (1.01 x 3) + (16.00 x 2) = 60.05 g/mol

To calculate the number of moles, we divide the mass of the acetic acid by its molar mass:
30 g / 60.05 g/mol = 0.499 moles

Step 2: Calculate the mass of the solvent.

We are given that the density of the solvent is 1.25 g/cm3. Since we want to find the mass of the solvent in kilograms, we need to convert the volume of the solvent from cubic centimeters to cubic decimeters (1 dm3 = 1000 cm3):
1 dm3 = 1000 cm3

The mass of the solvent can be calculated by multiplying the volume of the solvent by its density:
1 dm3 x 1.25 g/cm3 = 1250 g
Converting to kilograms:
1250 g / 1000 = 1.25 kg

Step 3: Calculate the molality.

Now that we have the number of moles of acetic acid (0.499 moles) and the mass of the solvent (1.25 kg), we can calculate the molality using the following formula:
Molality = moles of solute / mass of solvent
Molality = 0.499 moles / 1.25 kg = 0.399 mol/kg

Therefore, the molality of the solution is 0.399 mol/kg.