the freezing point of water is -1.86 degree Cm, if 5.00 g Na2SO4 is desolve at 45.0g H2o the freezing point is changed by -3.82 degree C. Calculate the Van't Hoff Factor for Na2SO4

To calculate the Van't Hoff factor (i), we can use the formula:

i = (∆Tf / Kf) * 1 / m

Where:
∆Tf is the change in freezing point (in this case, -3.82 degrees Celsius),
Kf is the cryoscopic constant (freezing point depression constant) for the solvent (water), and
m is the molality of the solute (Na2SO4).

First, let's calculate the molality (m). The molality is defined as the number of moles of solute per kilogram of solvent. We have the mass of the solute (5.00 g Na2SO4) and the mass of the solvent (45.0 g H2O).

1. Convert the mass of the solute (Na2SO4) to moles:
Molar mass of Na2SO4 = 2(22.99 g/mol of Na) + 32.06 g/mol of S + 4(16.00 g/mol of O)
= 22.99 g/mol(2 Na) + 32.06 g/mol(S) + 16.00 g/mol(4 O)
= 22.99 g/mol(2) + 32.06 g/mol + 16.00 g/mol(4)
= 45.98 g + 32.06 g + 64.00 g
= 142.04 g/mol

Moles of Na2SO4 = mass / molar mass
= 5.00 g / 142.04 g/mol
= 0.0352 mol

2. Convert the mass of the solvent (H2O) to kilograms:
Mass of H2O = 45.0 g = 0.045 kg

Now that we have the molality (m) as 0.0352 mol/kg, we can proceed with calculating the Van't Hoff factor (i). However, we need to find the cryoscopic constant (Kf) for water.

The cryoscopic constant for water (Kf) is 1.86 degree Celsius * molality^-1. This is given in the question as the freezing point depression per molality of water.

Kf = 1.86 °C * molality^-1 = 1.86 °C * kg/mol

With Kf and the change in freezing point (∆Tf) known, we can calculate the Van't Hoff factor (i):

i = (∆Tf / Kf) * 1 / m
= (-3.82 °C / (1.86 °C * kg/mol)) * (1 / 0.0352 mol/kg)

Now plug in the values to find the Van't Hoff factor:
i = (-3.82 °C / (1.86 °C * kg/mol)) * (1 / 0.0352 mol/kg)